X-RAY FLUORESCENCE

INSTRUMENT CALIBRATION

Theory and Application

by

Brian Lee Francom

A senior thesis submitted to the faculty of

Brigham Young University-Idaho

in partial fulfillment of the requirements for the degree of

Bachelor of Science

Department of Physics

Brigham Young University-Idaho

December 2008

ii

Copyright copy 2008 Brian Lee Francom

All Rights Reserved

iii

BRIGHAM YOUNG UNIVERSITY-IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by

Brian Lee Francom

This thesis has been reviewed by the research committee senior thesis coordinator and

department chair and has been found to be satisfactory

___________________ __________________________________________

Date David Oliphant AdvisorSenior Thesis Coordinator

___________________ __________________________________________

Date Ryan Nielson Committee Member

___________________ __________________________________________

Date Ryan Dabell Committee Member

___________________ __________________________________________

Date Stephen Turcotte Chair

iv

ABSTRACT

X-RAY FLUORESCENCE

INSTRUMENT CALIBRATION

Theory and Application

Brian Lee Francom

Department of Physics

Bachelor of Science

This report unveils all the measures taken to fully implement and calibrate the newly

installed x-ray fluorescence (XRF) detector in the Brigham Young University-Idaho x-

ray diffraction (XRD) instrument X-ray and XRF theories are discussed Different

calibration methods discussed include linear and quadratic approximations linear and

cubis spline interpolations and optimization LabVIEW 71 programming code is

explained Resulting XRF measurements are compared with accepted values and show

a calibration with a mean error of plusmn003 keV

v

ACKNOWLEDGEMENTS

To my loving and patient wife Danielle

and to David Oliphant who has guided me in this project

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

ii

Copyright copy 2008 Brian Lee Francom

All Rights Reserved

iii

BRIGHAM YOUNG UNIVERSITY-IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by

Brian Lee Francom

This thesis has been reviewed by the research committee senior thesis coordinator and

department chair and has been found to be satisfactory

___________________ __________________________________________

Date David Oliphant AdvisorSenior Thesis Coordinator

___________________ __________________________________________

Date Ryan Nielson Committee Member

___________________ __________________________________________

Date Ryan Dabell Committee Member

___________________ __________________________________________

Date Stephen Turcotte Chair

iv

ABSTRACT

X-RAY FLUORESCENCE

INSTRUMENT CALIBRATION

Theory and Application

Brian Lee Francom

Department of Physics

Bachelor of Science

This report unveils all the measures taken to fully implement and calibrate the newly

installed x-ray fluorescence (XRF) detector in the Brigham Young University-Idaho x-

ray diffraction (XRD) instrument X-ray and XRF theories are discussed Different

calibration methods discussed include linear and quadratic approximations linear and

cubis spline interpolations and optimization LabVIEW 71 programming code is

explained Resulting XRF measurements are compared with accepted values and show

a calibration with a mean error of plusmn003 keV

v

ACKNOWLEDGEMENTS

To my loving and patient wife Danielle

and to David Oliphant who has guided me in this project

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

iii

BRIGHAM YOUNG UNIVERSITY-IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by

Brian Lee Francom

This thesis has been reviewed by the research committee senior thesis coordinator and

department chair and has been found to be satisfactory

___________________ __________________________________________

Date David Oliphant AdvisorSenior Thesis Coordinator

___________________ __________________________________________

Date Ryan Nielson Committee Member

___________________ __________________________________________

Date Ryan Dabell Committee Member

___________________ __________________________________________

Date Stephen Turcotte Chair

iv

ABSTRACT

X-RAY FLUORESCENCE

INSTRUMENT CALIBRATION

Theory and Application

Brian Lee Francom

Department of Physics

Bachelor of Science

This report unveils all the measures taken to fully implement and calibrate the newly

installed x-ray fluorescence (XRF) detector in the Brigham Young University-Idaho x-

ray diffraction (XRD) instrument X-ray and XRF theories are discussed Different

calibration methods discussed include linear and quadratic approximations linear and

cubis spline interpolations and optimization LabVIEW 71 programming code is

explained Resulting XRF measurements are compared with accepted values and show

a calibration with a mean error of plusmn003 keV

v

ACKNOWLEDGEMENTS

To my loving and patient wife Danielle

and to David Oliphant who has guided me in this project

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

iv

ABSTRACT

X-RAY FLUORESCENCE

INSTRUMENT CALIBRATION

Theory and Application

Brian Lee Francom

Department of Physics

Bachelor of Science

This report unveils all the measures taken to fully implement and calibrate the newly

installed x-ray fluorescence (XRF) detector in the Brigham Young University-Idaho x-

ray diffraction (XRD) instrument X-ray and XRF theories are discussed Different

calibration methods discussed include linear and quadratic approximations linear and

cubis spline interpolations and optimization LabVIEW 71 programming code is

explained Resulting XRF measurements are compared with accepted values and show

a calibration with a mean error of plusmn003 keV

v

ACKNOWLEDGEMENTS

To my loving and patient wife Danielle

and to David Oliphant who has guided me in this project

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

v

ACKNOWLEDGEMENTS

To my loving and patient wife Danielle

and to David Oliphant who has guided me in this project

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

vi

Contents

ABSTRACT iv ACKNOWLEDGEMENTS v

List of Figures vii List of Tables viii

Chapter 1 Introduction 1 11 History of XRF 1 12 Basic XRF Setup 1

Chapter 2 Review of Theory 5

21 XRF Theory 5 211 Elastic and Inelastic X-ray Scattering 5

212 Characteristic Radiation and its Measurement 6 213 Continuous Radiation 7

22 Calibration Theory 8

221 Linear and Quadratic Approximations 9 222 Linear and Cubic Spline Interpolation 10

223 Optimization Method 11

224 Calibration Sample 11

Chapter 3 BYU-Idaho XRF Instrumentation 13 31 Previous Work 13 32 Specifications 13

