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2 Principles of X-ray Spectrometry 2.1 Analytical Performance

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X-ray analysis has been established as an important method for element analysis. Already since Moseley's discovery in 1913 that the energies of the X-ray lines of individual elements differ from each other and depend on the square of the atomic number of the emitting atoms, preconditions for using this method for element analyses were given. However, it took several years until the first usable equipment for routine analyses was available. In the 1930s the first laboratory instruments were available, but they were not yet suited for routine analyses.

To this purpose, various instrumental prerequisites had to be developed, such as an effective excitation source with sufficient intensity and high stability, the supply of dispersive elements, i.e. crystals with high reflectivity and sufficient size, and then also synthetic multilayers with larger d-spacings, detectors with sufficient counting capacity, instruments that allow for simple and safe operation, in particular for sample positioning, and later also for radiation protection, possibilities for measurement in vacuum, as well as the effective recording of the measurement data and their evaluation. The first applications focused on the identification of the elements present in a sample, i.e. a purely qualitative analysis. In this way, some elements could even be discovered, such as hafnium in 1923 (Coster, v.Hevesy), rhenium in 1925 (Tacke 1925), and technetium in 1947 (Perrier and Segrè 1947).

However, very soon the mass fractions of the different elements in the examined materials became interesting, mainly for the quantitative assessment of the investigated materials.

After the availability of the first commercial equipment, very fast development and distribution of X-ray spectrometry began. The following characteristics of X-ray spectrometry have undoubtedly been of assistance in this process:

 X-ray spectra have much less lines per element than optical spectra. This means that the lines in the spectrum are easy to identify and due to the corresponding small number of line interferences the requirements for the spectrometer resolution are not very high.

 All important parameters for the spectrometry depend on the atomic number of the considered element, which significantly supports the interpretation and evaluation of the spectra.

 The analysis can be carried out on very different sample qualities. Both compact solid samples and powder samples as also liquids and layered materials can be directly examined.

 The analysis is nondestructive, i.e. the material to be examined is not consumed or changed by the analysis. Therefore, the sample is available for further or repeated examinations.

 A large element and concentration range is covered. All elements except very light elements can be analyzed. The detectable element contents range from a few milligrams per kilogram to pure elements, i.e. at least 5 orders of magnitude. In cases of specific excitation geometries, instrument designs, or preparation methods, the detection limits can even be lowered to the sub-milligram per kilogram range.

 The development of novel components for X-ray analysis, such as X-ray optics and energy-dispersive (ED) detectors, initialized a strong dynamic in the development of new methodical possibilities. In recent years, therefore, a clear extension of the application range of X-ray spectrometry could be observed.

The analytical performance of X-ray fluorescence spectrometry (XRF), however, is characterized by further properties, which, in some cases, have a limiting character.

 The analysis can be carried out with very high precision because the statistical error can be kept very small due to the high measurable intensities. Typical analytical errors for the analysis of homogeneous samples are between 0.3 and 0.5 rel. wt%. With corresponding methods, these limits can be even further reduced.

 The analytical accuracy can be influenced by the type of sample preparation, the selection of measurement conditions, the measurement sequences, and the effort on data processing.

 The abovementioned high accuracies can be achieved only by comparative measurements with samples of exactly known composition, i.e. by calibrations using reference samples or primary substances (pure substances).

 The strong matrix dependence of the method can be considered as a limiting factor. This means that the element intensities have a nonlinear dependence on the sample composition. This makes quantifications more difficult and complex.During the development of X-ray spectrometry, it has been found that most of the interactions of both the incident radiation and the fluorescence radiation with the sample are physically very well understood and mathematically describable.This means that X-ray spectrometry is a very well understood analytical method, which now can be used even standard-less, i.e. quantifications are possible without the use of reference samples, only based on fundamental parameters such as absorption cross sections, transition probabilities, fluorescence yields, and others. This widely reduces the effort for the analyses of unknown samples, but it can also reduce the accuracy of an analysis. In particular, exact knowledge of the fundamental parameters and of the measuring geometry is required for high accuracy. On the other hand, in the case of inaccurate knowledge of these parameters, the analysis accuracy is limited.

 Typically, the analyzed sample volume is not very large. It is determined by the size of the area under investigation and the information depth, i.e. the thickness of the material that can be penetrated by the excited fluorescence radiation and contributes therefore to the measurement signal. For correct analysis, this volume should be representative of the material to be characterized.The size of the excited area can be easily adjusted and depends substantially on the homogeneity of the sample. The depth of penetration depends on the energy of the fluorescence radiation of the investigated element as well as on its absorption in the sample, i.e. from the composition of the matrix of the sample.

