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.

中文翻译：

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波长色散 X 射线荧光光谱法测定 62 种国际地球化学标准物质的普通和不确定加权线性回归的基质效应校正以及主要元素平均浓度和总不确定度的比较

摘要 在 X 射线荧光 (XRF) 光谱法中，首次对两种类型的线性回归（普通和基于不确定性的加权）进行了基质效应校正，并比较了岩石和矿物中主要元素的测定。首先对来自不同实验室的 62 种国际地球化学参考材料 (GRM) 的分析数据进行处理，以获得更好的平均值估计值，以及更低的不确定性（更窄的平均值置信限），这些数据用于 XRF 校准。从每个 GRM 的响应中减去空白强度，并估计各自的不确定性。基于不确定性的加权最小二乘线性回归 (UWLR) 模型，在统计上比普通的最小二乘线性回归 (OLR) 模型更合适，提供了比 OLR 更可靠的回归方程。所有计算和基质效应校正都是通过新开发的在线计算机程序实现的。同样，介绍并比较了涉及 11 个 α 和 26 个 α (alpha) 的矩阵效应校正。涉及 26 α 的最佳 UWLR 方法已成功应用于 62 个 GRM 和 4 个类似的复杂岩石矩阵作为校准器。两项评估都证实了 UWLR 模型的有用性。该 UWLR 模型还与 OLR 26 α 模型进行了比较，将 62 个 GRM 视为未知数，并显示其性能更好。因此，可以推荐 UWLR 模型以及所提出的 26 α 矩阵效应校正方法作为校准 XRF 仪器的最合适程序，而不是常用的 OLR 模型。这是第一次 26 α 有利于更好地估计用于岩石和矿物样品中主要元素测定的影响系数。由于 UWLR 校准基于多种岩石和矿物类型的大量 GRM，因此它应该适用于各种地质材料。