Chapter 4 Study 15 41 The Best Calibration Method 15

42 Code Development 15 421 LabVIEW 71 Basics 15 422 Creating the Calibration Program 15

43 Calibration Sample Development 17 431 Sample Preparation 17

44 Implementing the Calibration Program 19 Chapter 5 Conclusion 21

Bibliography 23 Appendix A Various X-Ray Spectra 24 Appendix B A Typical Spectrum Data File 27 Appendix C X-ray Energy Tables 28

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

vii

List of Figures

Figure 1 The components of basic XRF instrumentation setup A picture of the

setup is shown in Figure 12 2

Figure 2 A simplistic spectrum Each pair of peaks typically represents one

element in the sample 2

Figure 3 The BYU-Idaho XRFXRD instrument 3 Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the

K-shell electron (b) The atom returns to ground state by transitioning

an L-shell electron to the K-shell 6

Figure 5 Four common electron transitions used in XRF measurements 7 Figure 6 A simplistic spectrum with peaks from two elements Typically each

element in the sample will have pronounced Kα and Kβ peaks The

continuous radiation of noise in the spectrum is called bremsstrahlung 8 Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes

represent channels The numbers represent a count of x-rays for a

specific energy 8

Figure 8 The linear approximation method 10

Figure 9 The linear interpolation method 11

Figure 10 The cubic spline interpolation method 11 Figure 11 The XRF detector 14 Figure 12 An inside look of the XRF instrument At top middle is the x-ray tube

At right is the sample for testing At bottom left is the XRF detector 14 Figure 13 The block diagram view of the LabVIEW 71 calibration program 16

Figure 14 The sample used for calibration 18 Figure 15 The front panel view of the LabVIEW 71 calibration program 20

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

viii

List of Tables

Table 1 Characteristic x-ray energies for select elements 17 Table 2 Compounds used in the calibration sample 18

Table 3 Trace amounts in the compounds listed in Table 2 18 Table 4 Experimental values and accepted values along with the corresponding

errors 21

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

ix

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 1

1

Chapter 1 Introduction

11 History of XRF

X-ray fluorescence (XRF) has been proven to be a very useful technique for elemental

analysis of materials Since its early beginnings the field of XRF has blossomed into

one of the most important tools in materials analysis The benefits of using XRF

rather than a traditional analysis method are that it is quick non-destructive and all-

inclusive (multiple tests are not required)

The power of XRF analysis was first realized by Henry Moseley in 1912

seventeen years after Wilhelm Roumlntgen had discovered the x-ray Moseley found that

it was possible to excite a sample and gather information from the x-rays being

emitted Although Moseley was using electrons to excite the sample it was realized

years later that x-rays could be used instead The use of x-rays had a great advantage

over the use of electrons when electrons were used it was only possible to analyze

materials with a very high melting point because of the inefficient energy conversion

by electrons [1] After this discovery a greater variety of materials were enabled to be

analyzed making XRF an even more versatile analysis method

12 Basic XRF Setup

The setup of XRF instrumentation is really quite simple it generally consists of four

basic components [1]

1 An excitation source

2 A sample

3 A detector

4 A data collection and analyzing system

The excitation source is typically an x-ray tube but a radioactive isotope may

also be used the BYU-Idaho XRF instrument uses an x-ray tube The x-ray tube

sends a beam of x-rays with various energies to the sample and the sample absorbs

and emits the x-rays to the detector The detector senses each impinging x-ray and

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 1

2

sends electrical pulses to the data collection and analyzing system The analyzing

system categorizes each x-ray by its energy Then the data is collected and stored

this is typically done with a computer (Figure 1)

An XRF measurement essentially gives two pieces of information The energy

of an x-ray and how many x-rays were received (count number or intensity for that

energy) When graphed in a spectrum the energy of the x-rays is the independent

variable and the count number is the dependent variable A typical spectrum of such

data will show one or more peaks for each element present in the sample (Figure 2)

Figure 1 The components of basic XRF instrumentation setup A picture of the setup is shown in Figure 12

Figure 2 A simplistic spectrum Each pair of peaks typically represents one element in the sample

Intensity

Energy

X-ray Tube

Detector Analyzer

Computer (Data

collection and storage)

X-rays

Sample

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 1

3

While the XRF method is very quick and efficient it can also give very

inaccurate results if the instrument is not calibrated correctly This is a result of two

particular systematic errors First the instrument is not perfect and tends to drift from

previous calibrations and second characteristic x-ray energies are not totally unique

to an element and often overlap with other characteristic x-rays as illustrated in

