Classification and enumeration of solid-solid phase transition mechanisms

A crystal-structure match (CSM), the atom-to-atom correspondence between two crystalline phases, is used extensively to describe solid-solid phase transition (SSPT) mechanisms. However, existing computational methods cannot account for all possible CSMs. Here, we propose a formalism to classify all CSMs into a tree structure, which is independent of the choices of unit cell and supercell. We rigorously proved that only a finite number of noncongruent CSMs are of practical interest. By representing CSMs as integer matrices, we introduce the crystmatch method to exhaustively enumerate them, which uncontroversially solves the CSM optimization problem under any geometric criterion. For most SSPTs, crystmatch can reproduce all known deformation mechanisms and CSMs within 10 CPU minutes, while also revealing thousands of new candidates. The resulting database can be further used for comparing experimental phenomena, high-throughput energy barrier calculations, or machine learning.