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

# Fe crfeni crfe feni fig 55 a base concentration

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Fe Cr–Fe–Ni Cr–Fe Fe–Ni Fig. 5.5. ( a ) Base concentration coordinates for a ternary system, with intermedi- ate lines indicating constant concentration ratios (fixed matrix), and ( b ) constant values of a concentration. ( c ) Curves of counts versus concentration of the analyte element in matrices of fixed composition. ( d ) Counts versus concentration from var- ious matrix compositions, i.e., superposed datapoints from various curves as in ( c ) The inﬂuence coeﬃcients methods assume a linear relationship between an element count rate and its concentration, and attribute all deviations from linearity to the inﬂuence of the matrix. Corresponding counteracting “corrections” must therefore be applied to the measured data in order to transform them into the desired linear relationship. Thereby each element of the matrix is assigned a certain power (mathematically, an inﬂuence coef- ficient ) of attenuating or enhancing the measured count rate from the an- alyte element. The mathematical starting point is the formal relationship C i = R i M ( C 1 , C 2 , . . . , C n ). This is interpreted as a dominating linearity C i = R i , but modified by a function M ( C 1 , C 2 , . . . , C n ) that takes the correc- tive role of moving the scattered data-points to a straight line.

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5 Quantitative Analysis 329 Various functions M ( C 1 , C 2 , . . . , C n ) have been proposed in the litera- ture, with differing complexity and methods of defining their parameters (i.e., the inﬂuence coeﬃcients). The following paragraphs show relationships be- tween inﬂuence coeﬃcients and FPs. Direct excitation. The relationship between directly excited photon count rates, N i (or count-rate ratios R i ), and the concentration of the analyte ele- ment in a bulk specimen has been derived in Sect. 5.2. The indication S for the specimen and λ for the incident radiation is now omitted (see Appendix): N i = G i C i λ = λ Edge , i λ = λ min τ i N 0 ( λ ) d λ µ R i = N i N ( i ) = C i λ = λ Edge , i λ = λ min τ i N 0 ( λ ) d λ µ λ = λ Edge , i λ = λ min τ i N 0 ( λ ) d λ µ i . Introducing a term M , which is interpreted as the inﬂuence of the matrix on the analyte count rate, N i (or count-rate ratio, R i ), leads to M = M ( C 1 , C 2 , . . . , C n ) = λ = λ Edge , i λ = λ min τ i N 0 ( λ ) d λ µ i λ = λ Edge , i λ = λ min τ i N 0 ( λ ) d λ µ (5.21) R i = N i N ( i ) = C i M C i = MR i . In many publications the term “intensity” ( I i and I ( i ) ) is used synony- mously for the count rates N i and N ( i ) , respectively, from element i , and the third equation given here can then be rewritten accordingly as “ KIM” equation [34]: C i = K I i M (5.22) K = 1 I ( i ) .
330 M. Mantler In the count-rate equation, µ can be substituted by µ = n j =1 C j ( µ j + µ j ) = n j =1 C j µ j,λ sin ψ + µ j,i sin ψ = C i µ i + n j =1 , j = i C j µ j = 1 n j =1 , j = i C j µ i + n j =1 , j = i C j µ j = µ i 1 + n j =1 , j = i C j µ j µ i µ i µ = µ i 1 + n j =1 , j = i C j α ij (5.23) with α ij = µ j µ i µ i = µ j,λ sin ψ + µ j,i sin ψ µ i,λ sin ψ + µ i,i sin ψ µ i,λ sin ψ + µ i,i sin ψ . (5.24)

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• Spring '14
• MichaelDudley

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