Mois I. Aroyo

Bilbao Crystallographic Server: I. Databases and crystallographic computing programs

Abstract The Bilbao Crystallographic Server is a web site with crystallographic databases and programs available on-line at www.cryst.ehu.es. It has been operating for about six years and new applications are being added regularly. The programs available on the server do not need a local installation and can be used free of charge. The only requirement is an Internet connection and a web browser. The server is built on a core of databases, and contains different shells. The innermost one is formed by simple retrieval tools which serve as an interface to the databases and permit to obtain the stored symmetry information for space groups and layer groups. The k-vector database includes the Brillouin zones and the wave-vector types for all space groups. As a part of the server one can find also the database of incommensurate structures. The second shell contains applications which are essential for prob lems involving group-subgroup relations between space groups (e.g. subgroups and supergroups of space groups, splittings of Wyckoff positions), while the third shell contains more sophisticated programs for the computation of space-group representations and their correlations for group-subgroup related space groups. There are also programs for calculations focused on specific problems of solid-state physics. The aim of the article is to report on the current state of the server and to provide a brief description of the accessible databases and crystallographic computing programs. The use of the programs is demonstrated by illustrative examples.

Bilbao Crystallographic Server : Useful Databases and Tools for Phase-Transition Studies

Bilbao Crystallographic Server is a web site with crystallographic programs and databases available on-line. The programs give access to general information related to space groups (generators, general positions, Wyckoff positions, irreducible representations), group-subgroup or group-supergroup pairs of space groups, and/or results on specific crystal structures. The utility of the programs is illustrated by treating phase-transition problems related to structural pseudosymmetry.

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups.

The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line (http://www.cryst.ehu.es). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc.). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group-subgroup pairs of space groups and for the decompositions of Kronecker products of representations.

AMPLIMODES: symmetry-mode analysis on the Bilbao Crystallographic Server

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.

Mode crystallography of distorted structures

The description of displacive distorted structures in terms of symmetry-adapted modes is reviewed. A specific parameterization of the symmetry-mode decomposition of these pseudosymmetric structures defined on the setting of the experimental space group is proposed. This approach closely follows crystallographic conventions and permits a straightforward transformation between symmetry-mode and conventional descriptions of the structures. Multiple examples are presented showing the insight provided by the symmetry-mode approach. The methodology is shown at work, illustrating its various possibilities for improving the characterization of distorted structures, for example: detection of hidden structural correlations, identification of fundamental and marginal degrees of freedom, reduction of the effective number of atomic positional parameters, quantitative comparison of structures with the same or different space group, detection of false refinement minima, systematic characterization of thermal behavior, rationalization of phase diagrams and various symmetries in families of compounds etc. The close relation of the symmetry-mode description with the superspace formalism applied to commensurate superstructures is also discussed. Finally, the application of this methodology in the field of ab initio or first-principles calculations is outlined. At present, there are several freely available user-friendly computer tools for performing automatic symmetry-mode analyses. The use of these programs does not require a deep knowledge of group theory and can be applied either a posteriori to analyze a given distorted structure or a priori to parameterize the structure to be determined. It is hoped that this article will encourage the use of these tools. All the examples presented here have been worked out using the program AMPLIMODES [Orobengoa et al. (2009). J. Appl. Cryst. 42, 820-833].

Short-range B -site ordering in the inverse spinel ferrite NiFe 2 O 4

. The numberof experimentally observed Raman modes exceeds significantly that expected for a normal spinelstructure and the polarization properties of most of the Raman lines provide evidence for a micro-scopic symmetry lower than that given by the Fd¯3m space group. We argue that the experimentalresults can be explained by considering the short range 1:1 ordering of Ni

Topological quantum chemistry

Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.

A new computer tool at the Bilbao Crystallographic Server to detect and characterize pseudosymmetry

Abstract New ferroelectrics can be predicted by considering the existence of pseudosymmetry with respect to a higher symmetry structure using the so-called atomic displacement method and investigating the minimal supergroups of the given structure’s space group. This analysis can be performed with the new version of the computer program PSEUDO, located at the Bilbao Crystallographic Server. After defining the procedures for the detection and quantification of pseudosymmetry, we present the new program, illustrating its use with worked cases of polar structures from the literature which are either known or reported as possible ferroelectrics.

PSEUDO: a program for a pseudo- symmetry search

The program PSEUDO provides tools for the systematic search of pseudosymmetry, based on group±subgroup relations between space groups (Igartua et al., 1996). For a crystal structure L, speci®ed by its space group U, the cell parameters and the coordinates of the atoms in the asymmetric unit, the program searches for pseudosymmetry among all minimal supergroups Gk > U of the group U. The interpretation of a structural pseudosymmetry as a small distortion of a higher symmetric (prototype) structure H allows the following. (i) The prediction of phase transitions at higher temperature. If the distortion is small enough, it can be expected that the crystal acquires the more symmetric con®guration at a higher temperature after a phase transition (Igartua et al., 1996, 1999). (ii) The search for new ferroelastic and ferroelectric materials. Polar structures having atomic displacements smaller than 1 AE with respect to a hypothetical non-polar con®guration are considered as possible ferroelectrics (Abrahams & Keve, 1971; Kroumova et al., 2000). (iii) The detection of false symmetry assignments (overlooked symmetry) in crystal structure determination.

WYCKSPLIT: a computer program for determination of the relations of Wyckoff positions for a group-subgroup pair

The category Computer Program Abstracts provides a rapid means of communicating up-to-date information concerning both new programs or systems and significant updates to existing ones. Following normal submission, a Computer Program Abstract will be reviewed by one or two members of the IUCr Commission on Crystallographic Computing. It should not exceed 500 words in length and should follow the standard format given on page 189 of the June 1985 issue of the Journal [J. AppL Cryst. (1985). 18, 189190] and on the World Wide Web at http://www.iucr. org/journals/jac/software/. Lists of software presented and/or reviewed in the Journal of Applied Crystallography are available on the World Wide Web at the above address, together with information about the availability of the software where this is known.