Fundamental algorithm between concentration and intensity in XRF analysis 1—theory

Abstract

A new formalism is proposed to correct with accuracy the matrix effects in x‐ray fluorescence (XRF) analysis. It has been deduced from Sherman's equations and includes a new algorithm between concentration and intensity, theoretically exact, and explicit expressions permitting the calculation of αij and ρij coefficients that correct for absorption and enhancement effects, respectively. In other words, the concept of correction coefficients is established on a solid theoretical basis. In the second part, it will be shown how to adapt this new formalism to practical situations. From an estimate of composition calculated by the Claisse–Quintin algorithm and an appropriate calibration, the new algorithm is used to refine the estimated composition for greater accuracy. This last approach is equivalent to the ‘fundamental parameters’ method but is presented in a simpler version adaptable to any mini‐computer.

The Quest for a Fundamental Algorithm in X-Ray Fluorescence Analysis and Calibration

“…In the general case where both matrix effects, absorption and enhancement, are present, this latter algorithm becomes (16) which is the Fundamental Algorithm where…”

“…Clearly, the mathematical model proposed by Sherman is imperfect, but no model can account totally for all the subtleties of instrument response and X-ray interactions within the specimen. Nevertheless, experience shows that the model performs very well in practice [29] if all of these approximations are compensated by using an appropriate calibration procedure [3], as illustrated below. Willy de Jongh [11] was the first in 1973 to propose the philosophy of this calibration procedure that compares measured intensities to calculated intensities (he called them unrealistically "apparent concentrations").…”

“…A practical application of this analytical method is given in Ref. [29], where 15 different analytes were determined in many different types of alloys, covering large concentration ranges. However, the analyst must be aware of some precautions to take before using this equation:…”

“…It introduces a theoretical mean relative error of 0.05% only [4]. An experimental verification of this method done by Rousseau and Bouchard [29] on different types of alloy has confirmed its accuracy and versatility.…”

Calculation of Theoretical Alpha Coefficients for XRF Analysis of Major and Minor Elements in Iron-rich Geological Samples

“…Recently we have the Fundamental Algorithm proposed by Rousseau [11][12]. The above four algorithms for the correction of matrix effects are all concentration cor rection models in which mostly the L-T equation is used, especially in the analysis of fusion samples.…”