AMPLIMODES is a computer program available on the Bilbao Crystallographic Server that can perform a symmetry‐mode analysis of any distorted structure of displacive type. The analysis consists in ...decomposing the symmetry‐breaking distortion present in the distorted structure into contributions from different symmetry‐adapted modes. Given the high‐ and the low‐symmetry structures, AMPLIMODES determines the atomic displacements that relate them, defines a basis of symmetry‐adapted modes, and calculates the amplitudes and polarization vectors of the distortion modes of different symmetry frozen in the structure. The program uses a mode parameterization that is as close as possible to the crystallographic conventions, expressing all quantities for the asymmetric unit of the low‐symmetry structure. Distorted structures are often related to their higher‐symmetry counterparts by temperature‐ and/or pressure‐driven phase transitions, ferroic phase transitions being a particular example. The automatic symmetry‐mode analysis performed by AMPLIMODES can be very useful for establishing the driving mechanisms of such structural phase transitions or the fundamental instabilities at the origin of the distorted phases.
A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The ...double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin‐dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single‐ and double‐valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The program DSITESYM implements the so‐called site‐symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.
A new section of computer tools devoted to the double crystallographic groups has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The section includes databases of symmetry operations and irreducible representations of the double point and space groups and programs that compute the compatibility relations, generate relevant information related to the site‐symmetry approach, and calculate band representations and elementary band representations induced from any Wyckoff position of any double space group.
A quantitative comparison of similar crystal structures is often convenient to cross‐check different experimental and/or theoretical structural models of the same phase coming from different sources. ...It is also important for the identification of different phases with the same symmetry, and it is fundamental for the still open problem of the classification of structures into structure types. In most cases, even if the setting of its space group is fixed, there is more than one equivalent description for a given structure. The existence of various equivalent structure descriptions makes the comparison of different structural models a non‐trivial task in general. To deal with it, the program COMPSTRU has been developed, available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The program measures the similarity between two structures having the same space‐group symmetry (or space groups that form an enantiomorphic pair) with the same or different compositions, and under the condition that the sequence of the occupied Wyckoff positions is the same in both structures (isopointal structures). The efficiency and utility of the program are demonstrated by a number of illustrative examples. It is also shown how the program can be used to outline different structure types within a set of isopointal structures.
The program COMPSTRU, available on the Bilbao Crystallographic Server (http://www.cryst.ehu.es), for the comparison of structures is presented. The utility of the program is discussed and illustrated with several examples.
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.
The section of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) dedicated to subperiodic groups includes a new tool called LSITESYM for the study of materials with layer and multilayer ...symmetry. This new program, based on the site‐symmetry approach, establishes the symmetry relations between localized and extended crystal states using representations of layer groups. The efficiency and utility of the program LSITESYM is demonstrated by illustrative examples, which include the analysis of phonon symmetry in Aurivillius compounds and in van der Waals layered crystals MoS2 and WS2.
The program LSITESYM of the Bilbao Crystallographic Server (http://www.cryst.ehu.es), which establishes symmetry relations between localized and extended states in crystals with layer symmetry, is presented. The utility of the program is discussed and illustrated with several examples.
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