日本結晶学会誌
Online ISSN : 1884-5576
Print ISSN : 0369-4585
ISSN-L : 0369-4585
特集 結晶学と情報学の融合
パーシステントホモロジーを用いた非晶質物質の回折パターンの理解と二体相関に潜んだトポロジーの抽出
小原 真司坂田 修身小野寺 陽平大林 一平志賀 元紀平田 秋彦平岡 裕章
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2020 年 62 巻 1 号 p. 43-50

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The structure of disordered materials is still not well understood, due to the lack of structural information from diffraction data. In this article, attempts are made to reveal the information on the topology of crystalline and disordered materials by utilizing persistent homology analyses. The persistence diagram of silica (SiO2) glass indicates that the shape of rings in the glass is similar not only to those in the crystalline phase with comparable density (α-cristobalite), but also to rings present in crystalline phases with higher density (α-quartz and coesite). This behavior is a result of disorder, because the shape of rings in silica glass is buckled, which can be observed in high density crystalline phases. Furthermore, we have succeeded in revealing the differences, in terms of persistent homology, between tetrahedral networks and tetrahedral molecular liquids, and the difference between liquid and amorphous states. A combination of diffraction data and persistent homology analyses is a useful tool for allowing us to uncover structural features hidden in the pairwise correlations.

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