A fast algorithm to find reduced hyperplane unit cells and solve N‐dimensional Bézout's identities. Issue 5 (13th August 2021)

• Record Type: Journal Article
• Authors: Cayron, Cyril
• Is Part Of: Acta crystallographica. Volume 77:Issue 5(2021)
• Page Start: 453
• Page End: 459
• Publication Date: 2021-08-13
• Subjects: N‐dimensional Bézout's identity -- hyperplane unit cell -- integer relation -- twinning; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273321006835
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : 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 . Abstract : 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.