Layer groups: Brillouin‐zone and crystallographic databases on the Bilbao Crystallographic Server

Abstract

The section of the Bilbao Crystallographic Server (https://www.cryst.ehu.es/) dedicated to subperiodic groups contains crystallographic and Brillouin‐zone databases for the layer groups. The crystallographic databases include the generators/general positions (GENPOS), Wyckoff positions (WYCKPOS) and maximal subgroups (MAXSUB). The Brillouin‐zone database (LKVEC) offers k‐vector tables and Brillouin‐zone figures of all 80 layer groups which form the background of the classification of their irreducible representations. The symmetry properties of the wavevectors are described applying the so‐called reciprocal‐space‐group approach and this classification scheme is compared with that of Litvin & Wike [(1991), Character Tables and Compatibility Relations of the Eighty Layer Groups and Seventeen Plane Groups. New York: Plenum Press]. The specification of independent parameter ranges of k vectors in the representation domains of the Brillouin zones provides a solution to the problems of uniqueness and completeness of layer‐group representations. The Brillouin‐zone figures and k‐vector tables are described in detail and illustrated by several examples.

The set of databases of the Bilbao Crystallographic Server (https://www.cryst.ehu.es/) including crystallographic data on generators, general positions, Wyckoff positions, maximal subgroups and Brillouin‐zone figures and k‐vector tables for all 80 layer groups are discussed in detail and illustrated.