ndt sami mahmood

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Materials characterization is concerned with

investigating the properties of materials.

Some of the techniques designed for such

purposes, however, are invasive, resulting in

changing the nature of the examined object,

or its permanent loss in some cases. When

this is not acceptable, methods for non-destructive testing are highly demanded.

This text is devoted to the discussion of the

principles and applications of some of these

methods.

NonDistructive

Testing

Sami Mahmood, The University of Jordan



Chapter 1

Introduction to Non Destructive Testing



Introduction

Materials characterization involve techniques concerned with investigating the various physical,

chemical, structural or morphological properties of an object or a sample of interest. The

techniques are commonly based on measuring quantities, analyzing the measured quantities interms of appropriate scientific principles, and correlating the results of analysis with specific

material properties. Some of the techniques designed for such purposes are invasive, and may

result in changing the nature of the examined object, destroying its structure, or lead to its

permanent loss in some case. This is not acceptable when we need to preserve the investigated

object, or minimize its damage. When we examine the constituents of an archaeological artifact,

an irreplaceable coin, or a valuable stone, it is important to keep the examined object unaffected;

when we examine the performance of a device, or the parts of a spaceship or wind mill, we do not

want to induce damage by the measuring technique; when we examine the quality of water in an

aquifer, we do not want a method which results in polluting the water; and when we examine

healthy tissues or organ in a human body, we do not accept a technique which kills the examine

tissue or organ. Accordingly, great efforts were spent to design non-destructive testing methods,

and apply them for testing and evaluation a broad spectrum of applications.

Accurate information pertaining to the properties, performance, or condition of a material or object

is often needed in many fields. Examples of required material evaluation are: In food science, thequality of foods and drinks manufactured for human consumption; in civil engineering , the

strength and serviceability of construction materials for homes, roads and arches; in mechanical

engineering and industry, the durability of components used for building machines such as cars,

aircrafts, ships, and power plants; in medicine, diagnosis of defects and disorders in bones, tissues,

and organs; in science, the performance of components and devices used in scientific

instrumentation, the composition and structure of materials, and the properties of materials; and in

archeology, the composition and dating of historical structures, materials and artifacts.

Accordingly, and for obvious reasons, the testing and evaluation technique should not destroy the

object under investigation, or change its potential for future use. Conventional chemical methods

for identifying historical objects, for example, involved dissolving the object in an acid, which

entails permanent loss of the object. Consequently, the field of Nondestructive testing (NDT)

evolved with the recent advances in science and technology as an essential branch of science



concerned with performing measurements of materials in ways that do not impair their future

usefulness and functionality, in order to detect, locate, and evaluate discontinuities, defects and

imperfection; to make an assessment of the integrity properties and composition; and to measure

geometrical characteristics.

The definition of NDT could be misleading. The above definition could imply non-destructive

measurements of an object, without inducing a damaging effect by the interactions of the probe

(such as mechanical vibrations, radiation, or temperature) with the object material. Such

techniques involve in-field evaluation of the strength or performance of parts in large

constructions (such as a bridge or a building), or in machines such as the wings of an aircraft, or

the blades of a wind mill. In another example of a NDT using in-field non-contact technique, the

radiation used by a radar system to measure the speed of a car does not induce any damage. Also,

in some techniques it is possible to design a sample holder in which the object fits, and desired

parts of which can be safely examined (Fig. 1.1).

Fig. 1.1: Schematic diagrams of a measuring equipment with the object fitting in.

NDT nowadays is not limited to examples such as those mentioned above. Thanks to the great

advancement in experimental instrumentation requiring extremely small amounts of material for

testing, which made it possible to examine different aspects of an object by examining tiny parts

of it. Although for such techniques we need to extract a small sample from the object, such a

process does not induce significant damages to the object as a whole, and the technique is

considered a NDT method. Consequently, the NDT term was relaxed to imply that the measuring

technique does not impart damages or changes of the physical properties of the tested material.

DetectorOb ectSourse



An experimental setup designed to examine a given physical property usually includes a source

and a detector. In an experiment designed to investigate the structural characteristics of a sample

using x-ray diffraction experiment, the source produces an x-ray beam which is aimed at the

sample, and the detector measures the intensity of x-rays diffracted in different directions (Fig. 2).

For specific heat measurement, the source produces heat supplied to the sample, and the detector

is a thermometer which measures changes in the temperature of the sample as fixed amounts of

heat energy are supplied. In a simple experiment for measuring the electric resistance of a metallic

wire, the source produces an electric field which is applied across the wire, and a sensitive ammeter

is used to detect and measure the current. Thus, the x-ray beam, heat, and current in the above

examples are used to probe specific properties of the sample by measuring the response of the

material to interactions with these probes. In the example of x-ray diffraction, the interaction of

the material with the x-ray beam results in variations of the x-ray intensity scattered from the

sample in different directions, which are measured by the detector. In the case of specific heat

measurement, the heat raises the mean atomic or molecular velocity in the sample, and

consequently its temperature, which is measured by the thermometer. Finally, in measuring the

electrical resistance, electrons in the sample interact with the applied electric field and are driven

across the wire. The moving electrons scatter from crystal imperfections and impurities in the

sample (which is a source of electrical resistance), but in the presence of an applied field, the mean

drift velocity along the direction of the field is not zero, resulting in a current propagating along

the wire, which can be measured by an ammeter. In NDT, the interactions of the sample with the

probe should not result in changes in the properties or internal structure of the sample. So, x-rays

used should not, for example, destroy the crystallographic or molecular structure of the sample,

heat should not result in chemical reactions in the sample, and the applied field should not burn

the sample.



Fig. 1.2: Schematic diagram illustration of examining a small crystal by x-ray diffraction.

In the process of preparing a small sample for measurement, the sample needs to be treated in

special ways to fit the requirements of the measuring technique, such as grinding or polishing and

shaping small sections for x-ray diffraction and electron or optical microscopy, for example. In

this case, one should be careful not to change the nature of the sample such as introducing

impurities, or changing the structure of the sample by the grinding, sectioning, or polishing

process. For example, if a multi-layered structure is to be investigated, the process of taking a

small part of the sample for measurement should not cause mixing of the layers.

Experimental techniques for NDT are different for different materials. For homogeneous and

isotropic materials such as metals, plastics, and ceramics, whose properties are highly controlled

by manufacturing processes, NDT techniques may require small samples to detect the presence of

discontinuities, voids, or inclusions in the material. In such cases, data obtained by measuring the

whole sample reveal average values representing the properties of the material. For

inhomogeneous objects, however, local measurement techniques are required to probe local

variations of the properties across the sample. For such purposes, techniques involving focused

beams (such as the electron beam in an electron microscope, or focused x-ray beam in a

diffractometer) or sharp tips (as in an atomic force microscope) are required to examine local



properties by measuring small spots on the sample (Fig. 1.3). In addition, a focused beam is

required to investigate very small samples, such as small single crystals (Fig. 1.2).

Fig. 1.3: Schematic diagram of (a) atomic force microscopy (AFM); (b) X-ray diffraction (XRD)from a small spots of a sample, and (c) focused electron beam.

Electromagnetic waves (EM) do not need mechanical contact with the sample, and therefore

provide means for NDT of materials. However, problems related to the use of EM-based

techniques limit their use in some cases. For example, a technique based on measuring the

transmitted intensity is not appropriate for characterizing a sample which is too thick and non-

transparent to the EM radiation, and technique based on measuring the reflected intensity is not

appropriate to characterize a highly absorbing or transparent material.

(a) (b)

(c)



Different NDT techniques for materials characterization were developed on the basis of the

different aspects of interactions of waves and particles, and their attenuation in the material,

reflection from surfaces, and induced emission of particles and radiation from the material.

Examples of the basis of such technique are:

1. Probing signals emanating from samples: spectroscopic techniques for materials

characterization were designed on the basis of detection of radiation (such as gamma-rays) emitted

from the sample.

2. Interaction of particles or radiation with the material: Techniques for materials characterization

based on detecting induced emission were developed. These include x-ray fluorescence (XRF),

and energy dispersive x-ray spectroscopy (EDS) for elemental analyses, absorption and reflection

of radiation for optical properties of solids and medical diagnosis, electron, neutron, and x-ray

reflection for structural studies.

