The family of alpha coefficients in X‐ray fluorescence analysis

Abstract

The demand for comprehensive analysis of materials by XRF using automated instrumentation has led to increasing use of the coefficient approach for dealing with the ever-present interelement effect. A survey of the literature shows that this has often led to a multiplicity of families of calibration curves being replaced by a multiplicity of tables of correction coefficients. A practical approach is outlined which facilitates the recognition of (a) the alpha subset of influence coefficients, and (b) three related subsets of alpha coefficientsbasic, modified and hybrid. This mobility of alpha coefficients (alloys, oxides, fusions, solutions) coupled to their adaptability (geometry, primary radiation) and accessibility (theoretical, experimental) has wide implications. It permits a consolidated view of the influence coefficients, and comparison of the sign, magnitude and pattern of basic alphas so as to establish if and when there is consensus. The confirmed alpha coefficients thus obtained can then be transferred with confidence to suit specific operating conditions and methods. Examples are given using data that have appeared in XRF literature.

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

“…cs i-^ < u ea Au^l , and this is different from the algorithms of other workers [19]. It should be observed that for 'a® the eliminated component i in the left superscript is the analyte i itself, and the B in the right superscript denotes basic alpha coefficients which can be used for correcting matrix effects in the system.…”

“…In the analysis of oxides [19] in powder rocks or cement samples, both the basic alpha coefficients and the concentration of oxygen must be considered; hence, hybrid alpha coefficients should be used. For the case of oxides, we can derive the following formula from (7):…”

“…Therefore, the matrix correction of the volatile constituents becomes very important in the analysis of the major and minor constituents in glass discs. This loss of the volatile constituents is often referred to as the loss-on-ignition (LOI) and in XRF as the "LOI problem" [19]. The "LOI problem" can be treated quantitatively using influence coefficients.…”

“…Equation (19) can be used to transform the theoret ical alpha coefficients used in the L-T model whose eliminated component is analyte i(0) into those used in the D.J model whose eliminated component is the LOI. Hence, we can get Table 7 from Table 6 using (19).…”

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

“…However, this approach introduces more approximations and must be used with caution and applied with great care. The terminology "modified" and "hybrid" influence coefficients has been proposed by Lachance [30] in 1979 but his methods of calculation have not been retained.…”