2020 年 62 巻 1 号 p. 43-50
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.