3. Propagation of ultrasonic waves for materials characterization and medical applications.

4. Attenuation of x-ray in the material for x-ray tomography applications in materials and

medical sciences.

5. Interaction with electromagnetic fields and temperature gradients for transport, magnetic,

magneto-electric and magneto-optical properties.



Chapter 2

X-ray Imaging



2.1.

Materials Characterization by X-rays

X-rays are widely used for materials characterization in many disciplines, such as medical

sciences, materials science, geosciences and mineralogy, biology, and archaeology. Different

techniques of x-ray characterization based on different scientific principles were developedaccording to need. Thus, techniques based on measuring the attenuation (absorption) of x-rays in

materials were developed to observe variations, inhomogeneity, and defects in the material, and to

inspect the morphology and microstructure of objects. One of the widely used techniques for such

purposes is x-ray radiology (imaging). Other techniques based on measuring the reflected intensity

from the atomic planes in a material, and from aggregates of atoms in large molecular structures

were developed to investigate the crystalline structure and the atomic distributions, and to identify

the various phases existing in the material and determine their abundances in the measured sample.

In this context, x-ray diffraction (XRD) is widely used for structural and microstructural

characterization of materials in several fields, including and not limited to, physics and materials

science, chemistry and pharmacology, structural molecular biology, mineralogy, engineering, and

archaeology. Also, determination of the elemental composition of materials, and the chemical

stoichiometry of a sample is sometimes required. For such purposed, NDT techniques for

quantitative elemental analysis of samples were developed. XRD quantitative analysis can be

employed to determine the fractional masses of different phases existing in a multi-component

sample. However, dedicated techniques for elemental analysis based on the spectral characteristics

of radiation emitted by the different elements in the sample were developed. These include, and

are not limited to, x-ray fluorescence (XRF) spectroscopy using electromagnetic radiation for

atomic excitations, and energy dispersive x-ray spectroscopy (EDS) using electron beam excitation

in electron microscopes. Other techniques are available for materials characterization, but they are

not within the scope of this course, and our subsequent discussion of NDT techniques will be

limited to few examples, mainly relevant to materials science.

2.2.

X-ray Sources

X-rays are produced by different methods. Conventional x-ray tubes are used to produce x-rays by

bombarding a metallic target by an accelerated beam of electrons (Fig. 2.1). The x-rays produced

in such a way are characterized by a wide distribution of wavelengths (or energies) resulting from



the deceleration of electrons in the metal ( Bremsstrahlung ), and essentially monochromatic x-rays

resulting from the atomic transitions within the metal atoms (characteristic atomic spectra).

Fig.2.2. shows the spectrum generated by the tube. The thick-lined continuous spectrum is the

Bremsstrahlung, while the thin-lined, sharp peaks result from atomic transitions. Since in many

applications the polychromatic spectrum yields measurements which are difficult to analyze and

interpret, monochromatic x-ray beams are required. This is obtained by filtering the spectrum,

leaving the wavelength of interest. The intense atomic x-ray line ( K α line) produced by a

conventional x-ray tube is often used for real applications. This line has a characteristic wavelength

depending on the material of the metal target, and does not depend on the experimental conditions

of producing the spectrum. The most commonly used x-ray tubes in small laboratory equipment is

Cu-tube which produces x-ray beam with a mean wavelength of λ = 1.5418 Å. This line, in fact,

consists of two closely separated lines, namely, Cu- K α1 and Cu- K α2 lines. The above mentioned

wavelength is the average value for these two lines, which is used in experiments where distinction

between the two lines is difficult. Disadvantage of this technique of producing x-rays is that the

intensity of the beam is weak (partially due to the filtering process), but for many applications, the

obtained intensity is useful for characterization purposes. Advantages of this technique is its low

cost and availability within reach.

Fig. 2.1: schematic diagram of a conventional x-ray tube.



Fig. 2.2: x-ray spectrum generated by a conventional x-ray tube.

Sometimes higher intensities than can be provided by a conventional x-ray tube are required toobserve small variations of the properties of a sample, or to measure an extremely small sample

which gives a weak signal when using a conventional x-ray source. In such cases, intense x-ray

beams produced by large electron accelerators such as synchrotron light sources become very

valuable for materials characterization. In such a facility, electrons circulating in the storage ring

with very high speed emit radiation with high intensity as a consequence of their acceleration. The

radiation is passed through beam-lines equipped with dedicated beam optics to provide the beam

energy required for different applications (for example infrared spectroscopy, soft or hard x-ray

spectroscopy, structural studies). Although synchrotron radiation has an obvious advantage over

the conventional x-ray sources in the sense that it can provide intense beam over a wide range of

wavelengths, it has disadvantages in the sense that operating a synchrotron facility is relatively

much more expensive, and requires higher level of technical skills compared with conventional

Kα

K

Wavelen th λ

I n t e n s i t



techniques. Also, synchrotron facilities are not always available for measurements at the time

needed.

Fig. 2.3: Illustration of different parts of a synchrotron radiation facility.

2.3.

Radiography

X-ray imaging (radiology) techniques are designed to obtain images of bodies based on the

absorption of x-rays by the different parts of the imaged body. For conventional x-ray imaging in

medical and dental fields, x-rays are allowed to pass through the body, and the transmittedradiation is collected on a photographic film containing material like silver halide. X-rays have the

property of partially converting silver halide crystals in the film to metallic silver, in proportion to

the intensity of the radiation reaching the film. Different absorption levels of x-rays occur in

materials with different densities and compositions. Accordingly, different intensities of x-rays are

transmitted from different parts of the investigated body, depending on the different levels of

Beam lines

Storage ring

Bending magnet

Booster ring

Electron source



absorption in the materials along the path of the beam, forming spots with different shades of grey,

and therefore forming the image. This can be developed and fixed in a similar way to normal

photographic film. The resolution of the technique is about 0.5 mm.

Fig. 2.4 shows an X-ray image obtained according to the discussed procedure. Notice that the

highly absorbing material (bones in this case) appeared as a light image on the dark background

produced by the high intensity x-ray falling on the film. Less dense material (such as at the joints)

appeared grey. A disadvantage of this technique is that the absorption is monitored along the beam

through the whole thickness of the body, and if different structures are penetrated by the beam,

their absorption effects overlap and their images become difficult to resolve.

Fig. 2.4: X-ray photograph from a conventional medical imaging method.

In industry, this technique can be used for the inspection of internal defects in materials. The object

to be tested is placed between the source of radiation and the film. As the beam passes through

voids, its attenuation is less than beam passing through homogeneous regions with no voids.

Accordingly, beams transmitted through regions with voids make darkened areas on the film, on

a clear background (see Fig. 2.5 [1]).



Fig. 2.5: Illustration of the imaging of voids in a sample using radiology.

Advantages of Radiography [1]

Information on sample characteristics is easily obtained as it is presented pictorially. A permanent record of the information is provided, which may be viewed at a time and

place distant from the test.

Useful for thin sections.

Sensitivity declared on each film.

Suitable for any material.

Disadvantages of Radiography

Generally an inability to cope with thick sections. Possible health hazard due to exposure to radiation.

Need to direct the beam accurately for two-dimensional defects.

Film processing and viewing facilities are necessary.

Not suitable for surface defects, since it is a technique based on probing the material

along the path of the beam.



The technique does not provide information related to the depth of a defect below the

surface of the sample

X-ray tomography

According to the previous discussion, the traditional radiography technique does not provide a

clear picture of the imaged object, and may hide some important information as a consequence of

overlapping structures. For example, a dense object will mask the image of a low-absorbing object

situated behind along the beam direction. Further, the direction of the beam in the imaging process

controls what you see on the film, since this technique is based on shadowing the object (see

illustration in Fig. 2.6). In order to observe the details of the structure of an object, the object

should be imaged from different angles, and the information obtained from absorptions along thedifferent directions should be used to reconstruct a two-dimensional or a three-dimensional image.

For this purpose, a more suitable technique is needed.

Fig. 2.6: Schematic diagram illustrating the images observed by illuminating an object along twodifferent directions.

