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Title: Matching Crystal Structures Atom-to-Atom

Abstract

Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and 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.

Authors:
 [1];  [1];  [1]
  1. National Renewable Energy Laboratory (NREL), Golden, CO (United States)
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1603932
Report Number(s):
NREL/JA-5K00-76277
DOE Contract Number:  
AC36-08GO28308
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 152; Journal Issue: 7
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; crystal lattices; metric geometry; optimization problems; functions and mappings; polymorphism; phase transitions; crystal structure

Citation Formats

Therrien, Felix, Graf, Peter A, and Stevanovic, Vladan. Matching Crystal Structures Atom-to-Atom. United States: N. p., 2020. Web. doi:10.1063/1.5131527.
Therrien, Felix, Graf, Peter A, & Stevanovic, Vladan. Matching Crystal Structures Atom-to-Atom. United States. doi:10.1063/1.5131527.
Therrien, Felix, Graf, Peter A, and Stevanovic, Vladan. Thu . "Matching Crystal Structures Atom-to-Atom". United States. doi:10.1063/1.5131527.
@article{osti_1603932,
title = {Matching Crystal Structures Atom-to-Atom},
author = {Therrien, Felix and Graf, Peter A and Stevanovic, Vladan},
abstractNote = {Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and 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.},
doi = {10.1063/1.5131527},
journal = {Journal of Chemical Physics},
number = 7,
volume = 152,
place = {United States},
year = {2020},
month = {2}
}

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