Section 212 These two errors can be resolved by implementing a good calibration

program and using it as often as necessary BYU-Idaho has an x-ray diffraction

(XRD) instrument which is located in the Geology Department laboratory (Figure 3)

Since it was recently adapted to also perform XRF with a newly installed Amptek x-

raygamma ray detector a proper calibration needed to be implemented This work

focuses on the measures taken to appropriately calibrate the BYU-Idaho XRF

instrument

Figure 3 The BYU-Idaho XRFXRD instrument

After calibration methods were researched and a better calibration program

was created and implemented the XRF measurements increased in accuracy Because

of this calibration users are now enabled to collect reproducible data with a mean

error of plusmn003 keV and a minimum error of plusmn001 keV

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 1

4

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

5

Chapter 2 Review of Theory

21 XRF Theory

211 Elastic and Inelastic X-ray Scattering

X-rays can interact with matter in several different ways this section will focus on

only the two most common interactions which are elastic and inelastic scattering

Scattering refers to the dispersed radiation that comes as a result of these interactions

[1]

Elastic scattering also referred to as coherent or Rayleigh scattering occurs

when an x-ray collides with an electron in an atom and no energy is lost in the

collision In this case the x-ray is best thought of as an electromagnetic wave An

electron in the atom is oscillated in this wave and the oscillating electron will radiate

an electromagnetic wave of the exact same energy as the incident x-ray This re-

radiated x-ray generally leaves the atom in a random direction

Inelastic scattering also referred to as incoherent or Compton scattering

occurs when an x-ray collides with an electron in an atom and its energy is transferred

in whole or in part to the electron In this case the x-ray is best thought of as a

photon This photon can either bump the electron into higher orbital energies or eject

the electron completely from the atom The incident x-ray photon will then deflect

away from the atom with a corresponding loss of energy (Figure 4)

The case in which the incident x-ray has sufficient energy to eject the electron

from the atom is called the photoelectric effect As a result of this effect the atom has

an electron vacancy and is considered to be in an unstable energy state Since XRF

involves the study of x-rays emitted from unstable atoms (see Section 212) the

photoelectric effect is instrumental to XRF in providing these unstable energy states

Electrons which are ejected due to the photoelectron effect can be studied using x-ray

photoelectron spectroscopy (XPS)

To visualize how an electron reacts to inelastic collisions the atomrsquos electronic

structure is modeled with various electron shells surrounding the nucleus The

innermost shell is called the K-shell the second innermost shell is called the L-shell

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

6

and so forth These shells represent different energies for orbitals having differing

quantum number n Other discrete energies exist within each shell which are due to

different subshells (orbitals of identical n but differing l) within each shell However

the energy differences between subshells are typically less than 050 keV The easiest

unstable energy state to visualize is one in which the electron from the K-shell is

ejected which is also the most commonly occurring state in XRF this is called a K-

shell vacancy as shown in Figure 4(a) Because of conservation of energy the

unstable atom will adjust its electron configuration to compensate for the lost energy

This phenomenon is discussed in the next section

212 Characteristic Radiation and its Measurement

Every element has a set of characteristic x-rays A characteristic x-ray has a very

specific energy that is unique to an element For example if an x-ray is measured to

have energy of 640 keV it is very likely that x-ray was emitted from an iron atom

Therefore a characteristic x-ray can be thought of as an elementrsquos ldquothumbprintrdquo

In the previous section it was mentioned that an incident x-ray of sufficient

energy will eject an electron from an atom leaving a vacancy The atom will then

adjust its electron configuration to be in the lowest energy state in other words an

electron in a higher shell will drop down to fill the vacancy The process of an

electron filling the vacancy creates an x-ray which is characteristic of a specific

electron transition for that element (Figure 4(b))

Figure 4 A simplistic model of the XRF process (a) An incident x-ray ejects the K-shell electron (b) The atom

returns to ground state by transitioning an L-shell electron to the K-shell

Typically most electron transitions occur from the L-shell to the K-shell

which is classified as a Kα transition The second most common electron transition

occurs from the M-shell to the K-shell which is classified as a Kβ transition Two

Incident

x-ray

Ejected

electron

(a) (b)

M

L

K

M

L

K

Characteristic

x-ray

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

7

other common transitions are the Lα and Lβ transitions (a transition from the M-shell

to the L-shell and from the N-shell to the L-shell respectively) When an atom

returns to its ground state it typically does so using more than one electron transition

As shown in Figure 5 XRF measurements are mainly concerned with these four

transitions because they are the most common and they are the most easily seen while

other transitions have characteristic energies that are out of the detectable range of the

BYU-Idaho XRF instrument (Figure 5)

Figure 5 Four common electron transitions used in XRF measurements

One can notice by looking at a table of characteristic x-ray energies that the Kα

and Lα energies for many elements are very similar (see Appendix C) [7] [8] For

example the Kα energy of titanium (4510 keV) is very close to the Lα energy of

barium (4467 keV) this introduces a difference of only 0043 keV [9] Thus a need

arises for better calibration in order to resolve overlapping energies

213 Continuous Radiation

In every XRF measurement where an x-ray tube is used for the excitation source a

broad range of energies is observed producing a non-linear background noise in the

spectrum The radiation that causes this is called continuous radiation or

bremsstrahlung (German for ldquobraking radiationrdquo) In the x-ray tube electrons are

accelerated over a large potential difference followed by rapid deceleration at the

anode From this a continuous range of x-rays are produced that may provide for

excitation of many different atoms [6] The noise created from continuous radiation

does not impede measurements providing the peaks of interest are relatively more

intense than the noise (Figure 6)

