Unravelling the density-driven modification of the topology generated by the interconnection of SiO₄ tetrahedra in silica polymorphs

Abstract

The topology of materials is an important structural feature, which cannot be determined from crystallographic information in crystalline materials and pairwise correlations in disordered materials. We extracted the density-driven modification of the topology of tetrahedral silica (SiO₂) crystals, siliceous zeolites (MFI, SOD, and FAU), and glass on the basis of the results of ring size, homology, cavity distribution, and tetrahedral order analyses. A series of analyses confirmed a universal feature that oxygen atoms are buckled in –Si–O– rings except in some symmetrical even-numbered rings such as twelvefold (Si–O)₁₂ rings in coesite and SOD/FAU. In addition, large cavities were found in β-cristobalites and siliceous zeolites, whose cavity volume ratios are much higher than that of SiO₂ glass. A comparison between α- and β-cristobalite indicated that the arrangement of oxygen atoms governs the formation of cavities. Moreover, a topological similarity between glass and MFI was found, in which fivefold and sevenfold rings are observed in the King ring size distribution. This feature can break their symmetry because these odd-number rings are not observed in other SiO₂ polymorphs. Moreover, it was suggested that SiO₂ glass is crystallographically an analogue to β-cristobalite in terms of the position of the diffraction peak, but topologically an analogue to MFI. It is demonstrated that the topological analyses provide us with crucial information for the design of novel nonequilibrium materials at high pressures and/or high temperatures by tuning density.