Curve-fitting regression: improving light element quantification with XRF

Abstract

Light elements are hard to quantify by X-ray fluorescence (XRF) spectrometry because, after a photoelectric excitation, they predominantly relax emitting Auger electrons, greatly reducing the fluorescence count thus limiting the signal-to-noise ratios (SNR) observed. Low SNR values have deleterious outcomes in model building. Notable in ordinary least squares (OLS) regression based on peak height, they also affect more robust regression methods, such as partial least squares regression. While low SNR can also be observed with low concentrations of heavier elements, this paper focuses on boron. To overcome the low SNR hurdle, curve-fitting regression (CFR), a novel method elaborated in this paper, seeks to fit full scans with summed Gaussian curves. The methodology was illustrated with pressed microcrystalline cellulose spiked with sodium tetraborate decahydrate (borax) powder samples. The calibration set ranged from 0% to 21.5% m/m boron, and a PANalytical Axios wavelength dispersive X-ray fluorescence system with rhodium source was used to perform the tests. A calibration curve with determination coefficient (R2) = 0.990 and root mean square error of calibration (RMSEC) = 0.7% m/m was produced with CFR versus RMSEC = 1.2% m/m with OLS regression. Validity of the method was tested with a set of 17 pearled samples containing a mixture of different oxides. Root mean square error of prediction (RMSEP) of 0.1% m/m was obtained with the validation set, using CFR against RMSEP = 0.99% m/m with OLS regression, thus illustrating the proposed method's potential. Copyright © 2017 John Wiley & Sons, Ltd.