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Siegbahn IUPAC Siegbahn IUPAC Siegbahn IUPAC Kα₁ K–L3 Lα₁ L3–M5 Mα₁ M5–N7 Kα₂ K–L2 Lα₂ L3–M4 Mα₂ M5–N6 Kß₁ K–M3 Lß₁ L2–M4 Mβ M4–N6 Kß₂ K–N3 Lß₂ L3–N5 Mγ M3–N5 Kß₃ K–M2 Lß₃ L1–M3 Mξ M4,5–N2,3 Kß₄ K–N5,4 Lß₄ L1–M2 Kß₅ K–M4,5 Lß₅ L2–O4,5 Lß₆ L3–N1 Lγ₁ L2–N4 Lγ₂ L1–N2 Lγ₃ L1–N3 Lγ₄ L1–O3 Lγ₅ L2–N1 Lγ₆ L2–O4 Lη L2–M1

Figure 2.5 Contributions to the attenuation coefficient for X-radiation of (a) carbon and (b) lead.

      

      2.2.4.2 Scattering

Scattering is the most important origin of the spectral background in X-ray spectrometry. The incident radiation is scattered at the electrons of the atoms of the sample. The scattering can be both elastic (Rayleigh or coherent scattering) and inelastic (Compton or incoherent scattering). All electrons of an atom contribute to the elastic scattering, i.e. the scattering intensity is proportional to the number of electrons or to the atomic number. Inelastic scattering can occur only at weakly bonded, i.e. outer electrons. Therefore, its intensity is mostly independent of the atomic number. This is demonstrated in Figure 2.6 showing the scatter coefficients for a few elements for an energy of 20 keV, which is close to Rh-Kα-radiation, the most often used target material for spectroscopic X-ray tubes (Section 5.3.2.1). The coefficients for the Rayleigh (elastic) scattering increase approximately proportionally with the atomic number whereas the coefficients for the Compton (inelastic) scattering show only a small dependence on atomic number; only for the lightest elements they are slightly larger than for most other elements.

Figure 2.6 Elastic and inelastic scattering coefficients for selected elements at 20 keV.

This means, that the ratio I^inelastic/I^elastic is dependent on the sample composition. For light matrices the ratio is large due to the small contribution of elastic scattering, and for heavy matrices it is small due to the larger contribution of elastic scattering. This is demonstrated in Figure 2.7. Panel (a) shows the elastically and inelastically scattered fluorescence radiation of the X-ray tube for four different samples normalized to the Compton peak of the scattered Rh-Kα-radiation of the tube. Panel (b) shows the ratio of inelastic and elastic scattered fluorescence radiation of the X-ray tube as a function of the mean atomic number of the sample for a given measurement geometry. This different scattering behavior can be helpful in the quantitative analysis of the sample.

With the help of the Compton–Rayleigh ratio the mean atomic number of the sample can be determined. The mean atomic number can then be used for an averaged description of the absorption properties of the sample. Another application is the normalization of the fluorescence intensity of analytes to the Compton intensity. Knowledge of the mean atomic number of the sample can be further used to determine elements that cannot be measured by XRF, such as oxygen in oxides, as a difference to 100 wt%.

The continuous background of a spectrum is mainly caused by the scattered continuous bremsstrahlung of the X-ray tube at the sample, both by elastic and inelastic scattering. As demonstrated in Figure 2.7, the elastic scattering decreases with decreasing average atomic number of the sample. Nevertheless, the intensity of the scattered tube radiation is considerable in relation to the fluorescence intensity of the light matrix elements. This is also caused

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