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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. 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:
ORCiD logo [1];  [2]; ORCiD logo [1]
  1. Colorado School of Mines, Golden, CO (United States); National Renewable Energy Lab. (NREL), Golden, CO (United States)
  2. National Renewable Energy Lab. (NREL), Golden, CO (United States)
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Next Generation of Materials Design (CNGMD)
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
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. doi:10.1063/1.5131527.
Therrien, Félix, Graf, Peter, and Stevanović, 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, 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 = {2020},
month = {2}
}

Journal Article:
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Works referenced in this record:

Mismatched lattices patched up
journal, March 2016

  • Poeppelmeier, Kenneth R.; Rondinelli, James M.
  • Nature Chemistry, Vol. 8, Issue 4
  • DOI: 10.1038/nchem.2477

Computational Approach for Epitaxial Polymorph Stabilization through Substrate Selection
journal, May 2016

  • Ding, Hong; Dwaraknath, Shyam S.; Garten, Lauren
  • ACS Applied Materials & Interfaces, Vol. 8, Issue 20
  • DOI: 10.1021/acsami.6b01630

A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

  • Henkelman, Graeme; Uberuaga, Blas P.; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22, p. 9901-9904
  • DOI: 10.1063/1.1329672

A generalized solid-state nudged elastic band method
journal, February 2012

  • Sheppard, Daniel; Xiao, Penghao; Chemelewski, William
  • The Journal of Chemical Physics, Vol. 136, Issue 7
  • DOI: 10.1063/1.3684549

Finding transition states for crystalline solid-solid phase transformations
journal, April 2005

  • Caspersen, K. J.; Carter, E. A.
  • Proceedings of the National Academy of Sciences, Vol. 102, Issue 19
  • DOI: 10.1073/pnas.0408127102

Variable cell nudged elastic band method for studying solid–solid structural phase transitions
journal, September 2013

  • Qian, Guang-Rui; Dong, Xiao; Zhou, Xiang-Feng
  • Computer Physics Communications, Vol. 184, Issue 9
  • DOI: 10.1016/j.cpc.2013.04.004

O-Lattice calculation of an F.C.C.–B.C.C. interface
journal, February 1974


Bollmann's 0-Iattice theory; a geometrical approach to interface structure
journal, January 1976


CSL/DSC Lattice model for general crystalcrystal boundaries and their line defects
journal, August 1982


Crystallography and morphology of Widmanstätten cementite in austenite
journal, August 1998


Crystallographic study of grain refinement in aluminum alloys using the edge-to-edge matching model
journal, March 2005


Lattice match: An application to heteroepitaxy
journal, January 1984

  • Zur, A.; McGill, T. C.
  • Journal of Applied Physics, Vol. 55, Issue 2
  • DOI: 10.1063/1.333084

MPInterfaces: A Materials Project based Python tool for high-throughput computational screening of interfacial systems
journal, September 2016


Determination of low-strain interfaces via geometric matching
journal, August 2017


Metrics for measuring distances in configuration spaces
journal, November 2013

  • Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian
  • The Journal of Chemical Physics, Vol. 139, Issue 18
  • DOI: 10.1063/1.4828704

How to quantify energy landscapes of solids
journal, March 2009

  • Oganov, Artem R.; Valle, Mario
  • The Journal of Chemical Physics, Vol. 130, Issue 10
  • DOI: 10.1063/1.3079326

On representing chemical environments
journal, May 2013


Proposed definition of crystal substructure and substructural similarity
journal, August 2014


Comparing molecules and solids across structural and alchemical space
journal, January 2016

  • De, Sandip; Bartók, Albert P.; Csányi, Gábor
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 20
  • DOI: 10.1039/c6cp00415f

A fingerprint based metric for measuring similarities of crystalline structures
journal, January 2016

  • Zhu, Li; Amsler, Maximilian; Fuhrer, Tobias
  • The Journal of Chemical Physics, Vol. 144, Issue 3
  • DOI: 10.1063/1.4940026

Determination of reduced cells
journal, January 1970


A unified algorithm for determining the reduced (Niggli) cell
journal, March 1976


Predicting kinetics of polymorphic transformations from structure mapping and coordination analysis
journal, March 2018


Identifying duplicate crystal structures: XtalComp, an open-source solution
journal, March 2012


Maximal symmetry transition paths for reconstructive phase transitions
journal, June 2007


A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration
journal, March 2019


Method for registration of 3-D shapes
conference, April 1992

  • Besl, Paul J.; McKay, Neil D.
  • Robotics - DL tentative, SPIE Proceedings
  • DOI: 10.1117/12.57955

Iterative Global Similarity Points: A Robust Coarse-to-Fine Integration Solution for Pairwise 3D Point Cloud Registration
conference, September 2018

  • Pan, Yue; Yang, Bisheng; Liang, Fuxun
  • 2018 International Conference on 3D Vision (3DV)
  • DOI: 10.1109/3DV.2018.00030

Recent developments and trends in point set registration methods
journal, July 2017

  • Maiseli, Baraka; Gu, Yanfeng; Gao, Huijun
  • Journal of Visual Communication and Image Representation, Vol. 46
  • DOI: 10.1016/j.jvcir.2017.03.012

The Hungarian method for the assignment problem
journal, March 1955


hcp-bcc structural phase transformation of titanium: Analytic model calculations
journal, November 2004


Nucleation mechanism for the direct graphite-to-diamond phase transition
journal, July 2011

  • Khaliullin, Rustam Z.; Eshet, Hagai; Kühne, Thomas D.
  • Nature Materials, Vol. 10, Issue 9
  • DOI: 10.1038/nmat3078

Communication: From graphite to diamond: Reaction pathways of the phase transition
journal, September 2012

  • Xiao, Penghao; Henkelman, Graeme
  • The Journal of Chemical Physics, Vol. 137, Issue 10
  • DOI: 10.1063/1.4752249

The transition mechanism between the CsCl-type and NaCl-type structures in CsCl
journal, March 1977


Transition path for the B 3 B 1 phase transformation in semiconductors
journal, October 2000


On the transition from the wurtzite to the NaCl type
journal, March 2001


Edge-to-edge matching model for predicting orientation relationships and habit planes—the improvements
journal, May 2005


The crystallographic mechanism of the martensite reaction in iron-carbon alloys
journal, March 1951


The crystallography of martensite transformations I
journal, January 1954


The crystallography of martensite transformations II
journal, January 1954


GPU-accelerated Hungarian algorithms for the Linear Assignment Problem
journal, September 2016


Structure of the Equilibrated Ni(111)‐ YSZ (111) Solid–Solid Interface
journal, October 2015

  • Nahor, Hadar; Kaplan, Wayne D.
  • Journal of the American Ceramic Society, Vol. 99, Issue 3
  • DOI: 10.1111/jace.14015

Atomic-scale characterization of Si(110)/6H-SiC(0001) heterostructure by HRTEM
journal, January 2016


R 1 -PCA: rotational invariant L 1 -norm principal component analysis for robust subspace factorization
conference, January 2006

  • Ding, Chris; Zhou, Ding; He, Xiaofeng
  • Proceedings of the 23rd international conference on Machine learning - ICML '06
  • DOI: 10.1145/1143844.1143880