Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass

TL;DR

This paper introduces a topological method called persistence diagrams to analyze medium-range order in amorphous materials, providing a robust, scalable way to distinguish structural features from crystalline and random configurations.

Contribution

The paper presents a novel topological approach using persistence diagrams to characterize medium-range order in amorphous materials, enhancing analysis robustness and scalability.

Findings

Persistence diagrams effectively distinguish amorphous, crystalline, and random structures.

The method reduces data complexity, enabling efficient structural analysis.

Potential applications extend to molecular liquids, granular materials, and metallic glasses.

Abstract

Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. The method is called the persistence diagram (PD) and it introduces scales into many-body atomic structures in order to characterize the size and shape. We first illustrate how perfect crystalline and random structures are represented in the PDs. Then, the medium-range order in the amorphous silica is characterized by using the PD. The PD approach reduces the size of the data tremendously to much smaller geometrical summaries and has a huge potential to be applied to broader areas including complex molecular liquid, granular materials, and metallic glasses.