Preview: Forthcoming article in Acta Crystallographica Section A: Foundations of Crystallography
Forthcoming article in Acta Crystallographica Section A Foundations and Advances
Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination
A general algorithm for generating isotropy subgroups in superspace
Irreducible representations can now be used to derive the isotropy subgroups at irrational wavevectors, making it relatively easy to explore the (3 + d)-dimensional superspace-group symmetries that arise from incommensurate modulations of a parent crystal structure. A general algorithm capable of arbitrary superpositions of multiple incommensurate and commensurate order parameters is presented.
Ordering of convex polyhedra and the Fedorov algorithm
The relation between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the ordering of convex n-acra is found. A method to weakly order the convex n-acra by the maximum extra valencies of their vertices is suggested.
Lattice reduction using a Euclidean algorithm
The reduction of a crystal lattice is considered. The reduction associated with the existence of a commensurate translation that leaves the crystal invariant is addressed, and a practical scheme for it is provided.