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

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 peakshifted 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 singlephase 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.

Fast and interpretable classification of small X-ray diffraction datasets using data augmentation and deep neural networks

“…Naturally, the F1 macro score is systematically lower than the F1 micro score, reflecting the The a-CNN trained after data augmentation has an accuracy of more than 93% and 89% for crystal dimensionality and space-group classifications, respectively. As far as we know, the accuracy is the higher up to date based on results found in literature for space-group classification algorithms trained with thousands of ICSD patterns and manual labelling by human experts 10,52 , and is also comparable to similar approaches in other kinds of diffraction data 8,19 . The neural network seems to be the most adequate method for high-throughput synthesis and characterization loops, as it also performs relatively well in terms of algorithm speed and in conditions of class imbalance.…”

Discovery of new materials using combinatorial synthesis and high-throughput characterization of thin-film materials libraries combined with computational methods

“…For high-throughput XRD several software developments already accelerated phase analysis in MLs. [49][50][51][52][53][54] Instead of having to analyze hundreds of diffractogram, e.g., by non-negative matrix factorization a set of e.g., tens of similar patterns can be obtained which are then the start for an in-depth analysis. Concepts for using machine learning for data-guided experimentation were introduced, e.g.…”

Identification of anomalous diffusion sources by unsupervised learning

“…The main idea of NMFk is to use the cohesion of the clusters (how compact they are) and the separation between them as a measure of the stability of the solutions of the minimization with different random initial guesses and hence the quality of a particular choice of N s . In previous works, NMFk even "shuffled" randomly the observed data C to increase the effect of robustness of the average solutions [41][42][43].…”