Quantitative XRD Analysis by Partial Least Squares Application in a Commercial Product

Abstract

A new approach to quantitative XRD by Partial Least Squares (PLS) used region(s) or the entirety of the diffraction pattern of calibration standards (also called a training set) in the model. The basic concept of this approach states that the information in many observed variables, expressed as matrix I = (i₁, i₂ … , i_k,) is concentrated onto a few underlying latent variables, called factors, by the process of data compression. In XRD, the data points of the diffraction pattern are compressed to few factors T, computed according to their ability to explain the variation in the diffraction pattern or matrix I. The procedure incorporates into the model that part of I that is correlated to C concentrations. Data compression preserves the redundancy between variables due to collinearity and stabilizies the predictions against noise in I. The resulting calibration model allows for detection of outliers. Another important effect of data reduction is the ability to analyze muticomponent systems even when lines of the components are overlapped, Examples of quantitative analysis by PLS are demonstrated in the analysis of a commercial product.