Quantifying Gibbs measures of disordered crystals up to the solid-liquid phase transition

TL;DR

This paper introduces a novel method to quantify the Gibbs measure of disordered crystals up to melting by reconstructing atomic lattices from Voronoi cell statistics, revealing fundamental phase signatures.

Contribution

It demonstrates that Voronoi cell analysis can fully reconstruct crystal lattices and identify phase-specific features, providing a new approach to study disordered condensed matter systems.

Findings

Voronoi cells reveal four large facets in silicon crystals up to melting.

These facets are consistent across all temperatures below melting.

The collection of facets offers an optimal representation of the crystal configuration.

Abstract

Quantifying the configuration space and the Gibbs measure of thermally disordered condensed matter systems has been a long standing problem. The challenge is to avoid the Gibbs paradox, which forbids any ordering or labeling of the atoms. Our key observation is that the lattice of a thermally disordered condensed matter system, in either solid, liquid or gas phase, can be fully reconstructed from the Voronoi cells of the atoms alone, even if these Voronoi cells are disassembled and randomly scrambled. In the example of the crystalline phase of silicon, the statistics of the Voronoi cells reveals the existence of four, and only four, large facets that are present with probability one for all temperatures up to the solid-liquid melting line. These four largest facets, which separate nearest-neighboring atoms, can be also be used to reconstruct the lattice of the crystal. Hence, their collection supplies the optimal representation of the configuration of the crystal. We conjecture that the existence of Voronoi facets that, despite their large thermal fluctuations, survive with probability one up to the melting temperature, is the fundamental signature of the crystalline solid phase and therefore key to quantifying the Gibbs measure over the entire solid phase.