High resolution x-ray diffractometry and topography ebook

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The rst successful period was completed in the beginning of the s by creating order in the periodic table of the elements and by the discovery of the missing elements Weebs and Leicester, X-ray uorescence XRF spectrometry has some unique features so that it became an irreplaceable tool for the analyst. Not may techniques had such a brilliant start to their analytical careers!

In addition, about instruments working in this mode are attached to the electron microprobes, mainly in Japan. Some energy-dispersive EDXRF instruments are working independently, and some others are attached to electron and other [e. About instruments are working now in total reection TRXRF and several in grazing emission modes Klockenka mper, We consider in our account only these parts of Particle-induced x-ray emission PIXE , electron microscope, and synchrotron arrangements which can be treated as x-ray attachments.

An auxiliary market was created also around the main equipment business, covering the spare parts, recent supplements, and service connected with the maintenance. An important body of scientic literature relates to x-ray spectrometry Copyright Marcel Dekker, Inc. Markowicz and Van Grieken, ; van Grieken et al. Literature about essentially diraction and scattering problems can also be very useful for the researchers working in the eld of XRF Fewster, Most of the simultaneous in- struments are installed in industry, and the sequential instruments are distributed over industry, analytical laboratories, and research institutes at universities and public services.

Moreover, it possesses the scarce virtue among spectral methodsthe upper useful limit reaches the concentration of several tens of percent of the total concentration for the main component.

The detection limits at the ppm level without preconcentration and the limits of precision and accuracy that can be obtained connected, in turn, to sample homogeneity and counting statistics determine the boundaries of its application. Earlier books describing the techniques are mentioned in the reference list Compton and Allison, ; Jenkins and De Vries, ; Birks, ; Dyson, ; Jenkins, ; Bertin, ; Tertian and Claisse, ; Lachance and Claisse, , Jenkins et al.

The purpose here is to describe the basic principles that allow wavelength dispersion of x-rays and to describe all the components of a spectrometer. The phenomenon of x-ray uorescence is only a small part of a much wider problem of the interaction of charged particles or photons with matter Feldman and Mayer, Dierent kinds of secondary particles are then emitted Fig.

Insofar as the fundamental principles are concerned, we may recall the law of Moseley Moseley, , , which is the basis of the qualitative application of XRF:. The relationship Copyright Marcel Dekker, Inc. Figure 1 Phenomena accompanying the interaction of x-rays with matter: a different applications for analytical purposes abbreviations of methods coupled with the use of particular phenomena are mentioned; b different versions according to the incidence and emergence angles Itotal reflection XRF or PIXE; IIgrazing emission XRF; IIIgrazing incidencegrazing emission XRF.

For high-Z elements, the XRF spectra become more complex and full exploitation for qualitative analysis of mixtures is not always simple. Practical unraveling of spectra is dealt with in Chapter 4. The intensity of any spectral line is proportional to the number of atoms emitting photons of energies attributed to this line. However, a simple linear proportionality is not the rule. From the concepts of mass attenuation coecients introduced in Chapter 1, it should be clear that the intensity of an analyte line of one species is attenuated by atoms of the same species and by any other atoms present in the matrix.

Matrix refers to all elements present in a sample except the analyte element. Attenuation by absorption re- presents a rst complication compromising the proportionality. If the matrix contains elements with absorption edges of slightly lower energy than the energy of the characteristic line of the analyte, strong absorption can occur.

On the one hand, this results in further attenuation of the analyte line and, on the other hand, in enhancement of the spectral line related to the said absorption edge of the other matrix element. This phenomenon is known as secondary uorescence. The process may be re- peated with respect to all matrix elements with an absorption edge with a lower energy than the energy of a uorescence line emitted by another matrix element.

Secondary and higher-order uorescence is the major complication deteriorating the simple proportion- ality between intensity and concentration. In Figure 3, three typical kinds of relationship between the relative intensity mea- sured intensity divided by the intensity obtained for the pure element and concentration expressed as weight fraction are represented.

Curve I is obtained when the analyte line undergoes absorption only. If enhancement occurs, the analyte line intensity is higher than expected from primary excitation only and the curve is situated above the diagonal. A similar curve, however, can be obtained when the mass attenuation coecient of the matrix is lower than the related coecient of the element for its own radiation, as shown in the case for Fe in FeO curve II.

