Comparison of matrix-effect corrections for ordinary and uncertainty weighted linear regressions and determination of major element mean concentrations and total uncertainties of sixty-two international geochemical reference materials from wavelength-dispersive X-ray fluorescence spectrometry

Abstract

In X-ray fluorescence (XRF) spectrometry, matrix-effect corrections for two types of linear regressions (ordinary and uncertainty-based weighted) have been performed for the first time and compared for the determination of major elements in rocks and minerals. The analytical data from different laboratories for 62 international geochemical reference materials (GRMs) were first processed to obtain better estimates of the mean values, along with lower uncertainties (narrower confidence limits of the mean), which were used in the XRF calibrations. The blank intensities were subtracted from the response for each GRM and the respective uncertainties were estimated. The uncertainty-based weighted least-squares linear regression (UWLR) model, being statistically more appropriate than the ordinary least-squares linear regression (OLR) model, provided more reliable regression equations than the OLR. All calculations and matrix-effect corrections were achieved through a newly developed online computer program. Similarly, matrix-effect corrections involving 11 α and 26 α (alphas) are presented and compared. The best UWLR method involving 26 α was successfully applied to the 62 GRMs and 4 similarly complex rock matrices as the calibrators. Both evaluations confirmed the usefulness of the UWLR model. This UWLR model was also compared with the OLR 26 α model for 62 GRMs treated as unknowns and shown to perform better. Thus, the UWLR model, along with the proposed matrix-effect correction method of 26 α, can be recommended as the most appropriate procedure for the calibration of XRF instruments, instead of the commonly used OLR models. This is the first time when 26 α are advantageously in a better estimate of influence coefficients used for major element determinations in rock and mineral samples. Because the UWLR calibration is based on a large number of GRMs of many rock and mineral types, it should be useful for all kinds of geological materials.