A Topological Framework for Local Structure Analysis in Condensed Matter

TL;DR

This paper introduces a topological framework based on Voronoi cell topology for analyzing local structures in both ordered and disordered condensed matter systems, addressing challenges posed by imperfections and thermal effects.

Contribution

It presents a unified, practical topological method for classifying local structures in complex materials, improving upon traditional continuous approaches.

Findings

Topological description effectively captures local structural variations.

Method links local topology to physical behavior and defect identification.

Application potential in analyzing high-temperature deformations and disordered systems.

Abstract

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent particles, understanding that structure is a primary objective of condensed matter research. Although perfect crystals are fully described by a set of translation and basis vectors, real-world materials are never perfect, as thermal vibrations and defects introduce significant deviation from ideal order. Meanwhile, liquids and glasses present yet more complexity. A complete understanding of structure thus remains a central, open problem. Here we propose a unified mathematical framework, based on the topology of the Voronoi cell of a particle, for classifying local structure in ordered and disordered systems that is powerful and practical. We explain the underlying reason why this topological description of local structure is better suited for structural analysis than continuous descriptions. We demonstrate the connection of this approach to the behavior of physical systems and explore how crystalline structure is compromised at elevated temperatures. We also illustrate potential applications to identifying defects in plastically deformed polycrystals at high temperatures, automating analysis of complex structures, and characterizing general disordered systems.