32 research outputs found
Irreducible Representations of Diperiodic Groups
The irreducible representations of all of the 80 diperiodic groups, being the
symmetries of the systems translationally periodical in two directions, are
calculated. To this end, each of these groups is factorized as the product of a
generalized translational group and an axial point group. The results are
presented in the form of the tables, containing the matrices of the irreducible
representations of the generators of the groups. General properties and some
physical applications (degeneracy and topology of the energy bands, selection
rules, etc.) are discussed.Comment: 30 pages, 5 figures, 28 tables, 18 refs, LaTex2.0
Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space groups
International audienceThe Second Report of the Subcommittee on the Nomenclature of n-Dimensional Crystallography recommends specific symbols for R-irreducible groups in 4 and higher dimensions (nD), for centrings, for Bravais classes, for arithmetic crystal classes and for space groups (space-group types). The relation with higher-dimensional crystallographic groups used for the description of aperiodic crystals is brie Ě„y discussed. The Introduction discusses the general definitions used in the Report