Rapid identification of structural phases in combinatorial thin-film libraries using x-ray diffraction and non-negative matrix factorization

Abstract

In this work we apply a technique called non-negative matrix factorization (NMF) to the problem of analyzing hundreds of x-ray microdiffraction (microXRD) patterns from a combinatorial materials library. An in-house scanning x-ray microdiffractometer is used to obtain microXRD patterns from 273 different compositions on a single composition spread library. NMF is then used to identify the unique microXRD patterns present in the system and quantify the contribution of each of these basis patterns to each experimental diffraction pattern. As a baseline, the results of NMF are compared to the results obtained using principle component analysis. The basis patterns found using NMF are then compared to reference patterns from a database of known structural patterns in order to identify known structures. As an example system, we explore a region of the Fe-Ga-Pd ternary system. The use of NMF in this case reduces the arduous task of analyzing hundreds of microXRD patterns to the much smaller task of identifying only nine microXRD patterns.

On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets

“…When this is performed on a large number of x-ray diffraction patterns taken across a composition spread, the algorithms can be used to guide and delineate structural phase boundaries leading to rapid construction of a composition-structure relationship, often an end goal of many materials science experiments303132. The learned composition-structure relationship from diffraction data can also be extrapolated to relationships between structure and functional properties such as magnetostriction or piezoelectricity3334, with structural phase boundaries indicating potential regions of significant change in functional properties.…”

Constraint Reasoning and Kernel Clustering for Pattern Decomposition with Scaling

“…As discussed in Section 3.2, the pure CP approach suffers from very poor scaling. On the other end, datadriven approaches such as non-negative matrix factorization (NMF) used in the literature [14] for such problems suffer, as we will show, from low accuracy -to the point that "solutions" found by them for material discovery instances can be meaningless. Our hybrid method avoids both of these extreme kinds of failures, in scaling and in accuracy.…”

“…Doing this automatically, without human interaction, is a long standing problem in combinatorial crystallography. Several recent algorithms have been proposed which correctly solve the phase map for limited cases [3,4,14,15]. In 2007, Long et al [15] suggested a hierarchical agglomerative clustering (HAC) approach which aims to cluster the observed patterns that involve the same subset of basis patterns, but relies on a manual inspection in order to discover the actual basis patterns.…”

“…In 2007, Long et al [15] suggested a hierarchical agglomerative clustering (HAC) approach which aims to cluster the observed patterns that involve the same subset of basis patterns, but relies on a manual inspection in order to discover the actual basis patterns. In a follow-up paper, Long et al [14] applied non-negative matrix factorization (NMF), which approximates (through gradient descent) the observed diffraction patterns with a linear combination of positive basis patterns. A main limitation of both approaches lies in the assumption that peaks of a phase will always appear at the same position and with the same relative intensities in any pattern.…”

SMT-Aided Combinatorial Materials Discovery

“…Most of the solutions in the literature are based on unsupervised machine learning techniques, such as clustering and non-negative matrix factorization [13,12]. While these approaches are quite effective at extracting information from large amounts of noisy data, their major limitation is that it is hard to enforce the physical constraints of the problem at the same time.…”