High-throughput powder diffraction. III. The application of full-profile pattern matching and multivariate statistical analysis to round-robin-type data sets

Abstract

Powder pattern matching techniques, using all the experimentally measured data points, coupled with cluster analysis, fuzzy clustering and multivariate statistical methods are used, with appropriate visualization tools, to analyse a set of 27 powder diffraction patterns of alumina collected at seven different laboratories on different instruments as part of an International Center for Diffraction Data Grant-in-Aid program. In their original form, the data factor into six distinct clusters. However, when a non-linear shift of the form \Delta \left({2\theta } \right)\, = \,a_0 \, + \,a_1 \sin \theta (wherea0anda1are refinable constants) is applied to optimize the correlations between patterns, clustering produces a large 25-pattern set with two outliers. The first outlier is a synchrotron data set at a different wavelength from the other data, and the second is distinguished by the absence ofKα2lines,i.e.it uses Ge-monochromated incident X-rays. Fuzzy clustering, in which samples may belong to more than one cluster, is introduced as a complementary method of pinpointing problematic diffraction patterns. In contrast to the usual methodology associated with the analysis of round-robin data, this process is carried out in a routine way, with minimal user interaction or supervision, using thePolySNAPsoftware.