In the 1970s, a novel x-ray imaging technique was developed, the computed tomography (CT)

technique which images a slice of the body. This technique is based on passing a narrow,



collimated x-ray beam through the body, and detecting the transmitted intensity. Measurements

are carried out at as many spots of the imaged body as demanded by the desired resolution of the

technique; this is done by moving the beam across the body (scanning the body). In this manner,

the scanned slice can be viewed as being divided into the desired number of elements ( pixels). The

body is then rotated about the body axis perpendicular to the imaged slice (or the beam is rotated

about the body axis) by a small angle (like 1°), and the scan is repeated. The transmitted intensity

is subtracted from the incident intensity to obtain the total absorption (called a projection) along

the path of the beam. This absorption is caused by all the elements through which the beam passes,

and these elements cannot be distinguished by the measured projection. However, by analyzing all

projections obtained by scanning at different angles, the absorption by each element can be

estimated rather accurately, depending on the number of measurements made. The absorption by

each element is characterized by a number, which refers to the amount of the radiation absorbed

by the element. The image is reconstructed from these values by assigning a gray level to each

number.

The number of pixels in a given image determines the resolution of the image. Better resolution is

obtained by increasing the number of pixels as sown by Fig. 2.7 and 2.8. But to determine the gray

level of N pixels, we need at least N projections. For example, in reconstructing a 100×100 image

(using 10,000 pixels) a 100 projections measured at a 100 different angles give the necessary

number to estimate the absorption (gray level) by each pixel. Analysis of these projections,

however, yields an estimate of the gray levels of the pixels which is close, but not exactly equal to

the true absorption values. Measurements at more angles would refine the result and yield better

estimates, and thus a better quality of the image. In the following example, we consider a simple

2×2 image.



Fig. 2.7: Illustration of the improved resolution of an image with the increase in the number of pixels.

Fig. 2.8: Image of a triangle constructed by different numbers of pixels: 4 in the upper panels(2×2 image), 16 in the middle panels (4×4 image), and 64 in the lower panels (8×8 image). Notice how the image improves by increasing the number of pixels. A very large number of pixels is required for a high resolution image.



Suppose that the true absorptions in the four pixels (corresponding to their true shades of gray) are

1, 4, 2, and 8 as shown in Fig. 2.9. Then experimental measurements of the projections in the two

different directions shown in the figure yield the values: 5 and 10 in the first direction, and 6 and

9 in the second. Each projection gives the total absorption by the pixels through which the beam

passes, but we do not know the absorption by each pixel. We then need to carry out a mathematical

reconstruction of the image by determining the absorption in each pixel using the available

information (the four measured projections). This is done by the iterative procedure discussed

below.

Fig. 2.9: Projections measured in two different directions of beams passing through a sectiondivided into 4 pixels.

We start with each pixel assigned a zero absorption. Then the projection along each beam line is

divided equally between the two pixels it passes through, which results in estimated absorptions

of 2.5, 2.5, 5, and 5 as shown in Fig. 2.10. Notice how far the values determined by this first

iteration are from the true values. Although the absorptions estimated by this iteration are

consistent with the projections in the first direction, they give projections (7.5 and 7.5) which are

significantly different from the measured values of 6 and 9 in the second direction). To refine the

results and obtain more reliable values, the mathematical reconstruction procedure performs a

second iteration by consider the projections in the second direction. In the lower two pixels, the

measured projection is 9, and therefore, the value of 7.5 calculated in the first iteration should be

1 8

24

5 10

6

9

Angle 1

Angle 2



increased by 1.5 to obtain the correct measured value. Thus, 0.75 should be added to the absorption

calculated in the first iteration for each of these two pixels, resulting in 3.25 in the lower left pixel,

and 5.75 in the lower right pixel. Similarly, the absorption by each of the upper two pixels should

be reduced by 0.75 in order to give the measured projection of 6, resulting in 1.75 in the upper left

pixel and 4.25 in the upper right pixel. Notice that the calculated absorptions in the second iteration

give the right measured projections along the two direction, and can be considered as estimates of

the gray levels of the four pixels. However, the calculated absorptions are still significantly

different from the true values, and the obtained image from this mathematical reconstruction is not

reliable.

Fig. 2.10: First iteration of the mathematical reconstruction of the 2×2 image.

To improve the mathematical construction of the image, further refinements of the calculated

image can be done by making additional measurements of the projections along other directions.

The measured projections in the directions of angle 3 and angle 4 are 12 and 3, respectively (Fig.

2.11), which are significantly different from the calculated projection of 7.5 in in each of these

directions. Therefore, additional iteration of the calculations can be performed by considering the

projections along these directions. By comparing the measured and calculated projections we

conclude that a value of 2.25 should be added to the absorption of each of the upper left and lowerright pixels, giving values of 4 and 8, respectively. Similarly, the absorption of each of the upper

right and lower left pixels should be reduced by 2.25 in order to obtain the measured projection of

3 in the direction of angle 4. This results in absorptions of 2 and 1 in these pixels, respectively.

The final values in Fig. 2.11 are the true absorption values, and are consistent with the measured

2.5 5

52.5

5 10

Angle 1

3.25 5.75

4.251.756

9

Angle 2



projections in all directions. Thus, the iterative calculation led to the true values of gray levels in

this simple case.

Fig. 2.11: Second iteration to improve the mathematical reconstruction of the 2×2 image.

In real applications, a large number of pixels is required to construct an accurate image Fig. 2.12).

However, the exact shades of gray may not be attainable by the iterative calculation process in the

case of high number of pixels. In this case, we compare the calculated and measured projections,

and look for convergence of the results. The calculation is considered sufficiently precise and

iteration is terminated when the difference between calculated and measured projections is smaller

than an acceptable value (5% for example). Notice that higher precisions require more iterations,

and more time, and a compromise between the image quality and time minimization should be

made.

Fig. 2.12: CT scan with canvas size 241×285 (left) and 630×630 (right).

1 8

24

3 12

Angle 3

Angle 4



Two-dimensional (2-D) computed tomography (CT) imaging in digital radiography is a powerful

technique in industry for non-destructive testing of internal features of an object to identify

defects and part geometry. The earliest and simplest CT digital radiography scanner for medical

applications consisted of a single source and detector, both of which rotate about the object (a

human head) to produce a 2-D image. A three-dimensional image can be constructed by

performing multiple CT scans from successive slices separated by very small distances (as

deemed by the resolution) along the axis of rotation. Such 3-D scans can be used for a variety of

purposes such as viewing the shape of defects and the internal structure of an object (Fig. 2.13

[2]).

Fig. 2.13: Schematic diagram illustrating the multiple CT scans to produce a 3-D image.

This technique is time consuming, and a more advanced tomographic scanner was designed on

the basis of using a fan beam and multiple detectors (Fig. 2.14 [3]). In this method, all spots of

the scanned slice are examined simultaneously in a given beam direction, and an accurate image

of the slice is constructed from the data collected by rotating both source and detectors about the

object axis. In digital industrial radiography scanner, the object positioned on a turntable can be

both translated and rotated.

Radiography

X-ray beam



Fig. 2.14: 2D – CT system for reconstruction of one object layer by one fan beam x-ray scan. The

attenuated X-ray data are collected at short time intervals, and the X-ray measurements are then

digitized and the image is reconstructed and displayed as a 2-D image on the computer screen.

Another scanner was designed to reconstruct a 3D-CT image of an object using a cone beam as

illustrated in Fig. 2.15. The object is irradiated, and data on the attenuation of x-rays are obtained

as the object rotates in the X-ray cone. The set of projections obtained in this way is used to

reconstruct the 3D structure of the object.

Fig. 2.15: 3-D imaging of an object by a cone beam.



Radiography is used in industry for metal casting inspection. Digital radiography applied to

evaluate the quality of metal casting and detect flows in the product can save time and cost of

inspection. Further, digital imaging provide the opportunity to process the images and obtain

necessary information. Fig. 2.16 shows a photograph of an aluminum casting, and a slice of the

cone beam CT scan which reveals the presence of flaws in the casting [3].

Fig. 2.16: A photograph of an aluminum casting (left) and a slice of the CT scan (right) (Taken

from Ref. [3]).

