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Updated: May 2, 2026

Fully Autonomous Characterization and Data Collection from Crystals of Biological Macromolecules
Published on: March 22, 2019
Brillouin-zone database on the Bilbao Crystallographic Server
Mois I Aroyo1, Danel Orobengoa1, Gemma de la Flor1
1Departamento Física de la Materia Condensada, Universidad del País Vasco (UPV/EHU), Bilbao, Spain.
Abstract:
The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) 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.
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