Hierarchical structures of amorphous solids characterized by persistent homology

TL;DR

This paper introduces a topological approach using persistent homology to analyze and classify hierarchical structures in various amorphous solids, revealing detailed geometric features and their relation to material properties.

Contribution

It presents a novel application of persistent homology to characterize hierarchical structures in amorphous solids, providing deeper geometric insights than traditional methods.

Findings

Classified atomic rings in silica glass into short- and medium-range orders.

Unveiled hierarchical ring structures and their relation to diffraction peaks.

Demonstrated applicability to different amorphous systems like Lennard-Jones and Cu-Zr glasses.

Abstract

This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones system, and Cu-Zr metallic glass as standard examples of continuous random network and random packing structures. In silica glass, the method classified the atomic rings as short-range and medium-range orders and unveiled hierarchical ring structures among them. These detailed geometric characterizations clarified a real space origin of the first sharp diffraction peak and also indicated that PDs contain information on elastic response. Even in the Lennard-Jones system and Cu-Zr metallic glass, the hierarchical structures in the atomic configurations were derived in a similar way using PDs, although the glass structures and properties substantially differ from silica glass. These results suggest that the PDs provide a unified method that extracts greater depth of geometric information in amorphous solids than conventional methods.