Graph theory-based structural analysis on density anomaly of silica glass

Analyzing the atomic structure of glassy materials is a tremendous challenge both experimentally and computationally, and the lack of direct, detailed insights into glass structure hinders our ability to navigate structure-property relationships. For instance, the structural origin of the density anomaly in silica glasses - the negative thermal expansion coefficient - is still poorly understood. Simulations based on molecular dynamics (MD) produce atomically resolved structures, but quantifying the role of disorder in the density anomaly is challenging. Here, we propose to use a a graph-theoretical approach to assess topological differences between disordered structural arrangements from MD trajectories of silica glasses. A graph similarity metric quantifies the similarity between the covalent networks and can characterize the nature of the disordered solid, by comparing to reference crystalline solids, or with glasses in different thermodynamic states . This approach involves casting all-atom glass configurations as networks, and subsequently applying a graph-similarity metric (D-measure). Calculated D-measure values are then taken as the topological distances between two configurations. By measuring the topological distances of silica glass configurations across a range of temperatures, distinct structural features could be observed at temperatures higher than the fictive temperature. In addition, we compared topological distances between local atomic environments in the glass and crystalline silica phases. This approach suggests that more coesite-like and quartz-like local structures emerge in silica glasses when the density is at a minimum during the heating process.