In a special case, the mutual relation between attenuation Figure 2 Representation of Moseleys law of K and L spectral lines. The eects just discussed are all energy wavelength dependent. This means that any calculations converting intensities into concentration should include the attenuation and higher-order uorescence eects and also integrate over all energies present in the exciting primary beam above the value of the absorption edge and over all uorescence lines.

This is an ab initio approach for conversion of intensities into concentration implemented by several authors. We mention here the articles by Gillam and Heal , Sherman , , Shiraiwa and Fujino , , who in the s and the s proposed suitable equations.

Sparks and Li-Xing implemented small corrections and rene- ments concerning the details of these expressions, and de Boer and de Boer and Brouwer gave solutions to some dicult exponential integrals related to the en- hancement. Important contributions to the numerical side of quantitative XRF are due to Fernandez , Fernandez and Molinari , Rousseau et al. It should be emphasized that Fernandez solved the transport equations for x-ray beams, the very general and powerful but dicult tool for the description of particle beams.

Likewise, Gardner and Hawthorne obtained similar results by Monte Carlo simulation of x-ray excitation. A specic approach was presented by Dane et al. Then, the idea of processing whole sets of solutions populations or strings or generations has been introduced, instead of processing the particular concentration values in consecutive iterations. In the fundamental parameter methods, the incidence and takeo angles are the important parameters.

As a rule, they are kept constant during the traditional run of the analysis. However, there have been signicant eorts to use the angle-resolved version Figure 3 Absorption phenomena in a heavy matrix curve I , in a light matrix curve II , and in a neural matrix curve III. For a complete treatment of equations deriving the line intensities in x-ray uor- escence spectrum from the elemental sample composition, the reader referred is to Chapter 5.

Wave- length dispersion of electromagnetic radiation in the x-ray region cannot be performed, as a rule, by normal gratings but only by diraction on crystals or, for the long-wavelength regions, on multilayers. We briey explain the principles because the construction features of the monochromator are directly derived from them. Consider a monochromatic beam of x-rays of wavelength l with their electrical vectors of equal amplitude in phase along any point of the direction of propagation.

Assume further that the beam is parallel and is incident on a crystal at an angle W between a given crystal plane and all the planes parallel to this rst and the incident beam di- rection.

The beam is scattered and diracted rays of equal l result but interfering con- structively only in those directions for which the phase relationship is conserved.

This happens at an angle W for scattered rays 1 and 2 Fig. From Figure 4, it is clear that ABBCd sin Wd sin Wnl or, according to Bragg and Bragg , who rst formulated this relation, written as nl 2d sin W 2 where n denotes the number of wavelength dierences between the rays scattered by the adjacent planes.

If n 1, the dierence is one wavelength and the diraction is said to be of rst order. If n 2, the dierence is two wavelengths and the diraction is second order, and so on.

All x-rays emitted at angles dierent than W cancel because they are out of phase and destructive interference occurs. ABC is the path difference. However, diraction is by no means equal to reection in classical optics, because the diraction is a volume not a surface process. It is less ecient with a great loss of intensity and is performed only under particular angular conditions; that is, according to Braggs law. Full analogy between the reection of x-rays and the reection of optical rays happens only at grazing incident angles i.

This is intrinsically a consequence of the refraction index, which is slightly smaller than 1 for x-rays. There are continuous eorts to construct a real mirror on the basis of multilayers, which would eciently reect x-rays under large incident angles, at least for soft x-rays Kearney et al. Thus, the static condition for obtaining diraction of a monochromatic x-ray beam in some direction in the volume surrounding the analyzing crystal is given.

What happens in the case of a polychromatic beam of x-rays? For a crystal, one set of planes is selected for dierent reasons and d is constant. If only rst-order diraction is considered and constructive interference must be realized for all l present in the incident beam, then W is the only variable: l constantsin W 2a The signal arriving from the diraction angle W is detected by a detector placed on a goniometer arm.