Nucleus

Kα

Kβ Lα

Lβ N

M

L

K

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

8

Figure 6 A simplistic spectrum with peaks from two elements Typically each element in the sample will have

pronounced Kα and Kβ peaks The continuous radiation of noise in the spectrum is called bremsstrahlung

22 Calibration Theory

Since characteristic x-rays are the main factor in making an XRF measurement it is

essential to be able to accurately measure their energies this can only be done after a

calibration is performed In this case the equipment needing calibration is the

detector and multi-channel analyzer (MCA) system

Once an x-ray impinges on the detector the detector sends an electrical pulse

to the MCA One can think of the MCA as a desktop coin sorter Just as the coin

sorter will place each coin in its appropriate bin depending on the coinrsquos size the

MCA will ldquoplacerdquo each x-ray in its appropriate channel depending on the x-rayrsquos

energy The data recorded is an array of numbers each number representing the total

count of x-rays for that energy (intensity) The number placement in the array

represents the channel number in ascending order (Figure 7)

Figure 7 A detailed view of the multi-channel analyzer (MCA) The small boxes represent channels The numbers

represent a count of x-rays for a specific energy

1 keV 5 keV 10 keV 15 keV 20 keV

Detector

1 2 1 1 6 8 9 3 2 1 3 7 1 4 3 0 1 1 0 0

Multi-Channel Analyzer

Intensity

Energy

bremsstrahlung

Kα peaks

Kβ peaks

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

9

A calibration is a process in which specific energy values are assigned to the

correct channel in the MCA This is done by sending x-rays of known energy values

to the MCA once the user identifies the channels where the x-rays were sorted he or

she can assign the known energy values to those channels Since it is not practical to

assign energy values to each channel manually the calibration process consists of

identifying six to eight channels with known energy values and then applying a curve

fitting technique to those data points Through this method all the channels in the

MCA can be calibrated indirectly

Many calibration methods exist For this work it suffices to review three

methods Each method assumes that the calibration data has at least six data points

221 Linear and Quadratic Approximations

A linear or quadratic approximation is one of the most general curve-fitting

techniques In cases where the data appear to be linear a linear approximation can be

sufficient To do this one would apply the least-squares regression equations to find

the slope and intercept of the fitted line These equations are

bmxy

x

y

s

srm

xmyb

Equation (1) represents the linear fit where x represents the channel number

(independent variable) and y represents the energy (dependent variable) The symbols

xs and ys are the sample standard deviations of the channel data and the energy data

respectively m is the slope of the line b is the y-intercept of the line r is the

correlation coefficient and x y are the mean x and y values [2]

A linear approximation is the easiest calibration to perform but it also

introduces the most error (about plusmn01 keV) this results because the MCA does not

have a perfect linear correlation between energy and channel number Therefore it

does not result in the desired accuracy (Figure 8) A slightly better approximation is

done with a quadratic least-squares regression yet this still results in a higher error

than what is desired with an error of about plusmn005 keV This results because these two

approximation methods fit a single curve to the whole data set

(2)

(1)

(3)

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

10

222 Linear and Cubic Spline Interpolation

The spline interpolation method is used to interpolate between every data point for a

more accurate calibration (it is also used for extrapolation near the end points of the

graph) This method has the advantage of uniquely fitting a line between pairs of data

points hence it is not a general fit like the approximation method A linear

interpolation involves taking two data points and fitting a line between those points

(Figure 9) This is done for every gap between two adjacent data points The

equations for the linear interpolation are the same as equations (1) (2) and (3) only

using two data points at a time

The cubic spline interpolation method involves the same design as the linear

interpolation only creating polynomials for the curve fitting [3] This requires that

three or more points are used for each calculation (Figure 10) For a cubic spline

interpolation

1010 yDyCByAyy

where

01

1

xx

xxA

AB 1

2

01

3

6

1xxAAC 2

01

3

6

1xxBBD

Similar to the linear interpolation x is the independent variable (channel

number) and y is the dependent variable (energy) The functions A B C and D are

Figure 8 The linear approximation method

Energy

Channel Number

(4)

(5)

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

11

used as substitutions to the main equation (4) and are all functions of x Using the

cubic spline interpolation method the error is reduced to about plusmn002 keV

223 Optimization Method

In principle the optimization method would provide the most accurate calibration by

using the whole data set taken from the calibration sample rather than six to eight data

points as used in the approximation and spline interpolation methods In the

optimization method the calibration spectrum is compared point by point with a

predicted spectrum which simulates what the calibration spectrum should look like

As the two spectra are compared the calibration spectrum is adjusted to achieve

minimum error with respect to the predicted spectrum The goal is to provide a

calibration spectrum that has a very high correlation coefficient with the predicted

spectrum

In order to create a predicted spectrum a correct set of all the peaks would

need to be modeled this would include the proper modeling of the peak intensities