 X-ray fluorescence is known as a nondestructive analysis method that is capable of analyzing materials in various aggregate states, i.e. liquids, solid samples, or powders. Nevertheless, in many cases modifications of the material to be examined may be necessary for the analysis. These preparation procedures may be necessary, for example,to adjust the material to be investigated to the instrument geometry, for example, by detaching parts from a larger piece of the material, by filling loose powder into a sample cup, or by pressing it into tablets;to generate a sufficient representativity of the analyzed sample volume for the entire sample material, for example, by producing a planar sample surface or by cleaning the surface from contaminations; orto avoid or reduce the influence of inhomogeneities of the sample material on the analysis result, for example, by homogenization through grinding, by dilution, or by the manufacturing of fusion beads.

 However, the analyses can mostly be carried out without any changes in the aggregate state of the sample, i.e. the dissolution of solid samples is not required. Therefore, the effort for sample preparation compared to optical methods is relatively low and no or only slight dilution effects reduce the sensitivity of trace detection and therefore avoid analytical errors by contaminations.Nevertheless, it should be noted that even in the case of XRF, sample preparation must be carried out very carefully in order to achieve the desired analytical accuracy.

 Besides the analysis of homogeneous volume samples, the characterization of layered systems with XRF is also possible. Under certain conditions, both thickness and composition of layers can be determined. In this case, the mass per unit area can be determined by measurement, which then has to be converted into layer thicknesses and mass fractions by using the material density.The determination of layer thicknesses is a very common analytical problem in industrial process control of mechanical and electronic components or many other electroplated products.

 Another very important property of X-ray spectrometry is the possibility of automation, in particular, the automation of the measurement process, including data evaluation. In case there is no change in the sample type even sample preparation can be automated. This results in a fast analysis, but above all it provides for an analysis independent of subjective influences. Sample preparation and measuring operation can then be carried out under equivalent conditions, which reduces the uncertainty range of the measurement.Apart from this effect, the ongoing costs for analyses are reduced by means of automation.

 The analytical problem of X-ray spectrometry can be very different and can be classified into various “degrees of difficulty.”Qualitative analysis can be considered as a simple task. In this case, it is only necessary to determine whether certain elements are present in the sample or not.The next stage involves the monitoring of concentration ranges for selected elements. In this instance, it must be determined whether the mass fractions of the elements under consideration in the sample material are below or above a certain limit. Here, often no direct quantitative analyses are required but only a monitoring of the intensity level of the analyte. In this case, the matrix influence can be neglected because samples of similar qualities are investigated and their matrices do not change significantly.Without doubt, the most demanding analytical problem is the quantitative analysis. Here, the elements present in a sample have to be identified at first – for samples of same quality as in the case of quality control in the production process, this is not necessary – and then their mass fractions or their layer parameters have to be determined.

 The requirements regarding accuracy and sensitivity of the analysis can be very different, resulting in the selection ofthe sample preparation method (homogenization of the sample, elimination of influences of the surface roughness or of mineralogical effects)the measuring conditions (excitation conditions, measuring times, measuring medium)the evaluation model and, if available, of the reference samples to be used for the calibration to the accuracy requirements.

 Further, X-ray spectrometry can also determine element distributions of large sample areas by using specific excitation conditions. For this purpose, the incident beam has to be concentrated on a small sample area. The sample then needs to be moved under the fixed beam into the measuring position. This offers the possibility for the analysis of non-regular sample surfaces and additionally for the characterization of inhomogeneous materials.

 By using specific excitation geometries and conditions, it is possible to influence the sensitivity of the method. For example, in the case of a grazing incidence of the primary beam, the spectral background is greatly reduced and hence the sensitivity of the measurement is significantly increased.A similar effect can be obtained by using monoenergetic radiation for the excitation. Here also, the spectral background is reduced and an improvement in sensitivity can be achieved.

 A large number of different X-ray spectrometry instruments are available, each of which is designed for specific analytical tasks. A more detailed discussion of the individual instrument types can be found in Section 4.3.

 The radiation sources used in laboratory analyses today are X-ray tubes. In the past, isotope sources have been used as well. Another radiation source includes synchrotrons. Their radiation properties, i.e. the high beam brilliance, the polarization of the synchrotron radiation, or the possibility of generating monoenergetic radiation by means of appropriate X-ray optics, allow the use of very dedicated measuring geometries and measurement methods. As a result, new analysis methods are often developed at these radiation sources, which subsequently can be transferred into routine practice. However, these special analyses methods are not discussed within this scope since the very high instrumental effort and the limited availability of measurement time at these sources restrict their routine use.Another type of interesting X-ray source are plasmas in which atoms are ionized by extremely high temperatures. These atoms then emit X-radiation when transferred back to the ground state. It is usually radiation in the lower energy range. Because the plasma is often generated by a laser impact, these sources can be pulsed and consequently be used for time-resolved studies. However, these sources are not yet suitable for real routine use.

X-Ray Fluorescence Spectroscopy for Laboratory Applications

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