[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

Tertiary excitation while secondary excitation is

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Tertiary Excitation While secondary excitation is appropriately accounted for in most professional environments in XRF, the possibility of computing the contribution of tertiary excitation is a feature of only the more advanced implementations. The rea- son is that such contributions are often assumed to be negligible except for a few (in general well-known) cases, and that computing them is dispropor- tionately time consuming due to nested integrations, which require numerical evaluation. The mathematical derivation of the equation for tertiary excitation fol- lows the same basic concept as for secondary excitation and can be carried out without any principal difficulty [53]. There remains, however, an addi- tional integral (nested into that over the energy), which requires numeri- cal solution. The resulting equation assumes that lines K of elements k are excited by primary radiation (direct excitation). They excite lines J of ele- ments j (secondary excitation step), which in turn excite the analyte line of element i (tertiary excitation). The dimensionless variable t is temporarily used for the integrations. N i, sec , observed = 1 4 G i C i k K C k g K × E = E max E = E Edge K j J C j g J τ i,K J τ j,K τ k N o ( E ) µ L iJK d E
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5 Quantitative Analysis 325 L iJK = 1 ( µ S,E ) 2 ln 1 + µ S,E µ S,K ln 1 + µ S,E µ S,J + 1 µ S,E · µ S,i ln 1 + µ S,E µ S,K ln 1 + µ S,i µ S,J + 1 ( µ S,i ) 2 ln 1 + µ S,i µ S,K ln 1 + µ S,i µ S,J + 1 µ S,E + 1 µ S,i 1 µ S,J ln 1 + µ S,J µ S,K + 1 µ S,K ln 1 + µ S,K µ S,J 1 µ S,E µ K J 0 1 µ S,E t + µ S,K log 1 + t t d t 1 µ S,i µ J K 0 1 µ S,i t + µ S,J log 1 + t t d t. (5.18) 5.2.4 Use of Standards [24] Standards are made from reference materials (see Sect. 5.9 for types and defin- itions) with accurately known composition, by following the same preparatory steps as for the unknown specimen. The effective size as well as the surface quality of standard and unknown specimens should be the same. In light ele- ment analysis, the microstructure of a specimen as well as the chemical state of the analyzed atoms may affect the measured count rates and must therefore be identical for standard(s) and unknown. Thin films can be used as standards without principal difficulties, but in practice the error frames associated with their thickness and density are limiting factors; they are, however, very useful for the analysis of other thin layers made by the same technique. The purpose of using standards is twofold: By building count-rate ratios, unknown factors in the FP equations cancel and are thereby eliminated (see later). The second is more subtle. The FP model is not a perfect description of reality. Besides the fact that the parameters themselves are subject to inaccuracies, most models are incomplete by neglecting the real geometry (e.g., beam divergences), several types of interactions (such as scattering), and other influence factors (microstructure, chemical state, varying spectral distribution of the primary beam across the specimen, etc.). If the assumption holds that
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