Also a proper bremsstrahlung would need to be modeled and included in the

spectrum There exists a detailed article which describes the appropriate methods for

peak simulation by E D Greaves et al [4] While the optimization method could

reduce the error to plusmn001 keV or better simulating a predicted spectrum is difficult

and time consuming Therefore the optimization method is not practical in this case

224 Calibration Sample

The calibration sample preferably contains an adequate number of elements to provide

sufficient peaks for calibration typically there are at least six to eight peaks in the

Figure 9 The linear interpolation method Figure 10 The cubic spline interpolation method

Energy

Channel Number

Energy

Channel Number

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 2

12

spectrum These peaks should be separated from other peaks by at least 3 to 4 keV to

avoid confusion in assigning peaks to their corresponding elements The

concentration of each element should be adjusted such that all peak intensities are

approximately equal

A calibration sample made from a variety of compounds should be

homogeneous To ensure this is done all compounds to be included are crushed into a

fine powder using a mortar and pestle The mixture is then made into a slurry using

acetone set into a sample plate and smoothed out to dry the sample plate allows for

easy insertion into the XRF instrument A well prepared and easily accessible

calibration sample will improve the calibration procedure

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 3

13

Chapter 3 BYU-Idaho XRF Instrumentation

31 Previous Work

This work mainly follows that of Lance Nelson and David Oliphant Lance Nelson

worked to install a new XRD detector which was donated to BYU-Idaho His study

was focused on the anatomy of x-ray detectors and their application [5] David

Oliphant has spent much time installing and implementing an Amptek XRF detector in

the XRFXRD instrument and it is ready for calibration and measurements (Figure

11)

Amptek the company that produced the XRF detector and the MCA provides

software to run both of these components This software has been installed on the

computer in the XRF laboratory The software enables the user to easily run an

experiment and record the data The software also includes a built-in linear and

quadratic approximation calibration feature After some use of this calibration feature

we concluded that it could not provide an accuracy of plusmn001 keV

32 Specifications

The x-ray tube in the instrument produces x-rays with energies up to about 30 keV

The XRF detector is not very sensitive in the range between 0 keV and 3 keV and

measurements in this range tend to be quite problematic consequently data in this

range do not serve for accurate XRF measurements and are typically ignored

The MCA has a total of 16000 channels this allows a maximum resolution of

about 0003 keV per channel The resolution can be adjusted using the Amptek

software the maximum resolution can be obtained when the 16000 channel option is

selected We have chosen to use the 8000 channel option because minimum errors of

plusmn001 keV can still be obtained with this resolution and the XRF measurements take

about half the amount of time on this setting compared to using the 16000 channel

option

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 3

14

Figure 11 The XRF detector

Figure 12 An inside look of the XRF instrument At top middle

is the x-ray tube At right is the sample for testing At bottom

left is the XRF detector

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

15

Chapter 4 Study

41 The Best Calibration Method

Observation indicated that the most efficient calibration would result from using a

cubic spline interpolation this method gives the desired accuracy and LabVIEW 71

has a built-in spline interpolation function which is easy to use We concluded that the

linear and quadratic approximations and the linear interpolation do not give the

desired accuracy Using the optimization method can give an equally or more

accurate calibration than a spline interpolation but the underlying mathematics and

code necessary for this method were impractical Therefore for sakes of accuracy and

time a cubic spline interpolation method was used and implemented

42 Code Development

421 LabVIEW 71 Basics

LabVIEW 71 was the programming language of choice for its visual ease It is

relatively easy to debug and console inputoutput is simple to implement LabVIEW

71 employs small icons to represent functions and wires to represent data transfers

For and while loops can be easily performed these looping structures appear as boxes

in the block diagram There are also sub-programs called virtual instruments (VIrsquos)

that can be called to perform more complex functions Specifically some of the VIrsquos

that were used in this calibration program were the Peak Detection VI Spline

Interpolant VI Spline Interpolation VI and xy-Graph VI

422 Creating the Calibration Program

The goal of the calibration program was twofold First to read a calibration file and

calculate the cubic spline interpolation calibration and second to read a file

containing data from an unidentified sample and determine the elements in that

sample

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

16

The first objective in creating the calibration program was to enable reading of

the XRF calibration spectrum file This is done by using the ldquoread filerdquo icon These

spectrum data files always have header information which is easily skipped by

instructing the program to start reading after ldquoltltDATAgtgtrdquo An example of a typical

spectrum data file displaying the header information is shown in Appendix B

After reading the data and organizing it into a one dimensional array the next

step consisted of using the Peak Detection VI This VI searches through the data for

peak locations Its sensitivity can be controlled using the threshold and width values

Specifically the threshold is the intensity value below which peaks are neglected and

the width is the number of data points used in determining a peak similar to a width

value used in a smoothing function The threshold and width values should be

carefully chosen visually evaluating the spectrum in advance is helpful in determining

these values especially the threshold value The width value in practice is between 8

and 16 but should be no higher than 20 width values higher than 20 result in

inaccurate peak locations

Having obtained the peak locations the program pairs them with their

corresponding energy values These energy values are input by the user and

correspond to the known elements and their characteristic x-rays The program then

runs these values through a while loop to calculate the spline interpolation for

calibration After the spline interpolation routine the while loop yields a one

dimensional array containing the calibrated energies the number representing the

calibrated energy and the number placement in the array representing the

corresponding channel (Figure 13 shows the block diagram view) The calibrated

energies array is then ready to be used as a calibrated x-axis for an XRF measurement

