Topological Data Analysis for Revealing the Structural Origin of Density Anomalies in Silica Glass.

Topological data analysis (TDA) is a newly emerging and powerful tool for understanding the medium-range structure ordering of multiscale data. This study investigates the density anomalies observed during the cooling of liquid silica from a topological point of view using TDA. The density of liquid silica does not monotonically increase during cooling; it instead shows a maximum and minimum. Despite tremendous efforts, the structural origin of these density anomalies is not clearly understood. Our approach reveals that the one-dimensional topology of the -Si-Si- network changes at the temperatures at which the maximum and minimum densities are observed in our MD simulations, while those of the -O-O- and -Si-O- networks change at lower temperatures. Our ring analysis motivated by the TDA outcomes reveals that quantitative changes in -Si-Si- rings occur at the temperatures where the density is maximized and minimized, while those of the -O-O- and -Si-O- rings occur at lower temperatures; such findings are perfectly consistent with our TDA results. Our work demonstrates the value of new topological techniques in understanding the transitions in glassy materials and sheds light on the characterization of glass-liquid transitions.