The detector rotates around an axis through the macroscopic plane of the analyzing crystal. For a source at a xed position, the detector rotates over an angle 2W. The wavelength is calculated from constant 2d and sin W. Note that this holds only for the rst-order diraction. If the second-order diraction is used, the wavelength is equal to half of that value. The maximum wavelength l max that can be diracted in the rst-order diraction by a crystal is equal to 2d because sin W1.

Because wavelength and energy are related, one more equations must be given, al- lowing us to convert wavelengths into energy units: E l 3 where the energy E is in electron volts eV and l is in angstroms A.

It is a common practice that the units used by x-ray spectroscopists are still electron volts or kiloelectron volts for energy and angstroms for wavelength. When joules and nanometers are used, as required by the international rules, the numerical value of the conversion constant be- comes 1. The presence of dierent wavelengths of dierent order on the same goniometer position has a particular consequence for wavelength-dispersive spectrometry. For a given position of the goniometer and detector , one may have a rst-order wavelength, say 0.

Figures 5 and 6, reproduced from the work of Arai demonstrate a practical situation and Table 1 reprints a fragment from x-ray tables by Cauchois and Senemaud Similar compendia of spectral lines and attenuation coecients are easily available Birks, , as a rule covering the range of elements between lithium Z 3 to plutonium Z Much more controversial are the values of the mass attenuation coecients for low energies and for low-Z elements at the same time Henke et al.

If necessary, one can have access to the calcu- lation for even heavier elements So et al. It is easy to understand the practical value of such calculations for the analysis. However, it is much more dicult to estimate the accuracy of numerical calculations for transuranium elements. To sort out x-rays with Copyright Marcel Dekker, Inc. A detector is a device of which the principle can be most easily explained by assuming the particle character of electro- magnetic radiation.

This is one reason that the characteristic of the impacting photons is often expressed in terms of energy, not wavelength. From Arai, The dierences between wavelength-dispersive WD and energy-dispersive ED XRF are due not only to the dierent detectors but also to other factors: 1. The brightness of a WD spectrometer is very low, the attenuation in a crystal being responsible for an important part of losses. This problem may be overcome by the use of radiation sources of signicant intensity, the synchrotron being the best known but bound to the availability of this large facility.

The crystal is only the dispersive device, not the detecting device. The situation is dierent in EDXRF, for which detectors play a double role: as the dispersive device and as the detector at the same time. L II 2 This restriction on the geometrical eciency still makes the overall photon collection eciency of a wavelength-dispersive spectrometer worse.

However, the maximum count rate for an EDXRF instrument is 30 kcps for the whole spectrum, which severely limits the total number of accumulated counts and, consequently, limits the precision counting statistics. Similarly, the limitation on the total count rate leaves a small margin for trace element analysis.

From the assumption, the trace element, if present in a sample, can emit only a very small part of the total radiation emitted by a whole sample and there is also the background, participating in the total amount of counts.

Simultaneous WD instruments are composed of a series of individual crystal spectrometer channels operating simultaneously, but the number of channels is limited. A comparison of wavelength- and energy-dispersive versions of x-ray spectrometers is performed in a recent publication by Brill The analyzing crystal is the central point of the wavelength-dispersive instrument. On the left- hand side of the crystal, we nd 1 the source of excitation, 2 the lters and devices for shaping the exciting radiation collimators and masks , and 3 the sample.

On the right- hand side, we nd 4 devices for shaping the diracted beam collimators and 5 the detector. Signals from the detector are fed into the electronic circuitry where they are shaped to be processed by the computer software for data analysis.

This arrangement can be reduced or made more complicated according to the demand. However, all possible reductions lead to less exible devices, and complication does not necessarily enhance the quality of the instrument. Figure 7 A wavelength-dispersive spectrometer: FCproportional flow counter; SDscintilla- tion detector. Reprinted with permission of Siemens AG. Sources A variety of radiation sources, emitting either charged particles or g- or x-rays of sucient energy, are used for excitation of some or all elements of the periodic table and some or most of the spectral lines of analytical interest.

Other chapters deal with excitation by protons [proton-induced or sometimes particle-induced x-ray emission PIXE Chapter 12 ], by electrons [electron microprobe Chapter 13 ], or by x-rays emitted from secondary targets or from a synchrotron Chapter 8. Excitation by x-rays or soft g-rays from radioisotopes and x-rays from low-power tubes is mainly restricted to energy-dispersive spectrometers Chapter 3.

