“…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 reection 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 quantication 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. In order to make sure that we avoid systematic errors in the results of the PLS regression we utilized the DoE previously described by us 12,14 to determine several REEs (Ce, La, Nd, Pr, Sm) in ores by laboratory XRF and LIBS systems.…”