Statistically Coherent Calibration of X-Ray Fluorescence Spectrometry for Major Elements in Rocks and Minerals

Abstract

We applied both the ordinary linear regression (OLR) and the new uncertainty weighted linear regression (UWLR) models for the calibration and comparison of a XRF machine through 59 geochemical reference materials (GRMs) and a procedure blank sample. The mean concentration and uncertainty data for the GRMs used for the calibrations (Supplementary Materials) (available here) filewere achieved from an up-to-date compilation of chemical data and their processing from well-known discordancy and significance tests. The drift-corrected XRF intensity and its uncertainty were determined from mostly duplicate pressed powder pellets. The comparison of the OLR (linear correlation coefficient r∼0.9523–0.9964 and 0.9771–0.9999, respectively, for before and after matrix correction) and UWLR models (r∼0.9772–0.9976 and 0.9970–0.9999, respectively) clearly showed that the latter with generally higher values of r is preferable for routine calibrations of analytical procedures. Both calibrations were successfully applied to rock matrices, and the results were generally consistent with those obtained in other laboratories although the UWLR model showed mostly narrower confidence limits of the mean (slope and intercept) or lower uncertainties than the OLR. Similar sensitivity (∼2.69–46.17 kc·s−1·%−1 for the OLR and ∼2.78–59.69 kc·s−1·%−1 for the UWLR) also indicated that the UWLR could advantageously replace the OLR model. Another novel aspect is that the total uncertainty can be reported for individual chemical data. If the analytical instruments were routinely calibrated from the UWLR model, this action would make the science of geochemistry more quantitative than at present.

Fuzzy Decision Support System for the Calibration of Laboratory-Scale Mill Press Parameters

“…This approach has been successfully used to analyze various heavy mineral sand samples. Reference [19] compares two different regression models (OLR and uncertainty weighted linear regression) for the calibration and comparison of an XRF machine using 59 geochemical reference materials. Both calibrations have been successfully applied to rock matrices.…”

APMdisc: An online computer program for the geochemical discrimination of siliciclastic sediments from active and passive margins

“…Following Verma and Díaz-González (2020), as a further improvement of the APMdisc program, we have incorporated a Robustness module to better understand the effects of field changes (such as weathering, transportation, deposition, and diagenesis; e.g., Basu et al, 2016) and laboratory analysis uncertainties (Verma et al, 2018Verma, 2020). This module is added to the original version of the APMdisc (Figure 2).…”

“…These values were used for testing the robustness against analytical uncertainty. Finally, the robustness of some selected individual samples from the Sakarya Zone, NW Turkey (Sengün and Koralay, 2019), was also evaluated in terms of typical total uncertainties recently reported by Verma et al (2018Verma et al ( , 2019 for the analysis of geochemical reference materials.…”

“…The analytical uncertainties are seldom, if ever, presented for individual analyses, although recently Verma et al (2018Verma et al ( , 2019 demonstrated that it is feasible to do so provided that the calibration uncertainties are estimated and taken into account for total uncertainties. We used their total mean uncertainties to test the robustness of 4 individual samples reported by Sengün and Koralay (2019) in the Robustness module of analytical uncertainty.…”

“…Figure 8. One-axis discriminant function diagrams for the subdivision of Active (A) and Passive (P) margins for 4 selected samples from the Sakarya Zone, NW Turkey (Sengün and Koralay, 2019) and their stability against laboratory analytical uncertainties (Verma et al, 2018(Verma et al, , 2019 from Monte Carlo simulations: a) two active margin samples evaluated under the 99% uncertainty model; b) two passive margin samples evaluated under the 99% uncertainty model. One-axis discriminant function DF ilr(A-P)MT diagram for the subdivision of active (A) and passive (P) margins based on isometric (i) log-ratio transformation of system based on combined major and trace elements (MT).…”