Brillouin-zone database on the Bilbao Crystallographic Server

Aroyo M. I. , Orobengoa D., de la Flor G., Tasci E. S. , Perez-Mato J. M. , Wondratschek H.

ACTA CRYSTALLOGRAPHICA SECTION A, vol.70, pp.126-137, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70
  • Publication Date: 2014
  • Doi Number: 10.1107/s205327331303091x
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.126-137


The Brillouin-zone database of the Bilbao Crystallographic Server ( offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.