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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Bibliographic Details
Published inActa crystallographica. Section A, Foundations and advances Vol. 77; no. 5; pp. 453 - 459
Main Author Cayron, Cyril
Format Journal Article
LanguageEnglish
Published 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.09.2021
Subjects
hyperplane unit cell
integer relation
N‐dimensional Bézout's identity
Research Papers
twinning
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ISSN2053-2733
2053-2733
DOI10.1107/S2053273321006835

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Summary: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. The paper describes a method to determine a short unit cell attached to any hyperplane given by its integer vector p. Equivalently, it gives all the solutions of the N‐dimensional Bézout's identity associated with the coordinates of p.
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ISSN:2053-2733
2053-2733
DOI:10.1107/S2053273321006835