The ideal excitation source would be a tunable x-ray laser monochromatic and intense, allowing the best choice of exciting wavelength and often selective excitation , but this cannot be expected in the near future. Nevertheless, it is worth reading some treatises about recent and future progress in the eld Nagel, ; Jamelot, ; Fill, ; Crasemann, ; London, There are serious reasons for the slow progress in x-ray laser construction.

The primary reason is that the population inversion of electrons means a much larger deviation from the energetical equilibrium if done between the levels, allowing the emission of x-rays. Consequently, it demands an excessive pumping power, turning the pumped matter into a plasma. One must be aware that the x-ray laser would be even much more useful in the elds of x-ray microscopy, holography, litography, or for the research of time-resolved phenomena than as a source for XRF analysis on a routine basis.

The synchrotron is another modern source of x-ray radiation, but it cannot be considered as a tabletop instrument and a device for easy, inexpensive, and routine-based applications. From a practical point of view, vacuum x-ray tubes are the overwhelming choice among other potential excitation sources. High-power tubes are the only ones dealt with in detail in this chapter; low-power tubes are discussed in Chapter 3.

All modern tubes owe their existence to Coolidges hot-cathode x-ray tube as pre- sented in Physical Review some 85 years ago Coolidge, They essentially consist of a sealed glass tube containing a hot tungsten lament for the production of electrons, a cooled anode, and a beryllium window. From a variety of modications proposed over more than three-quarters of the century, two geometries have emerged as the most sui- table for all practical purposes [the end-window tube EWT and the side-window tube SWT ], but now the preponderance of the EWT pushes the SWT out of the market.

Perhaps, a future deeper orientation of the WDXRF toward the microprobe applications will renew the interest in SWT, which is much better in deriving parallel x-ray beams. The general requirements of the x-ray tube as a source are as follows: 1. Sucient photon ux over a wide spectral range, with increasing emphasis on the intensity of the long-wavelength tail of the white spectrum.

The actual vivid interest in low-Z element analysis will certainly activate research in this direction. Long-term stability reduces the frequency of recalibration in routine analyses; short-term stability is an absolute requirement for obtaining an acceptable precision.

Switchable tube potential kV , allowing the creation of the most eective excitation conditions for each element. Still, in more high-power constructions available on the market, putting a lter in the beam path is an easier solution than switching the voltage Shimadzu XRF For sure, the selection of the spectral region for the targeted excitation by the use of a single x-ray tube will never be as good as in dedicated synchrotron beam lines with Copyright Marcel Dekker, Inc.

The intensity of the analyte lines varies considerably with excitation conditions. An extreme example is given by Vrebos and Helsen a, b for simulated AlMo alloys. Freedom from too many interfering lines from the characteristic spectrum of the tube anode.

Freedom from interfering lines is important. The scattered characteristic lines of the anode may spectroscopically interfere with analyte lines, disturbing the qualitative recognition, the peak intensity estimation for the line of interest, and the accuracy of subsequent conversion of intensity to concentration.

This is found in the results obtained after correction by some algorithms as well as by fundamental parameter calculations.

Although there is some kind of a remedy by the use of more ecient spectral decon- volution methods Remond et al. An x-ray tube is characterized by its anode element a single element or two elements as in dual-anode tubes , its input power [expressed in watts W or kilowatts kW , typically between 0. The photon output of the tube or, more importantly, the photon ux hitting the sample expressed in counts per second per watt of input power is determined by a, the incidence angle of an electron beam on the anode, the takeo angle b for SWT , the distance t to the beryllium window, the thickness d of the beryllium window, and the distance between window and sample, t 0 Fig.

For an energy balance, see Bertin and some remarks by Wollman et al. The impact of the electrons creates an excitation volume from which the white and the characteristic radiation of the target escape.

An immediate consequence of this characteristic is that dual anodes are used only in a SWT, where a light element e. By switching the excitation voltage, x-rays are produced either in the upper lighter element layer or in the substrate higher-Z element , resulting in two distinct tube spectra with dierent yields in the low- and high-wavelength regions Fig. The smaller the distance t, the higher the output. A decrease of t to half of the original value increases the intensity roughly by a factor of 4.

