The Claisse–Quintin and Lachance–Claisse alpha correction algorithms and their modifications. A critical examination

Abstract

A slow progress has led us from a reduced formulation (Claisse-Quintin) to a perfected one combining: (1) an advanced knowledge (Tertian and co-workers, Lachance) of the properties of binary influence coefficients; and (2) Tertian's equation for the resultant third element effect in any multi-element system. The new algorithm is accurate and compares easily with typical fundamental parameter approaches (Criss and co-workers) or fundamental coefficient approaches (Broll and Tertian, Rousseau). It suffers from the same reservations as regards possible deviations between theoretical assumptions and experimental reality. A refined experimental study of suitable binary standards should help to reduce these uncertainties.

Determination of Optimum Conditions for X-Ray Fluorescence Analysis Using Coupling Equations

“…where as that of Tertian is as follows [26]: where C m = 1 -C i and C k is the concentration in the third control sample of element k. The values of the a ijk coefficients characterize the effect of the third k components on a ij and their calculation is based on ternary and binary hypothetical compositions.…”

“…It is worth noting that there is no unique formalism for estimation of correction coefficients. Sometimes, Equations (9) and (10), (11) can be applied, as previously reported in the literature [25,26].…”

Unification of fundamental matrix correction methods in X‐ray fluorescence analysis. Arguments for a new binary coefficient approach

“…This function is now fulfilled by Eqn (19), which receives general agreement. 37 In this new light, the binary coefficient model proves strictly equivalent to the foregoing algorithms, with specific advantages to be outlined in Section 9.…”

Use of Cm and cross product coefficients in influence coefficient algorithms for quantitative XRF analysis

“…Hence the concentrations in these two equations are explicitly subscripted bin. By substitution of Eqn (14) into Eqn (12): Influence coefficient algorithms for quantitative XRF 77 and rearranging yields…”

“…However, applying binary coefficients to multi-element specimens according to Tertian leads to crossed effect. A method to correct for this was proposed by Tertian 14 and involves the use of weighting factors based on the reciprocals of the relative intensities of the binaries involved. This is a cumbersome method, but theoretically valid, and it does not imply any approximation whatsoever.…”