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

# In 1955 sherman 52 following an in depth study of the

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In 1955 Sherman [52], following an in-depth study of the correlation between intensity and concentration, proposed the following expressions/ definitions: Q = I f 3 (0 , 0 , 1) I f 3 ( c 1 , c 2 , c 3 ) = T f 3 ( c 1 , c 2 , c 3 ) T f 3 (0 , 0 , 1) (5.34) and T f 3 ( c 1 , c 2 , c 3 ) = u 0 + c 1 c 3 u 1 + c 2 c 3 u 2 , where T is the time to accumulate N counts; u 0 , u 1 , and u 2 are coeﬃcients, and c are concentrations. The drawback in the case of the latter expression is that the correction terms involve multiplication by concentration ratios involving c 3 (the analyte) in the denominator of each of these ratios. In 1968 Criss and Birks [12] proposed an FP approach, which is still cur- rently used in one form or another. They also proposed an empirical inﬂuence coeﬃcient approach involving a suite of equations equal to 0. However, they adopted the definition for relative intensity as I i /I ( i ) (intensity of the speci- men divided by the intensity of the pure element i ), which is commonly used today, given that a relative intensity is in fact an apparent (i.e., uncorrected for matrix effects) concentration. Thus, ( R A α AA 1) C A + R A α AB C B + R A α AC · C C = 0 , (5.35) where R A = I i /I ( i ) ; α are inﬂuence coeﬃcients and C are concentrations. In 1973 Tertian [56] proposed equations of the following type relating con- centration to relative intensity c A = R A c A + α B A c B + α C A c C R A = I A I A 1 and K = 1 R A R A c A 1 c A (5.36) for binary contexts. A 1 is the pure element, K is an inﬂuence coeﬃcient, and c A is the concentration of the analyte in the binary system.

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5 Quantitative Analysis 337 In 1966 Lachance and Traill [33] proposed the following expression wherein the concentration of the analyte does not appear in the correction expression term quantifying the concentration of the analyte, i.e.: R A = C A 1 + C B α AB + C C α AC + · · · + C n α A n , (5.37a) which can be transformed for analysis as: C A = R A 1 + B α AB C B , (5.37b) where the inﬂuence coeﬃcient α AB is defined as α AB λ = µ B µ A µ A ; the subscript λ is used to indicate that the definition is for a monochromatic incident source, and µ is the total effective mass absorption coeﬃcient taking into account the spectrometer geometry. The proposed expression can be transformed in order to define and com- pute the intensity of the pure analyte, namely, I (A) = I A [1 + C B α AB + C C α AC + · · · ] C A . (5.38) By taking advantage of the fact that Criss and Birks’ FPs approach made it possible to generate R i values, and therefore possible to calculate in- ﬂuence coeﬃcients for binary contexts, Lachance [31] defined a theoretical inﬂuence coeﬃcient for the context { polychromatic incident source , matrix effect ( absorption and enhancement ), binary system } , namely, α ij, bin = C i R i, bin C j R i, bin . (5.39) Given that R i, bin could be computed from fundamental theory for both absorption and enhancement contexts confirmed the currently held general observation that inﬂuence coeﬃcients are not constants when the incident excitation source is polychromatic .
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