Radiography was also proposed as a nondestructive technique for evaluating the performance of

solid oxide fuel cells (SOFC). The electrode material in the SOFC contains pores, and

electrochemical reactions occur at the triple phase boundaries between the ionic, electronic, and

pore phases [4]. Therefore, understanding the microstructure of the anode material using non-

destructive techniques is essential for the evaluation of the SOFC performance. The development

and implementation of X-ray optics has improved the resolution of X-ray computed tomography

(CT) in both lab and synchrotron environments, leading to the development and employment of

X-ray nano- tomography in materials characterization.

Radiation is attenuated in matter by different processes such as Compton scattering, elastic

scattering, and photoelectric effect. The absorption coefficient of the material is the sum of the

contributions of all processes, which are energy dependent. The total absorption coefficient



decreases with increasing the energy of the incident radiation until the energy becomes equal to a

characteristic atomic transition energy of the absorbing element. At that energy, the absorption

coefficient increase suddenly, demonstrating an absorption edge as illustrated in Fig. 2.17.

Fig. 2.17: Mass absorption coefficient of a material showing the contributions of the different

processes, and the absorption edge in the total absorption coefficient.

If an x-ray with energy just above the absorption edge is used in CT, this beam will suffer more

absorption by the material than that with energy just below the absorption edge. Accordingly,

comparison CT scans of the material obtained by using x-rays with energy above and below the

absorption edge allows the identification of the distribution of the absorbing element in the

imaged section. This methodology can be used in industrial NDT of materials. Fig. 2.18 shows

two scans of electrode material for SOFC which is composed of Ni-Yttria Stabilized Zerconia

(Ni-YSZ). The upper scan was obtained with x-ray energy (8.317 keV) below the absorption

edge of Ni, whereas the lower scan was obtained with x-ray energy (8.357 keV) just above the

absorption edge. Notice the increased opacity of some grains in the scan with x-ray energy above

the absorption edge; these grains are identified as Ni grains. Notice that image (b) demonstrates

the phase contrast that allows separation of the different phases using absorption edge

tomography.



Fig. 2.18. a) CT scan of the sample with x-ray energy below the Ni edge, and b) CT scan of thesample with x-ray energy above the Ni edge. Example of a Ni grain which demonstrated greatdifference in opacity is shown within the square box.



In automotive industry, CT was used to inspect the quality of automotive parts. Fig. 2.19 shows a

mini-CT system designed to inspect samples of interest. Figure 2.20 shows different views of the

of the nozzles of a Diesel injector reconstructed with the Mini-CT system [5].

Fig. 2.19: Mini-CT System with part of the housing removed for visibility of the components.Left: X-ray source, center: manipulator with sample (fuel injector), right: detector. Footprint55×18 cm2.

Fig. 2.20: 3D picture and c) projection of a slice of an injector obtained from CT. Diameter ofthe cross section is approximately 2 mm.



As a further application of CT, the technique is used in cable industry to evaluate the quality of

wire connections in household appliances, automotive industry, among other industries.

Electrical wiring often uses crimped contacts where the conducting wire strands are squeezed in

the crimp barrel, and the insulated part of the wire is crimped at the insulation grip (Fig. 2.21)

[6]. A good electrical contact requires that the metal strands are tightly squeezed in the crimp

barrel, which provides the required contact quality, and reduces the oxidation effects between

wire strands which could be detrimental in electrical connections.

Fig. 2.21: crimped contact with conductor (wire) composed of wire strands (from ref. [6]).

The number and distribution of wire strands, as well as the quality of electrical contact and

deformation of the wire strands can be evaluated by CT scans at different positions in the

Crimp barrel

Insulation grip Stripping

length

Conductor strands

Insulated Conductor



crimped contact as indicated by the arrows in the lower panel of Fig. 2.21. Fig. 2.22 shows CT

scans at for different locations across the crimped contact.

Fig. 2.22: Computed tomography images at four different locations across the crimped contact.



Chapter 3

Principles and Applications of X-Ray

Diffraction



3.1. Introduction

Solid materials are composed of atoms or molecules bonded together rigidly, so that except for the

vibrational motions of atoms or ions about their equilibrium positions in the solid, these

constituents do not experience any motion with respect to one another. Broadly speaking, solidscan be crystalline, or non-crystalline (amorphous). In non-crystalline solids there is no correlation

between the positions of the atoms or molecules (Fig. 3.1 (A)). In a crystalline solid, however,

identical building blocks (basis) of the structure are arranged regularly in space (Fig. 3.1 (B)),

where their positions could be represented by a hypothetical regular array of points filling the

whole space (lattice).

Fig. 3.1: Two dimensional representation of (A) the atomic arrangement in an amorous solid, and

(B) atomic arrangement in a crystalline solid

The positions of the lattice points are described in terms of a set of primitive axes. A primitive

axis in a given direction is the shortest translation vector in that direction that takes the lattice into

(A) (B)



itself (translational symmetry). The primitive cell or unit cell is the smallest parallelogram (in two

dimensions) or parallelepiped (in three dimensions) constructed by the primitive axes, and contains

only one basis set. For example, in metals such as Fe or Cu, the basis is one metallic atom, and the

primitive cell contains only one Fe or Cu atom, respectively. In NaCl crystal, the basis is one NaCl

molecule, and the primitive cell therefore contains one Na+ and one Cl – ions. Figures (a), (b) and

(c) above show different choices of primitive axes, and the resulting primitive cell in each case.

Although the primitive cells may look different, they all have the same volume and contain the

same number of atoms. Notice that we can fill the whole space with the crystal structure by

performing all possible translations of the primitive cell along the primitive axes. In terms of the

primitive axes , ,, the lattice (which fills the whole space) is constructed by the translation

vector:

= + + 3.1

Here n1, n2, n3 are integers.

In the crystal structure, a basis is distributed identically around each lattice point. The crystal

structure is then defined by the lattice plus the basis. Fig. 3.2 shows the three different types ofcubic crystals: the simple cubic (sc), the body-centered cubic (bcc), and the face centered cubic

(fcc). Notice that all atoms in each cubic cell are identical, and thus the position of each atom can

be regarded as a lattice point.

Fig. 3.2: The three lattices of the cubic system.

sc bcc fcc

Question: Does the shaded triangular cell in Fig. 3.1 (d) above represent a primitive cell? Why?



If the atoms in a cubic cell are different, one should identify the basis, whose translation in space

would reproduce the crystal structure. The position of an atom in the basis can then be regarded as

a lattice point, and the type of lattice can be determined. For example, the basis in the cesium

chloride (CsCl) crystal is one Cs atom and one chlorine atom as illustrated in Fig. 3.3. Accordingly,

the lattice for this structure is simple cubic.

Fig. 3.3: The simple cubic unit cell (defined by the green balls at the corners of the cube) of the

CsCl structure.

3.2. Indexing crystal planes

As Fig. 3.1(B) illustrates, the atoms in a crystal can be viewed as being located at a parallel set of

crystallographic planes (or atomic planes) separated by equal distances (the d-spacing ). A plane

can be constructed by any two axes, and since there is an infinite number of sets of primitive axes,

we conclude that a crystal structure can be described by an infinite number of parallel sets of

crystallographic planes, each set having a unique d -spacing which is different from that of the

remaining sets. A parallel set of crystal planes is described by a set of integers, Miller indices (hkl ).

These indices are determined with respect to a set of axes, which can be primitive or non-primitive;

these axes are termed lattice constants. For all cubic lattices (simple, body centered or face



centered), Miller indices are usually evaluated with respect to the axes of the conventional cubic

cell, in which case there is only one lattice constant (a). Also, for the hexagonal system, Miller

indices are determined with respect to the axes of the conventional hexagonal cell, which is non-

primitive. In this case there are two lattice constants (a = b; c). Miller indices for a set of parallel

crystal planes are determined as follows:

1. Find the intercepts of three points on the plane with the axes , , in terms of the lattice

constants as in Fig. 3.4.

2. Take the reciprocals of these intercepts, and multiply by the smallest integer that converts

these reciprocals into a set of integers. This set of integers represented as (hkl ) is the Miller

indices of the plane.

Fig. 3.4: Indexing a crystal plane.

