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

Fe crfeni crfe feni fig 55 a base concentration

Info icon This preview shows pages 349–352. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Image of page 349

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 ) .
Image of page 350
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)
Image of page 351

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 352
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern