A self‐consistent calibration method for industrial X‐ray spectrometric analyses

Abstract

A fast, efficient calibration procedure is proposed based on the accurate analysis of multicomponent systems by means of the influence coefficient method. It relies on a series of well designed additions made to a suitable standard composition, the latter also being used as a reference sample. We show that, for an n element composition, using the hypothesis of constant coefficients, (n + 1) preparations – allowing n(n + 1) intensity measurements – are in principle sufficient to calculate the n2 calibration parameters [i.e. n(n − 1) influence coefficients and n referenc relative intensities] which are necessary for a complete analysis. Actual analyses are carried out by measuring the fluorescent intensities using the ratio (i.e. unknown/standard) method, and then calculating the concentrations from the usual relationships through an iterative calculation, preferably executed by a computer program. A detailed description of a typical application is given, which involved the study of fused specimens (borax fusion) of bauxite and resulted in the very accurate analysis of calcined samples, as well as the direct analysis of raw bauxites following an adequate treatment of the ignition loss problem. While the method is immediately applicable to every system studied in either solid or liquid solution, it clearly extends to compact systems over a suitable compositional range, provided that carefully controlled additions can be achieved and that all prepared samples are homogeneous.

Practical solutions to matrix effects in x-ray fluorescence analysis by mathematical methods

“…The mathematical and physical meanings, and effects of every variable in the equations are probed. In accordance with these investigations, it is possible to generalize earlier specific calculation problems (1)(2)(3)(4)(5)(6)(7)(8) encountered in XRF methods.…”

Energy‐dispersive x‐ray fluorescence analysis of geological materials in borax beads using Tertian's binary coefficient approach combined with internal standard addition

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Total X‐ray fluorescence analysis of geological samples using a low‐dilution lithium metaborate fusion method. Matrix corrections for major elements

“…( 1 ) The expression inside the brackets in Eqn ( trend is parallel to the actual concentration axis, Ci. ( 5 ) If the calculated emitter concentration is too high only for samples with a high absorber concentration q, then the factor qi is too large.…”