Examples of important planes in a cubic crystal

It is customary to draw crystal planes within the conventional cubic cell as shown in Fig. 3.5. In

some cases, however, the plane in the chosen cell has a zero intercept on one or more of the axes,

which is not acceptable for indexing the set of planes. In this case, we choose another member of

the set in a neighboring cell. In Fig. 3.6 we show a plane in a chosen cell with zero intercept on

the a-axis. We therefore take the plane in the back-cell with intercepts of – 1, 1, ∞, and the Miller



indices for the plane are 1 10. The bar on top of the first integer indicates that the intercept on

the a-axis in negative.

Fig. 3.5: Some crystal planes in a cubic crystal.

Fig. 3.6: The 1 10 plane in a cubic crystal.

3.3. Structure determination

The crystal structure is usually determined by the diffraction of electrons, neutrons, or x-rays. In a

θ – 2θ x-ray diffraction experiment, a parallel beam of monochromatic x-rays is incident at an angle

(1 10)

(1 10)

(111) (200)(100)



θ on the surface of the sample, and the diffracted intensity in a direction making an angle 2θ with

the incident beam is measured (Fig. 3.7). The rays reflected from successive crystal planes

separated by d interfere constructively when the optical path difference between these rays is an

integer multiple of the wave length λ of the radiation, resulting in a maximum intensity. According

to Bragg’s law, a peak in the diffracted intensity is observed at an angular position 2θ with respect

to the direction of incidence (see Fig. 3.7) provided that:

2 sin = 3.2

Fig. 3.7: Derivation of Bragg’s law.

If the sample is a single crystal , constructive interference from one set atomic planes parallel to

the sample surface results in a peak representing reflection from that set of planes as shown in Fig.

3.8. The first order reflection (n = 1) in very strong with respect to higher order reflection (n ≥ 2)

as the figure illustrates.



Fig. 3.8: Diffraction pattern from a ZnO hexagonal single crystal oriented such that the (002)

hexagonal basal plane is parallel to the sample surface. Notice that the second order reflection

(004) is much weaker than the first order reflection.

If the sample is a powder consisting of a huge number of randomly oriented small particles, or if

it is a polycrystalline film consisting of randomly oriented crystalline domains, then, in principle,all possible crystal planes exist with orientation parallel to the sample surface. When the diffracted

intensity is measured as the angle is scanned in a specified angular range, a peak is observed

whenever the d -spacing of a given set of planes satisfies Bragg’s law (Eq. 2). Consequently, a

diffraction pattern consisting of peaks in the scanned angular range is obtained (see Fig. 3.9), each

peak representing a set of planes with d -spacing determined by Eq. 2. The crystal structure can be

roughly determined from the d -spacings corresponding to the observed peaks, since there is a

relation between the d -spacing and the structural parameters (lattice constants and angles between

crystal axes) of any crystal structure.



Fig. 3.9: Powder diffraction pattern of a fcc crystal. Notice that the second order reflection (004)

is much weaker than the first order reflection.

Notice that the observed peaks in a diffraction pattern do not represent all crystal planes. For

example, there is no peak corresponding to (100) or (110) reflection in the pattern shown in Fig.

3.9. We refer to this fact as: some reflections are not allowed . Each crystal structure (sc, bcc, fcc,

or hexagonal, for example) is characterized by a specified set of reflections, from which we can

determine the structure. The conditions for allowed reflections in cubic crystals are:

1. All reflections are allowed by a sc structure.

2. Only reflections with h + k + l = even number are allowed by a bcc structure.

3. Only reflections with h, k , l , all even or all odd numbers are allowed by a fcc structure.

Accordingly, the crystal structure in Fig. 12 is fcc.

For indexing the peaks in the pattern of a cubic structure, we first recognize that the relation

between the d -spacing an the lattice constant (a) is given by:

= √ ℎ + + 3.3

Accordingly, Bragg’s law leads to the relation:



sin =

4 ℎ + + 3.4

Notice that h2 + k 2 + l 2 is an integer. Accordingly, if sin2θ for each peak in the pattern is divided

by sin2θ for the first peak, and the resulting fractions are multiplied by the smallest number that

makes them integers, then these integers are equal to h2 + k 2 + l 2 for the different peaks. From

these, h, k , and l for each peak is determined by inspecting the possible values of the indices which

give the obtained sum of their squares as illustrated in Tables 1 and 2 for fcc and bcc structures,

respectively.

Table 1: Indexing the diffraction peaks of a fcc structure

sin2θ/sin2θ1 3×( sin2θ/sin2θ1) (hkl )

1.000 3 (111)

1.333 4 (200)

2.667 8 (220)

3.667 11 (311)

4.000 12 (220)

5.333 16 (400)

8.000 24 (422)

9.000 27 (511)

10.667 32 (440)

We notice from the last column that h, k , and l are all even or all odd, from which we conclude

that the structure is fcc. We can then determine the lattice constant from the d-spacing and the

indices for any reflection. For example, if the first (111) reflection in Fig. 12 occurs at 2θ = 19°,

and we use x-rays with wavelength λ = 1.5418 Å (Cu-K α radiation), then:

= 2sin = 1.5418

2×sin9.5 = 4.6708 Å

= × 1 + 1 + 1 =4.6708× √ 3 = 8.0900 Å



Table 2: Indexing the diffraction peaks of a bcc structure

sin2θ/sin2θ1 2×( sin2θ/sin2θ1) (hkl )

1.000 2 (110)

2.000 4 (200)3.000 6 (211)

4.000 8 (220)

5.000 10 (310)

6.000 12 (222)

7.000 14 (321)

8.000 16 (400)

9.000 18 (411), (330)

The ratios in the first column are all integers, which may lead us to conclude that the structure is

sc. However, it is not possible to find a set of h, k , l integers such that h2 + k 2 + l 2 = 7, we multiply

the ratios by 2 and inspect the resulting integers. We notice that the resulting integers are all

possible in the sense that we can always find a set of indices whose sum of squares would give the

obtained integer as illustrated in Table 2. We also notice that h + k + l is always even, which

indicates that the structure is bcc.

Metallic iron has a bcc structure. The first peak in the diffraction pattern of iron using Cu-K α

radiation was found to be at 2θ = 44.65°. Accordingly:

= 1.54182sin22.325 =2.0294 Å

= × √ 2 = 2.87 Å

If the peaks in a diffraction pattern cannot all be indexed according to the above procedure (seeFig. 3.10), then the sample could have more than one structural phase. In this case, the peaks

corresponding to one of the phases are identified by the indexing procedure discussed above. The

remaining peaks can then be separated and indexed to identify the corresponding phase. Thus,

XRD is a technique which can be used to determine the structural characteristics of a given

crystalline phase. This provides means for investigating structural transformations, and structural



defects in materials. Also, the technique allows the detection of different structural phases in a

sample, which allows identification of the different minerals in a sample (see Fig. 3.11 for

example). In addition, the technique allows the evaluation of impurity phases and their abundance

in a synthesized or naturally occurring mineral.

Fig. 3.10: XRD pattern of a sample with a majority fcc phase (indexed peaks) and a secondary

impurity phase (starred peaks).



Fig. 3.11: XRD pattern of a sample containing different phases.

3.4.

Industrial applications of XRD

Analysis of the XRD pattern provides information on the phases existing in a sample, and the

structural characteristics of these phases. In addition, quantitative analysis of the patterns can

give a fairly accurate assessment of the weight fractions of these phases. Traditionally, such

analysis was based on single peak analysis where the concentration of the phase is proportional

to the peak intensity (area or height). This method is not accurate enough in many cases, due to

the overlap of the peak of a given phase with other peaks. Fitting routines and structural

refinement computer codes, such as Rietveld refinement method, were built for more accurate

assessment of the material characteristics. Fig. 3.12 shows the diffraction peaks of Portland

cement in the angular range between 31° and 35° [7]. Rietveld analysis of the pattern is

performed by fitting the experimental pattern with the correct ratios of the patterns



corresponding to the different phases existing in the measured sample. The analysis revealed the

presence of five different phases, and allowed quantitative evaluation of their concentrations in

weight %. These phases and their concentrations in Portland cement were: Ca3SiO5 (C3S; 50-

70%), Ca2SiO4 (C2S; 15-30%), Ca4(AlxFe1-x)4O10 (C4AF; 5-15%), Ca3Al2O6 (C3A; 5-10%) and

Ca1-xMgxO (lime; 0.5-2%). This example demonstrates the feasibility of employing XRD for

phase identification, and determination of the respective concentrations of the different phases.

