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Machine learning clustering technique applied to X-ray diffraction patterns to distinguish alloy substitutions

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SmFe12 is one of the candidate of the main phase in rare-earth permanent magnets [1]. The origin of intrinsic properties emerging at high temperature as well as that of the phase stability has not yet been clarified well. Introducing Ti and Zr to substitute Fe and Sm is found to improve the magnetic properties and the phase stability. To clarify the mechanism how the substitutions improve the properties, it is desired to identify substituted sites and its amount quantitatively, preferably with high throughput efficiency for accelerating the ‘materials tuning’. Motivated by the above, we have developed [2] a machine learning clustering technique to distinguish powder XRD patterns to get such microscopic identifications about the atomic substitutions. Ab initio calculations are used to generate supervising references for the machine learning of XRD patterns: We prepared several possible model structures with substituents located on each different sites over a range of substitution fractions. Geometrical optimizations for each model give slight different structures each other. Then we generated many XRD patterns calculated from each structure. We found that the DTW (dynamic time wrapping) analysis can capture slight shifts in XRD peak positions corresponding to the differences of each relaxed structure, distinguishing the fractions and positions of substituents. We have established such a clustering technique using Ward’s analysis on top of the DTW , being capable to sort out simulated XRD patterns based on the distinction. The established technique can hence learn the correspondence between XRD peak shifts and microscopic structures with substitutions over many supervising simulated data. Since the ab initio simulation can also give several properties such as magnetization for each structure, the correspondence in the machine learning can further predict functional properties of materials when it is applied to the experimental XRD patterns, not only being capable to distinguish the atomic substitutions. The ‘machine learning technique for XRD patterns’ developed here has therefore the wider range of applications not limited only on magnets, but further on those materials which properties are tuned by the atomic substitutions.

We also provide our updated challenges using deep learning technique applied to XRD patterns.


1. K. Kobayashi et al., J. Magn. Magn. Mater. 426, 273 (2017).

2. K. Utimula, R. Hunkao, M. Yano, H. Kimoto, K. Hongo, S. Kawaguchi, S.Suwanna, R. Maezono, arXiv:1810.03972.

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