E. Kroumova

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.

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.

SUPERGROUPS - a computer program for the determination of the supergroups of the space groups

The problem of the determination of the supergroups of a given space group is of rather general interest. It is useful in phase-transition problems, in the search for overlooked symmetries in a crystal structure determination, or in the detection of pseudosymmetries as a tool for predicting higher-temperature phase transitions (Igartua et al., 1996). In all these applications, it is not suf®cient to know the space-group types of the supergroups of a given group; rather, it is necessary to have available all the different supergroups Gj > H which are isomorphic to G, and are of the same index [i]. In the literature, there are very few papers treating the supergroups of space groups in any detail (Koch, 1984; Wondratschek & Aroyo, 2001). In the International Tables for Crystallography, Vol. A, Space Group Symmetry (1983), one ®nds only listings of minimal supergroups of space groups, which, in addition, are not explicit: they only provide for each space group H the list of those space-group types in which H occurs as a maximal subgroup, i.e to which minimal supergroups of H belong. It is rather dif®cult to determine all supergroups Gj > H if only the types of the minimal supergroups are known. The program SUPERGROUPS solves this problem for a given ®nite index [i].

Prediction of new displacive ferroelectrics through systematic pseudosymmetry search. Results for materials with Pba2 and Pmc21 symmetry

Polar structures with pseudosymmetry related to a hypothetical non-polar configuration are considered as good candidates for ferroelectrics. Recently, a procedure has been developed for a systematic pseudosymmetry search among structures with a given space-group symmetry. The aim of this paper is the extension of the pseudosymmetry procedure to the case of structures with polar symmetry and its application in the search for new ferroelectrics. The results obtained by the generalized pseudosymmetry search among the compounds with symmetries Pba2 and Pmc2(1) listed in the Inorganic Crystal Structure Database are discussed. The calculations have been performed by the program PSEUDO, which forms part of the Bilbao Crystallographic Server (http://www.cryst.ehu.es). In addition, an empirical relation between the atomic displacements necessary to reach the non-polar structure and the transition temperature is proposed and compared with the Abrahams-Kurtz-Jamieson relation.

Search for Pnma materials with high-temperature structural phase transitions

A systematic search for structures having a high-temperature structural phase transition can be carried out through the identification in the structural databases of those structures that can be considered pseudosymmetric. Pseudosymmetry in a crystal structure indicates the possibility of a similar configuration of higher symmetry. If the distortion relating both structures is small enough, it can be expected that the crystal acquires the more symmetric configuration through a Landau-type phase transition at a higher temperature. Here, we present the results of such a search among inorganic structures with space group Pnma retrieved from the Inorganic Crystal Structure Database. Pseudosymmetry has indeed been detected in those compounds with a known (displacive) Landau-type phase transition at higher temperatures. This is measured by a parameter Delta, which measures the maximal atomic displacement relating the pseudosymmetry-transformed structure and the original one. In most of these compounds with a known phase transition, this parameter was smaller than 1.0 Å for at least one minimal supergroup of Pnma. The database contains 144 additional structures with pseudosymmetry features under the same quantitative limit. A comparison of the Delta distributions in both sets of compounds suggests a smaller Delta window (with 0.7 Å as maximal value) for selecting the materials having maximal probability of exhibiting a phase transition at higher temperatures. A set of 58 compounds fulfils this criterion.

Systematic search of displacive ferroelectrics

Abstract Polar structures with pseudosymmetry related to a hypothetical non-polar configuration are considered as good candidates for displacive ferroelectrics. Recently we have developed a procedure for the systematic search of pseudosymmetric structures in the available databases. The aim of the present contribution is the generalization of the pseudosymmetry search procedure to include possible displacive ferroelectric structures which implies an additional optimization of the continuous parameter(s) describing the location of the non-polar symmetry elements. Here we present the results of the search for possible displacive ferroelectrics among the compounds with space group Pba 2, listed in the Inorganic Crystal Structure Database.

Ferroelectric–paraelectric phase transitions with no group–supergroup relation between the space groups of both phases?

The structures of Sr(3)(FeF(6))(2), beta-NbO(2), TlBO(2) and CrOF(3), previously reported as possible ferroelectrics with no group-supergroup relation between the ferroelectric and the paraelectric symmetries, have been carefully studied. We could not confirm any structural pseudosymmetry with respect to a space group which is not a supergroup of their room-temperature polar space group. In all cases, pseudosymmetry was indeed detected, but only for non-polar supergroups of the actual space groups of the structures. In this sense, the four compounds are possible ferroelectrics, but fulfilling the usual group-supergroup relation between the phase symmetries.