Quantification of local geometry and local symmetry in models of disordered materials

TL;DR

This paper introduces two new metrics to evaluate local geometry and symmetry in disordered material models, providing more sensitive assessments than traditional pair correlation-based metrics.

Contribution

The paper proposes novel metrics for assessing local geometric invariance and symmetry, enhancing the analysis of disordered material configurations without relying on group theory.

Findings

Metrics effectively rank SiO2 and a-Si configurations

Metrics are more sensitive to unphysical features than pair correlation methods

Implementation in reverse Monte Carlo shows limitations in energy landscape resolution

Abstract

We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first metric is that of geometric invariance: i.e., the extent to which the neighbour arrangements are as similar as possible for different atoms, allowing for variations in frame of reference. The second metric concerns the degree of local symmetry. We propose that for a set of configurations with equivalent pair correlations, ranking highly those configurations with low geometric invariance but with high local symmetry selects for structural simplicity in a way that does not rely on formal group theoretical language (and hence long-range periodic order). We show that these metrics rank a range of SiO2 and a-Si configurations in an intuitive manner, and are also significantly more sensitive to unphysical features of those configurations in a way that metrics based on pair correlations are not. We also report that implementation of the metrics within a reverse Monte Carlo algorithm gives rise to an energy landscape that is too coarse (at least in this initial implementation) for amorphous structure "solution".