A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplane...

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Detalles Bibliográficos
Autor principal: Cayron, Cyril
Formato: Online Artículo Texto
Lenguaje:English
Publicado: International Union of Crystallography 2021
Materias:
Research Papers
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8477640/
https://www.ncbi.nlm.nih.gov/pubmed/34473098
http://dx.doi.org/10.1107/S2053273321006835
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author Cayron, Cyril
author_facet Cayron, Cyril
author_sort Cayron, Cyril
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description Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them. Equivalently, it gives the solutions of the N-dimensional Bézout’s identity associated with the Miller indices of the hyperplane.
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spelling pubmed-84776402021-10-04 A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities Cayron, Cyril Acta Crystallogr A Found Adv Research Papers Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them. Equivalently, it gives the solutions of the N-dimensional Bézout’s identity associated with the Miller indices of the hyperplane. International Union of Crystallography 2021-08-13 /pmc/articles/PMC8477640/ /pubmed/34473098 http://dx.doi.org/10.1107/S2053273321006835 Text en © Cyril Cayron 2021 https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
spellingShingle Research Papers
Cayron, Cyril
A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title_full A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title_fullStr A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title_full_unstemmed A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title_short A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout’s identities
title_sort fast algorithm to find reduced hyperplane unit cells and solve n-dimensional bézout’s identities
topic Research Papers
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8477640/
https://www.ncbi.nlm.nih.gov/pubmed/34473098
http://dx.doi.org/10.1107/S2053273321006835
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