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.
Highlights
IntroductionThe Bilbao Crystallographic Server (https://www.cryst.ehu.es/) (Aroyo et al, 2006, 2011; Tasci et al, 2012) is a free web site that grants access to specialized databases and tools for the resolution of different types of crystallographic, structural chemistry and solid-state physics problems
The Bilbao Crystallographic Server (Aroyo et al, 2006, 2011; Tasci et al, 2012) is a free web site that grants access to specialized databases and tools for the resolution of different types of crystallographic, structural chemistry and solid-state physics problems
A recently implemented auxiliary tool permits the identification of the Wyckoff position and the site-symmetry operations of a point specified by its coordinate triplet [see Fig. 2(b)]
Summary
The Bilbao Crystallographic Server (https://www.cryst.ehu.es/) (Aroyo et al, 2006, 2011; Tasci et al, 2012) is a free web site that grants access to specialized databases and tools for the resolution of different types of crystallographic, structural chemistry and solid-state physics problems. A k-vector database with Brillouinzone figures and classification tables of the wavevectors for all 230 space groups (Aroyo et al, 2014) is available in the server, together with the magnetic and double-space-group databases. To the best of our knowledge, the only complete compilation of layer-group k vectors together with the Brillouin-zone diagrams is found in the work of Litvin & Wike (1991) (in the following, referred to as LW). In this description the k vectors are labelled following the classification scheme of space-group k vectors used by Cracknell et al (1979). The utility of the programs is demonstrated by several illustrative examples
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