Abstract
A deep machine-learning technique based on a convolutional neural network (CNN) is introduced. It has been used for the classification of powder X-ray diffraction (XRD) patterns in terms of crystal system, extinction group and space group. About 150 000 powder XRD patterns were collected and used as input for the CNN with no handcrafted engineering involved, and thereby an appropriate CNN architecture was obtained that allowed determination of the crystal system, extinction group and space group. In sharp contrast with the traditional use of powder XRD pattern analysis, the CNN never treats powder XRD patterns as a deconvoluted and discrete peak position or as intensity data, but instead the XRD patterns are regarded as nothing but a pattern similar to a picture. The CNN interprets features that humans cannot recognize in a powder XRD pattern. As a result, accuracy levels of 81.14, 83.83 and 94.99% were achieved for the space-group, extinction-group and crystal-system classifications, respectively. The well trained CNN was then used for symmetry identification of unknown novel inorganic compounds.
Highlights
It would be a very difficult to describe an actual crystal structure perfectly using only powder X-ray diffraction (XRD) patterns as the raw data source, because the threedimensional electron-density distribution is condensed into just one dimension in the powder diffraction pattern
One of the most outstanding achievements has been AlphaGo (Silver et al, 2016), which employed a convolutional neural network (CNN) for both the policy and value networks in reinforcement learning and thereby defeated a human champion. Inspired by such successful achievements, we have developed an appropriate CNN to be used with powder XRD pattern classification, and have utilized it for crystal-system, extinction-group and spacegroup determination
As a matter of fact, the CNN model cannot perform the complete indexing of a powder XRD pattern, but identifies the crystal system, extinction group and space group
Summary
It would be a very difficult to describe an actual crystal structure perfectly using only powder X-ray diffraction (XRD) patterns as the raw data source, because the threedimensional electron-density distribution is condensed into just one dimension in the powder diffraction pattern. The excessive feature engineering (dramatic data-dimension contraction), the shallow ANN and the small size of the training data set constituted a somewhat vicious circle, which imparted machine learning-based analysis with no merit by comparison with rule-based analysis prior to the advent of deep learning In contrast with such conventional approaches, we adopted a novel approach that coupled a deep convolutional neural network (CNN) with a seemingly overwhelming amount of powder XRD pattern data without the use of any handcrafted feature engineering. We constructed a virtuous circle that was composed of no feature engineering (no data contraction), but only contained a deep CNN architecture, and big data Such revolutionary and unprecedented CNN modelling for a powder XRD pattern classification enabled us to predict the crystal systems, the extinction groups and the space groups of totally unknown materials.
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