Further structural information provided by the analysis of the XRD patterns can give information

relevant to the mean grain size of each phase, and its chemical stoichiometry.

Fig. 3.12: Part of the XRD pattern of a cement sample showing the overlapping of the peakscorresponding to Ca3SiO5 (C3S), Ca2SiO4 (C2S), Ca4(AlxFe1-x)4O10 (C4AF), Ca3Al2O6 (C3A)and Ca1-xMgxO (lime). Taken from ref. [7].

XRD was also used to characterize the crystallinity and rigidity of industrial product. Fig. 3.13 presents an example of using XRD to characterize the rigidity and crystallinity of polyurethanes



(PU) as a function of experimental conditions adopted in preparing the PU products. The figureclearly shows the (006) reflection in the rigid PU, indicating relatively good crystallization,whereas this peak disappears completely in the soft PU sample, indicating poor crystallization[8].

Fig. 3.13: XRD patterns of rigid (a), semi rigid (b), and soft (c) Pus. Deconvolution of the peaksin the angular range of 5 – 40°. Taken from ref. [8]



XRD analysis was also used in sugar industry to analyze the ashes resulting from burning sugar

cane bagasse (the dry pulp remaining from sugar cane after juice extraction). These ashes are of

potential importance for the manufacture of cementing material. Fig. 3.14 shows XRD patterns

of three different samples of the bagasse ashes, where the different mineral phases were

identified [9].

Fig. 3.14: XRD patterns of bagasse ashes obtained in laboratory (LBA), Filter bagasse ashesobtained from combustion fumes (FBA), and bottom bagasse ashes (BBA).

A further application, is the use of XRD as a characterization tool in pharmaceutical industry.

This technique is used for the identification and quantification of the different phases in drugs.

Fig. 3.15 demonstrates the power of XRD in analyzing trace compounds with very low

concentrations in drugs [10].



Fig. 3.15: Detection of trace compounds in pharmaceutical drugs. Taken from [10].

X-ray diffraction is also used for material characterization in iron and steel industry. The

different phases in an examined sample can be identified, and their concentrations can be

evaluated by analyzing the peak intensities corresponding to the different phases. Fig. 3.16

shows XRD patterns of different samples of iron ores in the region of the main peaks of the

existing phases (Left). The figure clearly shows the presence of magnetite (Fe3O4) and hematite

(Fe2O3) iron oxide phases. The correlation between the concentration of hematite and its relative

peak intensity is shown in the right panel of the figure [11].



Fig. 3.16: XRD patterns of iron ore samples (left), and the calibration curve showing the relation between the relative peak intensity and the concentration of hematite.

In mining industry, workers are exposed to health hazards due to the presence of crystalline silica

(alpha-quartz) in airborne dust, which causes silicosis, a debilitating lung disease. Accordingly,

necessary measures should be taken to prevent the exposure of workers to this hazard, which require

accurate quantitative analysis of the amount of crystalline silica in the airborne dust in mines. The

conventional method used in mining industry to determine the concentration of respirable silica-containing dust is through the use of a sampling pump with a size-selective sampler and filter media.

The dust particles in the sampled dust are smaller than ten micron. Dust samples are collected onto a

filter, and consequently sent to laboratory for measuring the concentration of crystalline silica in the

dust using XRD technique [12].

The above mentioned applications of XRD demonstrate the importance of XRD as a method for

materials characterization in different industries. A wide range of applications of this technique

in the industry is available in the literature.



Chapter 4

Elemental Analysis



4 1 Introduction

While XRD technique is used for the identification of minerals, and the determination of the

concentrations of these minerals in examined samples, x-ray fluorescence (XRF) spectroscopy is

used for elemental analysis of a sample. This involves the identification of the different elementsand their concentrations in the sample, without reference to the crystallographic (mineralogical)

phase in which the element exists. The principles of the two techniques are different. XRD is based

on the detection of the intensity of x-rays reflected from crystallographic planes, demonstrating

peaks at angles satisfying the conditions for constructive interference between these rays.

However, XRF is based on detecting the energy dependence of the intensity of radiation emitted

by a sample.

Radiation passing through material interacts with the constituents of the material through different processes, leading to observed changes in the transmitted or scattered radiation. These changes can

be used to deduce information about the properties of the material.

Electrons in atoms are arranged in electronic shells with principal quantum numbers n = 1, 2, 3, 4,

… (historically called K , L, M , N , … shells, Fig. 4.1). An incident beam of radiation interacts

with the atomic electrons in the material through different elastic and inelastic processes. These

processes lead to the attenuation of radiation as it passes through the material. The absorption of

radiation depends on the energy of radiation, the absorbing material, and the type of interactioninvolved. If the detected beam at a given direction with respect to the direction of incidence has

the same energy as the incident beam, then the scattering is elastic. Radiation with different energy

detected in some directions is evidence of inelastic processes (Fig. 4.2).

Fig. 4.1: Atomic electrons in shells



Fig. 4.2: Schematic diagram of the scattering processes

It is worth mentioning at this point that inelastic processes involve complete absorption of a photon

and emission of another photon with a different energy, such as in the case of Compton scattering

(Fig. 4.3). The scattered photon in Fig. 4.3 is red-shifted indicating that its energy is lower than

that of the incident photon. Also, an important type of interaction of radiation with matter is the

photoelectric effect (Fig. 4.4). In this process, an incident photon with energy above the binding

energy of an electron in a shell is absorbed by the electron, which is consequently knocked out of

its shell leaving a hole in that shell. The excited atom then relaxes to a lower energy state by an

electron transfer from a shell farther from the nucleus to fill the vacancy. The difference in electron

energy in this transition is released in the form of an x-ray photon (for elements with atomicnumber Z > 13). This phenomenon is used for the experimental design of x-ray fluorescence (XRF)

spectrometry.

Transmission,

E0

Incidentbeam, E0

Elastic

scattering, E0

Inelastic

scattering, E



Fig. 4.3: Schematic diagram of Compton scattering.

Fig. 4.4: Illustration of x-ray fluorescence in the photoelectric effect.

If one of the electrons in the K -shell (n = 1) is ejected upon absorbing an incident photon, the shell

may be filled by an electron from the L shell (n = 2), in which case the K α x-ray photon is emitted.



If the K shell is filled by an electron from the M shell (n = 3), it emits the K β photon (Fig. 4.1) and

so on. This is the series of K lines. Similarly, series of L-lines and M -lines are emitted if the hole

is in the L-shell or M -shell, respectively. Due to the selection rules for atomic transitions, and the

splitting of the electron orbits in a given shell, the K α line is normally split into K α1 and K α2 lines.

Fig. 4.5 shows the characteristic transitions in Cu. Notice that due to the small splitting of the p-

levels in the M shell, splitting of the K β emission line was not observed by this particular

experiment. The energy of the K α lines of Cu is slightly above 8 keV, and the average wavelength

for the two lines is 1.5418 Å as mentioned in the XRD section. The energy of the two K α lines is

separated by only about 20 eV, which requires a relatively high energy resolution to observe the

splitting of the two lines.

Fig. 4.5:

Illustration of the energy diagram and K α and K β emission lines from a Cu target.



X-ray fluorescence is a powerful tool for nondestructive elemental analysis in environmental,

industrial, pharmaceutical, forensic, and scientific research applications. It is used to identify

elements and determine their concentrations in the sample of interest. In an XRF experiment,

fluoresce can be induced by energetic electrons, ions, or photons, and X-rays emitted by the various

elements in the sample are measured and analyzed. Two types of XRF systems are available,

namely, wavelength dispersive (WDXRF) spectrometers, and energy dispersive (EDXRF)

spectrometers. In WD spectrometry, the radiation emitted by a sample is dispersed into its

monochromatic components or wavelengths with the aid of an analyzing crystal. A specific

wavelength is then calculated from knowledge of the crystal structure and the diffraction angle. It

is well established that WDXRF has better spectral resolution than EDXRF (up to 10 times better

for some elements), and superior performance for light elements from boron (B) to chlorine (Cl)

[10]. Fig. 4.6 shows a schematic diagram of WDXRF spectrometer.