The program graphs the calibration spectrum and the spectrum to be identified in the

same plot using the calibrated x-axis

Figure 13 The block diagram view of the LabVIEW 71 calibration program

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

17

43 Calibration Sample Development

For the calibration sample elements were chosen from the periodic table based on the

energy differences between each element ensuring a difference of at least 3 to 4 keV

These elements along with their corresponding characteristic x-ray energies [9] are

shown in Table 1

Table 1 Characteristic x-ray energies for select elements

Element Name Kα Energy (keV)a Kβ Energy (keV)

a

Manganese 5899 6490

(Copper) 8048 8905

Bromine 11924 13292

Strontium 14165 15836

Molybdenum 17479 19607

Cadmium 23174 26095 aReference [9]

Because the anode in the x-ray tube is composed of copper many of the

characteristic x-rays of copper are reflected off the sample to the detector As a result

copper peaks are present in every XRF measurement It is a difficult process to

eliminate the copper peaks from the spectrum and seeing that the copper peaks did not

affect the measurement we determined that copper can be used as one of the

calibration elements

431 Sample Preparation

To create the sample compounds were obtained from the BYU-Idaho chemistry

department The manganese bromine strontium and cadmium compounds were

available but the molybdenum compound was not The compounds were available in

salt hydrated salt and hydrated nitrate forms

Before mixing the compounds a thorough study was performed to calculate

the proportionalities of the elements in each compound The goal was to make a

calibration sample that had equal amounts of the elements of interest this way it was

believed the intensities of each peak in the spectrum would be equal Using

molarities the mole per compound mass was formulated for each compound and was

used to calculate the correct proportions for the calibration sample After the sample

was constructed and measured observation showed that the manganese and strontium

peaks were five to six times the intensity of the other peaks and the cadmium peak

was 120 to 130 times the intensity of the other peaks Three more samples were

made in an effort to improve the intensity levels but all three still had disproportionate

intensity levels

The ratios of the intensity levels of the first four samples served as a means to

re-calculate the proportionalities and create a better sample A final sample was made

and measured and observation showed that the peak intensities were within two to

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

18

three times the intensities of the surrounding peaks The copper peak intensity was

disproportionately large however this intensity cannot be controlled because these

copper characteristic x-rays are emitted from the x-ray tube The actual amounts of

compounds used in the calibration sample and the trace amounts in the compounds are

shown in Table 2 and Table 3

Table 2 Compounds used in the calibration sample

Compound Amount Used (grams) plusmn00003 grams

MnCl2 4H2O 00117

KBr 00224

SrCl2 6H2O 00706

Cd(NO3)2 4H2O 40357

Table 3 Trace amounts in the compounds listed in Table 2

When creating the first four samples no acetone was necessary to combine

them since three of the compounds were hydrates The water in the compounds was

released when the mixture was crushed and combined providing a homogeneous

solution which was easily set into the sample plate The fifth and last sample did not

release as much water as the first four so a small amount of acetone was used to help

combine the mixture (Figure 14)

Figure 14 The sample used for calibration

Compound Cl Cu Fe Pb Zn Ba Other

MnCl2 4H2O - - 0005 0005 01 - 210

KBr 20 - 0005 0005 - 002 04

SrCl2 6H2O - - 5 ppm 5 ppm - 002 0521

Cd(NO3)2 4H2O 001 002 001 005 05 - 1135

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

19

44 Implementing the Calibration Program

Once the program was constructed the next step consisted of implementing the

program Initially we thought that one could simply upload the calibration file onto

the computer connected to the XRF instrument and use it in the Amptek software

Unfortunately this was not the case the software only allows its own calibrations to

be used This meant that another solution not involving the Amptek software had to

be employed

After some inspection it became apparent that a spectrum file from the XRF

instrument could be easily uploaded into the calibration program itself The

calibration program was modified to enable the spectrum file to be imported and then

plotted on the calibrated energy axis

The front panel of the program (Figure 15) was made so that the user could

input and adjust the known calibration energy values In the ldquoCalibrationrdquo box the

user can adjust the peak detection sensitivity values (threshold and width) Displayed

in this box is the calibration fit graph the number of calibration peaks detected and

the locations of the detected peaks The adjacent ldquoMaterials Identificationrdquo box

enables the user to adjust the peak detection sensitivity values for the unidentified

spectrum Displayed in this box are the number of peaks detected and the

corresponding element energies of those peaks The main graph displays both the

calibration spectrum (dashed line) and the spectrum for identification (solid line)

Upon running the program a dialog box opens which asks for a spectrum file

(typically from an unidentified sample) to be uploaded After the file is uploaded the

program runs the calibration process and plots the spectra The main graph in Figure

15 shows a spectrum taken from a silver ring To see spectra of the calibration and

other samples see Appendix A

By comparing two calibration spectra which were taken two and a half months

apart it is seen that the maximum drift in any energy value is approximately 003 keV

Since the MCA has this tendency to drift in accuracy over a two and a half month

period it is recommended that the calibration sample be tested and implemented at

least once a month to ensure accuracy

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 4

20

Figure 15 The front panel view of the LabVIEW 71 calibration program

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 5

21

Chapter 5 Conclusion

After calibration methods were researched and a better calibration program was

created and implemented several different samples were measured and compared to

the accepted values [9] These measurements along with their corresponding

accepted values are shown in Table 4

Table 4 Experimental values and accepted values along with the corresponding errors