However, the reduction of t in the classical setup is limited. The smaller the value of t, the more intense the bom- bardment by the electrons and subsequent heating of the window by the scattered elec- trons Fig. In a SWT, this bombardment is rather intensive because both the anode and the window are in this geometry at ground potential. In a EWT, to the contrary, the - lament and the window are both at ground potential, and heating of the window is neg- ligible.

For an EWT, however, t can be reduced to a certain extent only because it faces the anode at high potential Fig. Alternative Congurations To overcome the absorption of the low-wavelength tail of the continuum, a windowless conguration was considered. This is an obvious solution, but it requires that the whole spectrometer with sample, collimators, crystals, and ow counter be evacuated to the low pressure suitable for securing an acceptably long life for the tube lament and conducting analyses in the required range of the soft x-rays.

Nordfors advocated a dual-anode tube with two anodes physically separated. They were excited by deviating the electron beam to either of the two anodes Fig. Lack of stability prevented this solution from gaining commercial interest.

Probably, a modied version of this idea was introduced in the series x-ray spectrometers of Diano dual target dual lament; see Section VI. Tubes with exchangeable anodes are another possibility for solving the problem of comfortable switching between dierent anodes.

To the best of our knowledge, this solution is not commercially available because of the tedious exchange operation and diculties in rigorous repeating of previous conditions of the tube action. Using the sample as an anode is another solution, but then the application is bound to conducting materials. In a modied form, this solution is implemented in scanning electron microprobes.

Because this anode cannot be adequately cooled, the input power must be restricted to very low values, entailing low count rates and, consequently, reducing the precision that can be obtained within reasonable counting times. Another possibility is to apply an existing kW rotating anode x-ray tube gene- rator. Sucient intensity is obtained.

Part of this gain can be sacriced and Boehme and Nichols et al. This collimates the beam to about 30 mm and allows microuorescence. Squeezing the beam to more or less the same diameter is possible when applying the polycapillary lens, even more so with the single capillary.

These solutions are very restrictive for the beam intensity; thus, a reasonable device conguration includes an energy-dispersive detector instead. Optimization Because the takeo angle is a very important parameter, the surface of the anode can be formed in steps in such a way that the yield of low-wavelength radiation is optimized. As is clear from Figure 12, the step-shaped surface decreases the escape depths.

In a conventional EWT, the reduction of the anode to window distance t is limited Fig. In cubic system, there are three Bravais lattices; they are simple primitive ; body-centered and face-centered. Certain lattice, such as body centered cubic Cubic I and face centered cubic Cubic F , have "kinematically" forbidden reflections. In other words, due to the arrangements of the atoms in the unit cell, these are reflections where the intensity of the scattered wave is zero, given by, [].

The positions of the spots are determined by the size and shape of the unit cell and the symmetry. X-ray diffraction XRD is a technique used in materials science for determining the atomic and molecular structure of a material.

This is done by irradiating a sample of the material with incident X-rays and then measuring the intensities and scattering angles of the X-rays that are scattered by the material.

Approved for public release; distribution is unlimitedCalculations have been made in an attempt to predict the effects of microscopically fine twinning and of stacking faults on the x-ray diffraction patterns which can be expected from single crystals of materials having the face-centered-cubic or diamond cubic : Jr. Hugh Miller Davis. This was suspected from the time of the discovery of X-rays inbut it was not until that the German Max von Laue — convinced two of his colleagues to scatter X-rays from crystals.

If a diffraction pattern is obtained, he reasoned, then the X-rays. X-ray diffraction is a useful and powerful analysis technique for characterizing crystalline materials commonly employed in MSE, physics, and chemistry. This informative new book describes the principles of X-ray diffraction and its applications to materials characterization. It consists of three pa.

Correspondence to D. Zolotov, D. Download citation. Received : 22 October Revised : 21 December Accepted : 09 January Published : 14 June Issue Date : March Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative.

Skip to main content. Search SpringerLink Search. Abstract This paper is a continuation of previous studies on the development of X-ray topo-tomography using laboratory equipment. References 1.

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