Comparing crystal structures with symmetry and geometry

Abstract Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically meaningful. Here we introduce both a geo...

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Autores principales:	John C. Thomas, Anirudh Raju Natarajan, Anton Van der Ven
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Materials of engineering and construction. Mechanics of materials TA401-492 Computer software QA76.75-76.765
Acceso en línea:	https://doaj.org/article/02149c6aeff0428eb28b7f7b60254cf9
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spelling	oai:doaj.org-article:02149c6aeff0428eb28b7f7b60254cf92021-12-02T17:13:16ZComparing crystal structures with symmetry and geometry10.1038/s41524-021-00627-02057-3960https://doaj.org/article/02149c6aeff0428eb28b7f7b60254cf92021-10-01T00:00:00Zhttps://doi.org/10.1038/s41524-021-00627-0https://doaj.org/toc/2057-3960Abstract Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically meaningful. Here we introduce both a geometry-based and a symmetry-adapted similarity metric to compare crystal structures. Using crystal symmetry and combinatorial optimization we describe an algorithm to arrive at the structural relationship that minimizes these similarity metrics across all possible maps between any pair of crystal structures. The approach makes it possible to (i) identify pairs of crystal structures that are identical, (ii) quantitatively measure the similarity between crystal structures, and (iii) find and rank structural transformation pathways between any pair of crystal structures. We discuss the advantages of using the symmetry-adapted cost metric over the geometric cost. Finally, we show that all known structural transformation pathways between common crystal structures are recovered with the mapping algorithm. The methodology presented in this study will be of value to efforts that seek to catalogue crystal structures, identify structural transformation pathways or prune large first-principles datasets used to parameterize on-lattice Hamiltonians.John C. ThomasAnirudh Raju NatarajanAnton Van der VenNature PortfolioarticleMaterials of engineering and construction. Mechanics of materialsTA401-492Computer softwareQA76.75-76.765ENnpj Computational Materials, Vol 7, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Materials of engineering and construction. Mechanics of materials TA401-492 Computer software QA76.75-76.765
spellingShingle	Materials of engineering and construction. Mechanics of materials TA401-492 Computer software QA76.75-76.765 John C. Thomas Anirudh Raju Natarajan Anton Van der Ven Comparing crystal structures with symmetry and geometry
description	Abstract Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically meaningful. Here we introduce both a geometry-based and a symmetry-adapted similarity metric to compare crystal structures. Using crystal symmetry and combinatorial optimization we describe an algorithm to arrive at the structural relationship that minimizes these similarity metrics across all possible maps between any pair of crystal structures. The approach makes it possible to (i) identify pairs of crystal structures that are identical, (ii) quantitatively measure the similarity between crystal structures, and (iii) find and rank structural transformation pathways between any pair of crystal structures. We discuss the advantages of using the symmetry-adapted cost metric over the geometric cost. Finally, we show that all known structural transformation pathways between common crystal structures are recovered with the mapping algorithm. The methodology presented in this study will be of value to efforts that seek to catalogue crystal structures, identify structural transformation pathways or prune large first-principles datasets used to parameterize on-lattice Hamiltonians.
format	article
author	John C. Thomas Anirudh Raju Natarajan Anton Van der Ven
author_facet	John C. Thomas Anirudh Raju Natarajan Anton Van der Ven
author_sort	John C. Thomas
title	Comparing crystal structures with symmetry and geometry
title_short	Comparing crystal structures with symmetry and geometry
title_full	Comparing crystal structures with symmetry and geometry
title_fullStr	Comparing crystal structures with symmetry and geometry
title_full_unstemmed	Comparing crystal structures with symmetry and geometry
title_sort	comparing crystal structures with symmetry and geometry
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/02149c6aeff0428eb28b7f7b60254cf9
work_keys_str_mv	AT johncthomas comparingcrystalstructureswithsymmetryandgeometry AT anirudhrajunatarajan comparingcrystalstructureswithsymmetryandgeometry AT antonvanderven comparingcrystalstructureswithsymmetryandgeometry
_version_	1718381359587655680

Comparing crystal structures with symmetry and geometry

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