Revealing the Void-Size Distribution of Silica Glass using Persistent Homology

TL;DR

This study addresses the challenge of characterizing medium-range order in silica glass by applying persistent homology (PH) to atomistic simulations of glass under ambient and high-pressure conditions. By constructing persistence diagrams ($H_1$ for loops and $H_2$ for cavities) and filtering them to isolate chemically meaningful rings and voids, the authors quantify how ring-size and void-size distributions evolve during densification. They find pressure-driven topological transitions: rings contract toward smaller sizes and cavities shrink and eventually disappear, accompanied by a shift from corner-sharing to edge/face-sharing polyhedral connectivity. The PH-derived descriptors offer a robust, topology-based framework for linking structure to properties in oxide glasses and can be extended to other amorphous materials for targeted design.

Abstract

Oxide glasses have proven to be useful across a wide range of technological applications. Nevertheless, their medium-range structure has remained elusive. Previous studies focused on the ring statistics as a metric for the medium-range structure, which, however, provides an incomplete picture of the glassy structure. Here, we use atomistic simulations and state-of-the-art topological analysis tools, namely persistent homology (PH), to analyze the medium-range structure of the archetypal oxide glass (Silica) at ambient temperatures and with varying pressures. PH presents an unbiased definition of loops and voids, providing an advantage over other methods for studying the structure and topology of complex materials, such as glasses, across multiple length scales. We captured subtle topological transitions in medium-range order and cavity distributions, providing new insights into glass structure. Our work provides a robust way for extracting the void distribution of oxide glasses based on persistent homology.

Figures (25)

• Figure 1: (a) Schematic representation of the steps involved in the persistence diagrams construction. The steps involve having cloud points (left) and increasing of spheres' radii. When the spheres touch and make a closed loop, the coordinates of the radius at which this event happens are recorded as the birth time. With further increase of the radius, this loop will eventually close, and the radius at which this happens is recorded again as the death time of the loop. Both these birth and death pairs constitute a point on the persistence diagram (right), which is a histogram counting the number of voids on the birth-death plane. Persistence diagrams that correspond to (b) $H_1$ and (c) $H_2$ showing the topological feature of silica glass at 300 K and with 0 external pressure. The region highlighted by the transparent red box is for an island made of chemically connected loops, referred to later as rings as well. While the region highlighted in the yellow box is for the detected loops that are not chemically bonded. The insets in (b) and (c) show snapshots of loops and cavities detected in the glass. The silicon and oxygen atoms are colored in light brown and red, respectively.
• Figure 2: The density change during the cold compression at 300 K compared with the experimental data from Refs. Sato2008Petitgirard2017.
• Figure 3: Pair distances as a function of hydrostatic pressure (a) Si--O and (b) O--O calculated by fitting the first peak of the pair distribution functions (See Fig. \ref{['FIGS:rdf']} in SM) to a skewed normal distribution Sukhomlinov2017. Experimental values for the Si--O pair distances are also given as a reference Murakami2019Prescher2017Sato2010Benmore2010Meade1992.
• Figure 4: Pressure dependence of (a) mean Si--O coordination number SiO$_n$, (b) the SiO$_n$ species, (c) mean O--Si coordination number, and (d) oxygen species in the glasses during compression. The average experimental data of the CN of Si--O in (a), and CN of O--Si in (c) are from Refs. Kono2020Petitgirard2019Lee2019.
• Figure 5: SiO$_m$--SiO$_n$ sharing modes (a) Corner, (b) Edge, and (c) Face per polyhedron calculated as a function of pressure.