Element Name Transition Measured

Energy (keV)

Accepted

Energy (keV)b

Absolute

Error (keV)

Iron Kα 6388 6404 016

Iron Kβ 7052 7058 006

Silver Kα 22085 22163 078

Gold Lβ 11453 11442 011

Nickel Kα 7492 7478 014

Zinc Kα 8671 8639 032 bReference [9]

Mean Error Maximum Error Minimum Error

026 078 006

Measurements in the lower range of energies (3 to 15 keV) tend to have a

lower error amount and measurements in the higher range of energies (15 to 28 keV)

tend to have a higher error amount However as a result of the calibration the XRF

measurements have in general increased in accuracy Users are now able to collect

reliable sample data down to a mean error of about plusmn003 keV and a minimum error

of plusmn001 keV

Throughout the course of this project a variety of future supplementary

projects have been uncovered Prospective students will find this project helpful as

they consider the following possibilities

1 A study of the XRF detector sensitivities at low x-ray energies

There are many instances when an XRF measurement has detected excessive

noise in the lower range of the spectrum Often there tend to be large peaks

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

Chapter 5

22

around one or two keV A detailed study about this anomaly would be useful

since many elements have characteristic x-rays in this region

2 The development of a program that automatically qualifies elements in the

sample

The program written in this project is currently capable of detecting peaks in

an unidentified spectrum and the characteristic x-ray energies are listed

However extra effort is required on behalf of the user to look up the energies in a

list to identify which elements are present in the sample Furthermore the user

might need to identify two or more peaks for one element to be certain that it is

present in the sample With some alteration of the calibration program this

process could be automated

3 The development of a program that quantifies elements in the sample

Some quantifying work was performed in this project to determine correct

proportionalities for the calibration sample A deeper study of quantification can

be done using ratios of intensities of different peaks in the spectrum The

calibration program can be altered to make these calculations A program that

quantifies elements in the sample is useful in a variety of applications

4 The development of a calibration sample that has a larger energy range

The calibration sample in this project has eight useful peaks ranging from 6

keV to 23 keV A calibration sample can be made to have more than eight useful

peaks in a broader range of energies In the current calibration there was growing

error as energy increased in the 18 to 28 keV range A calibration sample with

more peaks in this range can substantially reduce this error

These different areas were lightly examined in this project but due to limited time

they were not studied in depth It is hopeful that a prospective student will choose to

further develop the BYU-Idaho XRF instrument

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

23

Bibliography

[1] R Jenkins X-Ray Fluorescence Spectrometry (John Wiley amp Sons Inc New

York 1999) 2nd

ed p 5-12 75-76

[2] M Sullivan Fundamentals of Statistics (Prentice Hall 2006) 2nd

ed tables

[3] W H Press S A Teukolsky W T Vetterling B P Flannery Numerical

Recipes in C (Press Syndicate of the University of Cambridge New York

1992) 2nd

ed p 105-116

[4] E D Greaves L Bennum F Palacios and J A Alfonso X-Ray Spectrom 34

196-199 (2005)

[5] L J Nelson Senior Thesis BYU-Idaho (2007)

[6] P V Espen in Handbook of X-Ray Spectrometry edited by R E V Grieken

and A A Markowicz (Marcel Dekker Inc New York 2002) Chap 4 p 239-

242

[7] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008

[8] HoribaJobin Yvon Table of X-Ray Emission Lines

wwwjobinyvoncomxray accessed 12072008 (modified)

