Unsupervised phase mapping of X-ray diffraction data by nonnegative matrix factorization integrated with custom clustering

Valentin Stanev,Graham Antoszewski,A Gilad Kusne,Ichiro Takeuchi,Velimir V Vesselinov,Boian S Alexandrov

doi:10.1038/s41524-018-0099-2

Abstract

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new method for pattern analysis and phase extraction of XRD datasets. The method expands the Nonnegative Matrix Factorization method, which has been used previously to analyze such datasets, by combining it with custom clustering and cross-correlation algorithms. This new method is capable of robust determination of the number of basis patterns present in the data which, in turn, enables straightforward identification of any possible peak-shifted patterns. Peak-shifting arises due to continuous change in the lattice constants as a function of composition and is ubiquitous in XRD datasets from composition spread libraries. Successful identification of the peak-shifted patterns allows proper quantification and classification of the basis XRD patterns, which is necessary in order to decipher the contribution of each unique single-phase structure to the multi-phase regions. The process can be utilized to determine accurately the compositional phase diagram of a system under study. The presented method is applied to one synthetic and one experimental dataset and demonstrates robust accuracy and identification abilities.

Highlights

Leveraging recently developed fast and reliable synthesis and characterization tools, compositional phase diagrams can be mapped with a high density of data points on a single library wafer.[1–5]
We show that the end members obtained by the extended NMF correctly represent the diffraction patterns of the unique crystal structures, and that their abundancies faithfully reflect the compositional phase diagram
The NMF algorithm can go from 1 to N, where N is the total number of individual X-ray extracts the original sounds from the recorded by the microphones mixtures of sounds, utilizing patterns), by obtaining sets of a large number of NMF minimization solutions for each K~. (Note that K~ serves to index the different constrained and regularized nonlinear optimization procedures NMF models, and is distinct from K, which is fixed, albeit unknown which minimizes an objective function representing discrepancy number.) NMFk leverages a custom clustering using Cosine between the observed and predicted mixtures

Summary

Introduction

Combinatorial approach to high-throughput experimental materials science has been successfully used to perform rapid mapping of composition-structure-property relationships in many complex systems. Leveraging recently developed fast and reliable synthesis and characterization tools, compositional phase diagrams can be mapped with a high density of data points on a single library wafer.[1–5]. These phase diagrams can be used to directly connect materials composition to desirable physical properties.[4,5]. Crucial for understanding the link between composition, structure and property is determining the constituent phases of materials from structural measurements such as X-ray diffraction (XRD). Creating rapid and reliable methods for automatic phase determination from XRD data has proven challenging. Various machine learning tools such as clustering and semi-supervised methods have been tested for this application.[7–18] One very promising technique for analyzing XRD data is Nonnegative Matrix

Methods

Results

Conclusion