Multivariate calibration in TXRF analysis of water

Abstract

The aim of this paper is the application of multivariate linear calibration for quantitative determination of elements (K, Cd, Co, Hg, As, Pb, Ni, and Al) in water by using Total Reflection X‐ray Fluorescence Analysis with partial least squares (PLS) as a regression method to improve a result of common univariate method. In purpose of elimination of matrix effects in X‐ray fluorescence analysis, experimental design was applied. As a set of standard samples for multivariate calibration, a five‐level eight‐factor calibration design of 25 samples was chosen, ensuring mutual orthogonality of factors. For model's validation, the independent test set of 15 samples was examined. The collection of spectra and quantitative measurements was carried out on S2 PICOFOX. The PLS regression was performed by using software package STATISTICA. Quality indicators of multivariate calibration as slope (b) and intercept (a) of calibration, correlation coefficient (r), determination coefficient (R2), root mean square errors of calibration and of prediction, standard errors of calibration and of prediction, biases of calibration, and biases of prediction were calculated. These results were compared with the univariate model, and as a result, the multivariate calibration method exceeds the univariate one. The obtained results could be applied in a laboratory for an analysis of water solutions in the concentration range 0.05–2.00 mg/L. In many real situations, when analytical chemist deals with multi‐element mixtures, multivariate calibration approach combined with orthogonal design for multivariate calibration set could be successfully used to improve a conventional univariate calibration.

Direct determination of lanthanides by LIBS in REE-rich ores: comparison between univariate and DoE based multivariate calibrations with respect to spectral resolution

“…This design is, however, best suited for a small concentration range (0-2 mg L À1 in ref. 47) due to the number of samples growing as n 2 regardless of the number of factors (e.g., 20 2 in the present work and 5 2 in ref. 47).…”

“…47) due to the number of samples growing as n 2 regardless of the number of factors (e.g., 20 2 in the present work and 5 2 in ref. 47). This problem was addressed by Kirsanov et al 48 by the development of a DoE based on the uniform distribution of experimental points in a multidimensional space.…”

“…45 This can be further developed by exclusion of all correlations between lanthanide concentrations in an orthogonal matrix design proposed by Brereton. 46 This DoE along with PLS-R was used by Shulyumova et al 47 to solve the problem of line overlapping (e.g., As/Pb characteristic lines) common for TXRF. This design is, however, best suited for a small concentration range (0-2 mg L À1 in ref.…”

Determination of Ce and La in REE-rich ores using handheld LIBS and PLS regression

“…The design of experiment (DoE) concept addresses this problem. 47 There are several approaches to construct DoE, among them: (1) full factorial design, 48 requiring excessive number of samples to cover all possible relations of concentrations of analytes to completely ll the hyperspace; (2) fractional factorial design, 49 which can reduce the number of required experiments; (3) an orthogonal matrix design proposed by Brereton and successfully used by Shulyumova et al 50 to solve a problem of line overlapping (e.g., As/Pb characteristic lines) common for total reection X-ray uorescence (TXRF); 51 (4) the uniform distribution of experimental points in a multidimensional space developed by Kirsanov et al 52 to analyze lanthanides in aqueous solutions using TXRF; 53 (5) Latin hypercube sampling, rst proposed by McKay et al, 54 which allowed us to construct DoE with extremely low correlation (<0.03) between any pair of ve REEs and applied to XRF and LIBS analysis of REE-rich ores. 12,14 Therefore, our study aims to close the gap on the evaluation of the potential of the handheld LIBS (SciAps Z-300, USA) as a tool for quantication of major REEs (lanthanum and cerium) in real REEs-rich niobium and uranium ores of geological origin with the use of multivariate PLS regression with the aim of developing strategy of the rapid screening analysis.…”

Multivariate calibration for the improvement of the quantification of cadmium in the presence of potassium as interferent by total reflection X‐ray fluorescence

“…In this area, there are some investigations reporting the partial least squares (PLS) calibration applied to liquid matrix and synchrotron radiation TXRF as an alternative to improve the quality of the quantifications in the presence of these interferences of the spectral type, which would help to improve the selectivity of these instrumental methods and therefore its accuracy.…”