Crystal planes and reciprocal space in Clifford geometric algebra

DOI10.1002/mma.1442zbMath1219.74009arXiv1306.1646OpenAlexW1973488643MaRDI QIDQ3087911

Eckhard M. S. Hitzer

Publication date: 17 August 2011

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.1646

zbMATH Keywords

crystallographyClifford geometric algebraphase anglestructure factors\(d\)-spacingBragg reflectionsinterfacial anglesreciprocal space

Mathematics Subject Classification ID

Crystalline structure (74E15) Clifford algebras, spinors (15A66)

Related Items (4)

Algebraic foundations of split hypercomplex nonlinear adaptive filtering ⋮ Double conformal geometric algebra ⋮ Geometric roots of \(-1\) in Clifford algebras \(C \ell_{p,q}\) with \(p + q \leq 4\) ⋮ Unified spatial intersection algorithms based on conformal geometric algebra

Uses Software

• CLUCalc
• KamiWaAi

Cites Work

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• Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups.
• Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like
• Euclidean geometric objects in the Clifford geometric algebra of \{origin, 3-space, infinity\}
• New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford
• Crystallographic space groups in geometric algebra
• Generalized Exponentials through Appell sets in R[sup n+1 and Bessel functions]

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