Mathematical matrix correction procedures for x‐ray fluorescence analysis. A critical survey

Abstract

The complexity of the intensity–concentration relationship in x‐ray fluorescence analysis as well as new requirements for speed and accuracy will induce analysts to resort more and more to mathematical methods for effecting matrix correction. A thorough study of Lachance–Traill coefficients, based on theoretically calculated fluorescence intensities, shows that all ‘binary’ coefficients vary systematically with composition under the usual working conditions with polychromatic excitation, while ‘multicomponent’ coefficients can no longer be represented (i.e. in the form of curves or diagrams) owing to the intricacy of third element effects. For these reasons, we are compelled to turn to a fundamental approach, where two methods are now competing: on the one hand, the classical fundamental parameter method, which permitted the abovementioned investigation, but does not in itself offer a sufficiently coherent solution to the problem of matrix correction; on the other, the new fundamental coefficient method, which accounts for all theoretical implications, but preserves the flexibility and adaptability of the older influence coefficient procedures. Utilizing such effective coefficients in a comparison standard correction algorithm allows one to solve any analytical problem, from the most complicated to the simpler ones, through a kind of ‘à la carte’ procedure. The so‐called empirical algorithms are in principle ineffective for treating the complex corrections which belong to the analysis of compact specimens (e.g. metal alloys). They must be reserved for simpler problems, notably the study of diluted specimens where an experimental calibration remains feasible.

X‐Ray Fluorescence Analysis

“…A thorough study (Tertian, 1986) of Lachance-Trail1 coefficients based on theoretically calculated fluorescence intensities shows that all binary coefficients vary systematically with composition. Both the and Lachance-Claisse models use higher order terms to correct for so-called crossed effects, which includes enhancement and third element effects.…”

A matrix effect correction algorithm for x‐ray fluorescence analysis of steel

“…To compensate for the deficiencies of this approach, and to take into account some uncertainties connected with the kind of sample involved and the range of concentrations, a crosscorrection term is included' which corrects for the combined effect of Fe and Ni on the analyte Cr. As a result, the expression (7) in which y is determined from the value of f(C) at This value of the maximum error is one order of magnitude less than the error given by Eqn (2). However, when crossed-effect terms are included, the volume of the coefficient matrices begins to increase with increasing number N of elements composing the specimens as N 3 .…”

Reference-free X-ray spectrometry based on metrology using synchrotron radiation

“…As this requirement can often not be fulfilled easily, various techniques to correct for matrix effects have been developed and validated. [12][13][14] In the case of inhomogeneous matrices, analytical expressions for the elemental concentrations can only be given when a complete description of the spatial distribution of the main matrix constituents can also be given. Otherwise, Monte Carlo based simulations may contribute in overcoming a lack of sufficient a priori knowledge concerning the spatial distribution of main matrix elements or, when including multiple scattering The solid angle of detection is defined by a known diaphragm placed in front of the Si(Li) detector at a given distance with respect to the center of the sample.…”