Matching Crystal Structures Atom-to-Atom

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 optimiza...

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Bibliographic Details
Published in:arXiv.org 2020-02
Main Authors: Therrien, Félix, Graf, Peter, Stevanović, Vladan
Format: Article
Language:English
Subjects:
Algorithms
Crystal structure
Crystals
Euclidean geometry
Grain boundaries
Matching
Materials science
Optimization
Periodic variations
Phase transitions
Solid phases
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.12965