Crystalline phase uniquely encoded by stable Voronoi facets

Establish that, for any crystalline phase of a condensed matter system, the set of facets of the atoms’ Voronoi cells that remain stable throughout the portion of the phase diagram corresponding to that phase fully and uniquely encodes the phase.

Background

The paper develops a Voronoi-cell-based framework to encode thermally disordered configurations and the associated Gibbs measure. Using crystalline silicon as a case study, the authors show that four large Voronoi facets persist with probability one up to the melting line and suffice to reconstruct the crystal lattice and quantify the Gibbs measure within the solid phase.

Motivated by this evidence, the authors formulate a general conjecture asserting that for any crystalline phase, the facets of Voronoi cells that remain stable across the relevant region of the phase diagram provide a complete and unique real-space encoding of that phase.