[9] Lawrence Berkeley National Laboratory Table of Radioactive Isotopes

httpielblgovtoi accessed 11212008

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

24

Appendix A Various X-Ray Spectra

This spectrum shows the peaks measured from the calibration sample

Cu

Br Sr

Mn Cd

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

25

A spectrum of a metal car key likely containing Ni and Zn

A spectrum of an unknown sample likely containing Fe

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

26

A spectrum of a US dollar coin likely containing Ni

A spectrum of an unknown rock sample likely containing Fe

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

27

Appendix B A Typical Spectrum Data File

ltltPMCA SPECTRUMgtgt

TAG - live_data

DESCRIPTION -

GAIN - 5

THRESHOLD - 50

LIVE_MODE - 0

PRESET_TIME - 0

LIVE_TIME - 4113826667

REAL_TIME - 4132213333

START_TIME - 11072008 135730

SERIAL_NUMBER - 2542

ltltCALIBRATIONgtgt

LABEL - Channel

0 0

1058 805

ltltROIgtgt

706 821

979 1104

1501 1621

1784 1918

2933 3091

ltltDATAgtgt

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

28

Appendix C X-ray Energy Tables

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

29

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

30

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W

31

Lα 27 45Rh Kβ 595 24Cr Lα 1084 83Bi Kβ 2272 45Rh

Kβ 281 17Cl Lβ 596 61Pm Kβ 1098 32Ge Kα 2317 48Cd

Lβ 283 45Rh Lα 606 64Gd Lβ 1107 78Pt Kβ 2382 46Pd

Lα 284 46Pd Lβ 621 62Sm Lα 1113 84Po Kα 2421 49In

Lβ 29 46Pd Lα 627 65Tb Kα 1122 34Se Kβ 2494 47Ag

Kα 296 18Ar Kα 64 26Fe Lα 1143 85At Kα 2527 50Sn

Lα 298 47Ag Lβ 646 63Eu Lβ 1144 79Au Kβ 261 48Cd

Mα 3 90Th Kβ 649 25Mn Kβ 1173 33As Kα 2636 51Sb

Mα 308 91Pa Lα 65 66Dy Lα 1173 86Rn Kβ 2728 49In

Lα 313 48Cd Lβ 671 64Gd Lβ 1182 80Hg Kα 2747 52Te

Lβ 315 47Ag Lα 672 67Ho Kα 1192 35Br Kβ 2849 50Sn

Mα 317 92U Kα 693 26Co Lα 1203 87Fr Kα 2861 53I

Kβ 319 18Ar Lα 695 68Er Lβ 1221 81Tl Kβ 2973 51Sb

Lα 329 49In Lβ 698 65Tb Lα 1234 88Ra Kα 2978 54Xe

Kα 331 19K Kβ 706 26Fe Kβ 125 34Se Kα 3097 55Cs

Lβ 332 48Cd Lα 718 69Tm Lβ 1261 82Pb Kβ 31 52Te

Lα 34 50Sn Lβ 725 66Dy Lα 1265 89Ac Kα 3219 56Ba

Lβ 349 49In Lα 742 70Yb Kα 1265 36Kr Kβ 3229 53I

Kβ 359 19K Kα 748 28Ni Lα 1297 90Th Kα 3344 57La

Lβ 36 50Sn Lβ 753 67Ho Lβ 1302 83Bi Kβ 3362 54Xe

Lα 36 51Sb Lα 76 71Lu Lα 1329 91Pa Kα 3472 58Ce

Kα 369 20Ca Kβ 765 26Co Kβ 1329 35Br Kβ 3499 55Cs

Lα 37 52Te Lβ 781 68Er Kα 134 37Rb Kα 3603 59Pr

Lβ 384 51Sb Lα 79 72Hf Lβ 1345 84Po Kβ 3638 56Ba

Lα 394 53I Kα 805 29Cu Lα 1361 92U Kα 3736 60Nd

Kβ 401 20Ca Lβ 81 69Tm Lβ 1388 85At Kβ 378 57La

Lβ 403 52Te Lα 815 73Ta Kβ 1411 36Kr Kα 3872 61Pm

Kα 409 21Sc Kβ 826 28Ni Kα 1417 38Sr Kβ 3928 58Ce

Lα 41 54Xe Lβ 84 70Yb Lβ 1432 86Rn Kα 4012 62Sm

Lβ 42 53I Lα 84 74W Lβ 1477 87Fr Kβ 4075 59Pr

Lα 429 55Cs Kα 864 30Zn Kα 1496 39Y Kα 4154 63Eu

Kβ 446 21Sc Lα 865 75Re Kβ 1496 37Rb Kβ 4227 60Nd

Lα 447 56Ba Lβ 871 71Lu Lβ 1524 88Ra Kα 43 64Gd

Kα 451 22Ti Lα 891 76Os Lβ 1571 89Ac Kβ 4383 61Pm

Lβ 462 55Cs Kβ 891 29Cu Kα 1578 40Zr Kα 4448 65Tb

Lα 465 57La Lβ 902 72Hf Kβ 1584 38Sr Kβ 4541 62Sm

Lβ 483 56Ba Lα 918 77Ir Lβ 162 90Th Kα 46 66Dy

Lα 484 58Ce Kα 925 31Ga Kα 1662 41Nb Kβ 4704 63Eu

Kβ 493 22Ti Lβ 934 73Ta Lβ 167 91Pa Kα 4755 67Ho

Kα 495 23V Lα 94 78Pt Kβ 1674 39Y Kβ 487 64Gd

Lα 503 59Pr Kβ 957 30Zn Lβ 1722 92U Kα 4913 68Er

Lβ 504 57La Lβ 967 74W Kα 1748 42Mo Kβ 5038 65Tb

Lα 523 60Nd Lα 971 79Au Kβ 1767 40Zr Kα 5074 69Tm

Lβ 526 58Ce Kα 989 32Ge Kα 1837 43Tc Kβ 5211 66Dy

Kα 541 24Cr Lα 99 80Hg Kβ 1862 41Nb Kα 5239 70Yb

Lα 543 61Pm Lβ 1001 75Re Kα 1928 44Ru Kβ 5388 67Ho

Kβ 543 23V Kβ 1026 31Ga Kβ 1961 42Mo Kα 5407 71Lu

Lβ 549 59Pr Lα 1027 81Tl Kα 2022 45Rh Kβ 5568 68Er

Lα 564 62Sm Lβ 1036 76Os Kβ 2062 43Tc Kα 5579 72Hf

Lβ 572 60Nd Kα 1054 33As Kα 2118 46Pd Kβ 5752 69Tm

Lα 585 63Eu Lα 1055 82Pb Kβ 2166 44Ru Kα 5753 73Ta

Kα 59 25Mn Lβ 1071 77Ir Kα 2216 47Ag Kα 5932 74W