Statistical Topology of Bond Networks with Applications to Silica

TL;DR

This paper introduces a probabilistic framework for analyzing disordered materials' structures using local atomic environment descriptors, demonstrated on silica glasses, bridging the gap between ordered and disordered material analysis.

Contribution

It proposes four novel descriptors for local atomic environments in disordered bond networks, unifying the analysis of ordered and disordered materials.

Findings

Descriptors effectively distinguish silica glasses formed at different cooling rates.

H1 barcode and coordination profile provide the best structural separation.

Framework offers a new way to analyze medium-range order in disordered materials.

Abstract

Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are not obvious analogues to unit cells for disordered materials despite the frequent existence of considerable medium-range order. This article views a material's structure as a collection of local atomic environments that are sampled from some underlying probability distribution of such environments, with the advantage of offering a unified description of both ordered and disordered materials. Crystalline materials can then be regarded as special cases where the underlying probability distribution is highly concentrated around the traditional unit cell. Four descriptors of local atomic environments suitable for disordered bond networks are proposed and applied to molecular dynamics simulations of silica glasses. Each of them reliably distinguishes the structure of glasses produced at different cooling rates, with the $H_1$ barcode and coordination profile providing the best separation.