Fig. 4.6: Schematic diagram of WDXRF spectrometer (taken from ref. [10]).

EDXRF permits detection of a broad range of elements simultaneously. The measurement

resolution depends in this case on the detector X-ray energy resolution and counting rate

performance. The conventional XRF uses a wide spectrum of x-ray energies to excite the



elements in the sample. When an x-ray tube is used as a source of x-rays, the Bremsstrahlung

contribution in the spectrum scatters in the sample without producing atomic excitations, thus

resulting in an increase in the intensity of the background of the spectrum, and a poor resolution.

This can be avoided by selecting a narrow characteristic X-ray line from the source spectrum to

be used for exciting atomic transitions and x-ray fluorescent X-rays in the sample. This

procedure leads to a great loss in intensity of the primary beam. Although this technique is used

in commercial XRF systems, it has a disadvantage of requiring a very high primary X-ray source

intensity to compensate for the large decrease in the X-ray intensity on the sample. However, the

development of the monochromatic micro-focus XRF system greatly improved signal-to-noise

ratio and provided a powerful technique for the measurement of trace element concentrations and

distributions for a large variety of important medical, environmental, and industrial applications.

Fig. 4.7 demonstrates the improved quality of the spectrum by using a monochromatic micro-focus system [13].

Fig. 4.7: XRF spectra obtained by using polychromatic conventional spectrometry (red, upperspectrum) and monochromatic micro-focus system (black, lower spectrum).



To eliminate the Bremsstrahlung background and improve resolution, other techniques were

developed to carry out XRF measurements. These include the particle-induced x-ray emission

(PIXE) based on using an energetic ion beam to excite fluorescence in the sample of interest.

Also, intense monochromatic beams from large accelerator facilities, such as synchrotron light

sources, were used for this purpose. Another experimental setup for XRF uses naturally

radioactive radiation sources. Radiation from 241Am isotopic was used as a source of radiation

for elemental analysis on the famous Explorer Mars Lander and other planetary and lunar probes.

Even though XRF systems employing radioactive sources have been used for environmental,

industrial, and mineralogical applications, the need to keep the amount of radioactive material

low for safety considerations leads to a reduced sensitivity and the need for long measuring time

and sampling area. In addition, naturally radioactive sources get weaker with time, where the

source should be replaced to obtain reasonable measuring sensitivity. These considerationslimited the widespread use of XRF systems based on radioactive sources.

4.2. Moseley’s Law

The energy of the fluoresced x-ray depends on the quantum numbers of the shells involved in the

electronic transitions, and on the atomic number of the fluorescing element in accordance with

Mosely’s law:

= ( 1 1

) 4.1

where E R is Rydberg energy (13.6 eV), and s is a screening factor, which is theoretically 1 for the

K lines. If this empirical relation is applied to Cu K -lines, then the energy of K α line is:

=13.6× 28 × ( 11 1

2) =7997 eV 4.2

The acceptable value of about 8055 eV indicates that the effective screening factor is s = 0.9 rather

than 1.

4.3. XRF spectrometry

Since the transition energy is characteristic of an element where it depends on its atomic number,

different elements emit radiations with different energies. This fact can be utilized to identify the



different elements in a sample by means of XRF spectroscopy. In this technique, a sample is

irradiated by a beam of x-rays generated by an x-ray source, which could be an x-ray tube or a

synchrotron light source. The synchrotron light source generates an x-ray beam by the accelerated

electrons in a storage ring (Fig. 4.8). This source has a great advantage over the conventional x-

ray tubes since it provides a very intense beam, allowing the investigation and analysis of very

weak signals. The target in the x-ray tube, and the accelerating voltage and current are chosen to

provide the required intensity. In both cases, a wide spectrum of x-rays is generated, and the

required x-ray monochromatic beam is obtained by passing the beam through an x-ray optics

assembly (Fig. 4.9). This process leads to significant loss in the intensity of x-ray beam used for

analysis. The selected energy of the x-ray beam by the beam optics should be higher than the

transition energies of metals to be analyzed. This is necessary in order to have enough energy to

induce the excitations required for analysis.

Fig. 4.8: Diagram of a synchrotron light source illustrating the generation of x-rays by the

revolving electron beam in the storage ring (outer ring).



Fig. 4.9: Setup for XRF experiment with focused beam [14].

The x-rays emitted by the sample are collected by a multichannel analyzer over a number of

channels (512, 1024, 2048, etc.). In general, higher the number of channels provides better

resolution. A spectrum such as that shown in Fig. 4.10 is observed on the screen of the computer

connected to the equipment for analysis. The figure shows energy dispersive XRF spectrum of a

standard sample containing Mn, Fe, Ni and Cu. The energy scale is calibrated for an XRF

experiment by plotting the known energies of the K α and K β lines for the different elements in the

standard sample against the channel number as shown in Fig. 4.11. In this particular experiment,

the calibration constant was found to be about 14 eV/channel [15].

Fig. 4.10: XRF spectrum of a standard sample containing Mn, Fe, Ni, and Cu [15].



Fig. 4.11: Calibration curve for XRF experiment using K α lines of Mn, Fe, Ni, and Cu, and K β line of Cu [15].

According to Moseley’s law (Eq. 4.1):

= 0.75× × 0.75× × 4.3

= 0.89× × 0.89× × 4.4

A plot of the square root of the energy against the atomic number of known elements in a standard

sample should give a straight line from the slope of which the value of Rydberg energy is

evaluated. Further, the screening factor can be determined from the calculated Rydberg energy and

the intercept of the straight line with one of the axes. Fig. 4.12 shows a plot of the square root of

the energy of K α and K β lines of the XRF spectrum of a standard sample containing Ca, Ti, Cr, Fe,

Ni, Zn and Br, as a function of atomic number. [15]. The Rydberg constant from the slope of the

straight line corresponding to K α lines was found to be 13.90 ± 0.2 eV, while that determined from

the straight line corresponding to K β lines was 13.53 ± 0.1 eV. These values are in good agreement

with the acceptable value of 13.6 eV. Further, the screening factor determined from K α and K β

lines was found to be s = 1.23 ± 0.1 and 1.78 ± 0.1, respectively. These values are significantly

different from the theoretical value of 1, which could be due to the fact that the outer shells (n = 2



and 3) are screened more than the K shell, resulting in an effective screening parameter higher than

1.

Fig. 4.12: Plot of the square root of the energy of K α and K β lines of the XRF spectrum of thestandard sample containing Ca, Ti, Cr, Fe, Ni, Zn and Br, as a function of atomic number.

The plot in Fig. 4.12 can be used to identify unknown elements in the sample. For example, if a

K α line with energy of 4.0 keV was detected in the XRF spectrum, Fig. 4.12 indicates that this line

corresponds to Z = 21 for Sc metal.

4.4. Lambert – Beer law

The intensity of x-rays after being transmitted through a material is attenuated (reduced) due to

interactions leading to absorption of the radiation by the material. The absorption of radiation

Question: use a modified version of equation 4.1 to determine the energy of Cu- K α line bycrudely assuming the theoretical screening parameter of 1 for the shell with n = 1, and adoptthe screening parameter of 1.23 for the shell with n = 2. Verify that the result is very close tothe standard energy of Cu- K α.



depends on absorbing material with a characteristic absorption coefficient μ (E), as well as on its

thickness of the absorber which is commonly expressed in terms of the surface density σ (in g/cm2).

The relation between the transmitted intensity from the absorber and the absorber thickness

(surface density) is described by the well-known Lambert – Beer law:

= −. ⇒ (

) = . 4.5

where I 0 is the incident intensity and I the intensity transmitted from the absorber. The absorption

coefficient (measured in units of cm2/g) is energy dependent. In an experiment, the fluorescence

radiation from a multi-element standard sample was allowed to pass through a set of aluminum

foils with the desired thickness (Fig. 4.13), and the transmitted intensity of the different lines was

determined. The intensity is normally determined by the area under the spectral peak.

