Matching Crystal Structures Atom-to-Atom

TL;DR

This paper introduces an optimization-based algorithm for atom-to-atom matching in crystal structures, enabling accurate modeling of phase transitions, interfaces, and quantifying structural similarities.

Contribution

It presents a novel algorithm for crystal matching that handles large structures and defines a rigorous metric for structural similarity.

Findings

Successfully models transformation pathways between polymorphs

Reproduces structures of semi-coherent interfaces

Defines a quantitative metric for crystal structure comparison

Abstract

Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In this work, we formulate the matching of crystals as an optimization problem where the goal is to find the alignment and the atom-to-atom map that minimize a given cost function such as the Euclidean distance between the atoms. We construct an algorithm that directly solves this problem for large finite portions of the crystals and retrieves the periodicity of the match subsequently. We demonstrate its capacity to describe transformation pathways between known polymorphs and to reproduce experimentally realized structures of semi-coherent interfaces. Additionally, from our findings we define a rigorous metric for measuring distances between crystal structures that can be used to properly quantify their geometric (Euclidean) closeness.