Brillouin-zone databases

The k-vector data of the Brillouin-zone database of the Bilbao Crystallographic Server are accessed by the retrieval tool KVEC which uses as input the ITA-number of the space group [1]. The output consists essentially of wave-vector tables and figures. There are several sets of figures and tables for the same space group when its Brillouin-zone shape depends on the lattice parameters of the reciprocal lattice. The k-vector data are the same for space groups of the same arithmetic crystal class.

In the k-vector tables, the wave-vector data of CDML [2] are compared with the Wyckoff-position data of ITA. Each k-vector type is specified by its label and coefficients as listed in CDML. The corresponding Wyckoff positions are described by Wyckoff letters, multiplicities and site-symmetry groups. The parameter descriptions specify the independent parameter ranges chosen in such a way that each orbit of the Wyckoff positions of ITA, i. e. each k-vector orbit is also listed exactly once. In the figures, the Brillouin zones of CDML and the conventional unit cells of ITA are displayed. The asymmetric units play the role of the representation domains of the Brillouin zones and they are chosen often in analogy to those of ITA.

[1] International tables for Crystallography, Volume A: Space-Group Symmetry (1983). Edited by Th. Hahn, 5th revised edition (2002). Dordrech: Kluwer Acad. Publ. Abbreviated ITA.

[2] Cracknell, A. P., Davies, B.L., Miller, S. C. & Love, W. F. (1979). Kronecker Product Tables. Volume 1. General Introduction and Tables of Irreducible Representation of Space Groups. New York: IFI/Plenum. Abbreviated CDML.

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