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. Here, 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]
- Colorado School of Mines, Golden, CO (United States); National Renewable Energy Lab. (NREL), Golden, CO (United States)
- National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Publication Date:
- Research Org.:
- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); USDOE Office of Energy Efficiency and Renewable Energy (EERE)
- OSTI Identifier:
- 1603932
- Alternate Identifier(s):
- OSTI ID: 1600852
- Report Number(s):
- NREL/JA-5K00-76277
Journal ID: ISSN 0021-9606; MainId:12719;UUID:1676ee1d-4b5e-ea11-9c31-ac162d87dfe5;MainAdminID:1199; TRN: US2104692
- Grant/Contract Number:
- AC36-08GO28308; DMR-1945010
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 152; Journal Issue: 7; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- 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, Félix, Graf, Peter, and Stevanović, Vladan. Matching Crystal Structures Atom-to-Atom. United States: N. p., 2020.
Web. doi:10.1063/1.5131527.
Therrien, Félix, Graf, Peter, & Stevanović, Vladan. Matching Crystal Structures Atom-to-Atom. United States. https://doi.org/10.1063/1.5131527
Therrien, Félix, Graf, Peter, and Stevanović, Vladan. Thu .
"Matching Crystal Structures Atom-to-Atom". United States. https://doi.org/10.1063/1.5131527. https://www.osti.gov/servlets/purl/1603932.
@article{osti_1603932,
title = {Matching Crystal Structures Atom-to-Atom},
author = {Therrien, Félix and Graf, Peter and Stevanović, 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. Here, 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 = {Thu Feb 20 00:00:00 EST 2020},
month = {Thu Feb 20 00:00:00 EST 2020}
}
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