Fig. 4.13: (a) an overview of the XRF setup for the x-ray experiments. (b) A schematic diagram

for an absorption experiment with the detector placed at a 90◦ angle. A collimator was used in

order to control the beam size, while Al foils were used to attenuate the intensity of the x-ray beam.The white arrow on the case of the x-ray source (a) indicates the path of the x-ray beam.

Fig. 4.14 shows the variation of the relative intensity with absorber thickness for four specific K α

emission lines from a standard sample containing Fe, Ni, Zn and Br with characteristic K α energies

at 6.4, 7.5, 8.6 and 11.92 keV, respectively. The slope of the best straight line fit to the experimental

data was used to determine the absorption coefficient of Al at different energies. Fig. 4.15 shows

good agreement between the experimental and theoretical values of the absorption coefficient of



Al. The higher experimental values could be due to underestimation of the absorber thickness, or

the presence of impurities with higher absorption coefficients in the Al foils.

Figure 4.14: Plot of the relative absorption of four characteristic K α energies of the standardobtained with Al foils of various surface densities.

6 7 8 9 10 11 120

20

40

60

80

100

120

( c m

2 / g

)

E (keV)

experimental

Theoretical

Fig. 4.15: Experimental and theoretical absorption coefficient of Al as a function of energy.



4.5. XRF applications on cultural heritage objects

Recently, considerable research has been focused on non-destructive techniques for the analysis

of objects of art and archaeology. Great efforts were spent to design experimental setups for

analyzing large outdoor monuments and archaeological objects, as well as for in-lab analysis ofsmall objects including artifacts, pieces of material, and historical coins.

Fig. 4.16 shows illustrates the procedure of the analysis of parts of a bronze monument in Victoria

Square, Athens, Greece. The spectrum of radiation emitted from a spot on the arm of the monument

revealed a brass composition with Cu and Zn being the main elements and Cr, Fe and Pb being

minor components. Also, Cl- K α and Ca- K α lines were detected, which could be attributed to

corrosion products, such as copper chlorides, or environmental contamination, such as bird dung.

Fig. 4.16: XRF application on an outdoor bronze monument (Victoria Square, Athens, Greece).The two photos show an overview and the detail of the in situ XRF measurement (right). The XRFspectrum (top right) corresponds to a spot on the arm [15].



A steamboat called ‘Patris’ sank in 1868 close to the Greek island Kea , and was not discovered

until 2007. After being at the bottom of the sea for almost 140 years, metal pieces and objects of

the boat were brought to the surface. The saltwater environment could be detrimental in terms of

metal corrosion. The treatment of these metal fragments and objects require knowledge of their

constituents, and identification of contact regions between different metals or alloys. Therefore,

non-destructive techniques for the analysis of the metal finds is necessary for conservation

purposes.

Fig. 4.17 shows an experimental setup for examining a metal fragment in the laboratory. The

resulting XRF spectrum revealed the presence of Fe, Cu, and Zn as major components of the

fragment. Although limited to qualitative analysis, the results of this experiment are still of

significant importance.

Fig. 4.17: In-laboratory XRF measurement of a fragment of pipe recovered from the ‘Patris’shipwreck. The main elements of the metallic fragment could be identified from the corresponding peaks in the XRF spectrum.

4.6. Quantitative XRF analysisQuantitative analysis of XRF spectrum is concerned with the identification of the elements in the

sample, and determination of their concentrations from the peak intensities. Although computer

packages were built and refined for quantitative analysis of XRF spectra, accurate determination



of the concentrations of the different elements in a sample is not an easy task due to several factors

including, and not limited to:

1. Accurate determination of the peak intensity (area) requires accurate knowledge of the

functional form of the background signal which can be complicated. Also, low signal to

noise ratio, and overlapping of peaks corresponding to different elements makes it difficult

to determine a peak intensity with sufficient accuracy (Fig. 4.18).

2.

The relative detection efficiency of the different spectral lines of a multi-element sample

could be significantly different, and detailed knowledge of such effect is needed.

3. When comparing the concentrations of two elements in a sample, knowledge of their

relative excitation probabilities is required for quantitative analysis.

4. The intensity of a spectral line of an element (say element i) does not depend only on the

concentration of that element in the sample, but also on the concentration of the otherelements (say elements j). This is due to the fact that some of the radiation emitted by

element i can be absorbed by interactions with elements j, or the radiation by element i

could be enhanced by emission lines of elements j. Detailed knowledge of these

interactions and accurate determination of their contributions to the quantitative analysis

of the concentration of element i is certainly not straight forward.

5. Fluorescence of atoms takes place at positions located at different depths under the sample

surface. The radiation then travels inside the material of the sample, and leaves the surface

toward the detector. While traveling inside the material, the radiation encounters

interactions and attenuations which depend on the energy, as well as on the distance

traveled in matter. These considerations should also be addressed in the process of

quantitative analysis.



Fig. 4.18: XRF spectrum (black line) from a 16th-century painting fragment measured with agermanium detector. The fitted spectrum is shown in red, and the contributions of the differentelements are shown in different colors.

Based on knowledge of the contributions of all factors to the generation and attenuation of a given

radiation from an element, computer codes can in principle be written to determine the

concentration of that element in the sample.

The concentrations of the various elements in a sample can also be determined with the aid of

reference samples prepared for that purpose. The reference sample should contain known

concentrations of the elements in the unknown sample. The concentration of an element can then

be determined by comparing the relative intensity of its radiation in the sample and in the reference.

4.7. Industrial and Environmental Applications of XRF

XRF is a well-established technique for materials characterization relevant to product control in

industry. Its applicability in elemental analysis of both conducting and non-conducting solids, its

accuracy and excellent precision for the analysis of a wide range of elements in a wide range of

concentrations (from ppm to 100%) made XRF an important technique for the testing and

evaluation of materials required for process and quality control. The technique is used for



elemental analysis of raw materials (such as mineral ores), intermediate products (such as sintered

calcined products) and final products (such as cement, mining, pure metals and alloys) [11].

The presence of heavy metals in soil can affect the quality of food, groundwater, micro-organisms

activity, plant growth etc. Heavy metals in the environment are produced by mining, smelting,

steel and iron industry, chemical industry, traffic, agriculture as well as domestic activities [16].

Perhaps chemical and metallurgical industries are the most important sources of heavy metals in

soils. Assessment of the concentrations of heavy metals in environments surrounding industrial

plants is therefore essential for environmental protection purposes, and health reasons. Several

non-destructive techniques were designed for this purpose. For the elemental analysis related to

the environment, XRF has the advantage of being a fast and inexpensive, with a simple sample

preparation.Beneficial utilization of industrial or agricultural wastes is of great importance for economic

reasons (they can be used as raw materials in industry), as well as environmental pollution control.

Metal matrix composites (MMCs) are superior to unreinforced alloys in terms of stability, and

better elastic and mechanical properties. Accordingly, there has been an increasing interest in

composites containing low density and low cost reinforcements.

Coconut is considered an important agricultural product in tropical countries, which can be used

as a new source of bio-fuel. Coconut shell is an agricultural waste that is available in very large

quantities throughout the producing countries around the world, and was burnt as a means of solid

waste disposal. This process resulting in significant contribution to CO2 and methane emissions,

and the production of ash as a byproduct. In light of the dramatic increase in the cost of fuel oil

and natural gas, coconut shell became an important source of fuel. The economic and

environmental aspects of coconut shell solid waste had consequently driven significant interest in

the characterization of coconut ash, where XRF technique was used for elemental analysis.

XRF analysis of coconut shell ash revealed the presence of hard minerals such as SiO2, Al2O3,

MgO and Fe2O3 as major constituents of the ash. The presence of such hard phases suggested that

the potential use of coconut shell ash as particulate reinforcement in various metal composites

[17].



Zinc oxide (ZnO) is a material with great importance in medical and industrial applications.

Specifically, the oxide is widely used in industries including, and not limited to, ceramics, rubber

fabrics, catalysis, fire-resistant materials and paint industry. Usually Pb and S exist in ZnO material

as secondary elements, which have a negative effect on the performance of the material. XRF

elemental analysis is a useful technique for evaluating the qulity of ZnO, and determining the

amounts of Pb and S in the oxide prior to use in a specific industry [18].



Chapter 5

Principles and Applications of Ultrasound

Testing



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