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