Multivariate versus traditional quantitative phase analysis of X-ray powder diffraction and fluorescence data of mixtures showing preferred orientation and microabsorption

Abstract

In materials and earth science, but also in chemistry, pharmaceutics and engineering, the quantification of elements and crystal phases in solid samples is often essential for a full characterization of materials. The most frequently used techniques for this purpose are X-ray fluorescence (XRF) for elemental analysis and X-ray powder diffraction (XRPD) for phase analysis. In both methods, relations between signal and quantity do exist but they are expressed in terms of complex equations including many parameters related to both sample and instruments, and the dependence on the active element or phase amounts to be determined is convoluted among those parameters. Often real-life samples hold relations not suitable for a direct quantification and, therefore, estimations based only on the values of the relative intensities are affected by large errors. Preferred orientation (PO) and microabsorption (MA) in XRPD cannot usually be avoided, and traditional corrections in Rietveld refinement, such as the Brindley MA correction, are not able, in general, to restore the correct phase quantification. In this work, a multivariate approach, where principal component analysis is exploited alone or combined with regression methods, is used on XRPD profiles collected on ad hoc designed mixtures to face and overcome the typical problems of traditional approaches. Moreover, the partial or no known crystal structure (PONKCS) method was tested on XRPD data, as an example of a hybrid approach between Rietveld and multivariate approaches, to correct for the MA effect. Particular attention is given to the comparison and selection of both method and pre-process, the two key steps for good performance when applying multivariate methods to obtain reliable quantitative estimations from XRPD data, especially when MA and PO are present. A similar approach was tested on XRF data to deal with matrix effects and compared with the more classical fundamental-parameter approach. Finally, useful indications to overcome the difficulties of the general user in managing the parameters for a successful application of multivariate approaches for XRPD and XRF data analysis are given.

PCA Analysis of In Situ X-ray Powder Diffraction and Imaging Data Shedding New Light on Solid-State Transformations: The Crystallization of Low Temperature Eutectic Mixtures

“…The main advantage is using the same "mathematical engine", i.e., PCA, to analyze both XRPD and imaging data. The raw data were thus subjected to PCA analysis to extract the trends in time dependent data sets, 30 obtaining quantitative estimates as a function of time (and thus temperatures) of the present phases 31 in both data sets (details of data analysis are given in the Experimental Section). To be able to perform PCA analysis on images they are transformed in advance from 2-D objects to 1-D arrays of color values and are organized in a matrix with one image per row.…”

“…The setup can collect simultaneous imaging and XRPD data, and PCA can analyze blindly both XRPD and imaging data from both solid and liquid phases, with PCA scores being the reaction coordinate of the investigated transformation for each data set. PCA proved to be a powerful tool to efficiently extract information from large amounts of data, being also able to be performed, complementarily to traditional approaches, to extract structural, phase composition and kinetic information, to highlight trends and track and correlate changes occurring during in situ experiments based on different techniques ranging from diffraction to spectroscopy. − Applying PCA to in situ XRPD and imaging data during crystallization and melting allows one to obtain a profile by measuring the solid/liquid ratio on the complementary fields of structural and morphological viewpoints. A phase transition can thus be analyzed like a traditional DSC but probing structural and morphological information by differential scanning diffraction (DSD) and imaging (DSI) respectively instead of energy.…”

New features of the RootProf program for model-free analysis of unidimensional profiles

“…Figure 4Score plot of the first two PCs for ternary mixtures composed as described byLopresti et al (2022). Weight fraction estimations for the three crystal phases obtained by semi-quantitative analysis are reported close to each representative point.…”