C. Capillas

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.

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.

Methods for pseudosymmetry evaluation: a comparison between the atomic displacements and electron density approaches

Abstract Structural pseudosymmetry is a fundamental property to be considered when trying to predict structural phase transitions at high temperatures. In the present work, two methods for detecting and characterizing pseudosymmetry, the here-called atomic displacements and electron density methods are briefly introduced, analyzed and compared. Conceptually both approaches are similar: the pseudosymmetry check is carried out with respect to a supergroup of the crystal space group. However, due to the different way of estimating the deviations between the initial and the possible high-symmetry structure, the two approaches study distinct and, to a certain extent, complementary aspects of the pseudosymmetry problem. This conclusion is also confirmed by the lack of functional relationship between the corresponding quantitative parameters used to estimate the structural pseudosymmetry. Several examples illustrate the main features of the two methods. The temperature dependences of the two parameters and their empirical relations with the transition temperature in ferroelectric transitions are discussed. Algorithmic procedures based on the two approaches have been implemented in two computer programs. They form part of the Bilbao Crystallographic Server as free web tools.

The Bilbao Crystallographic Server

The Bilbao Crystallographic Server, http://www.cryst.ehu.es, is a web site providing free online access to crystallographic programs and databases. The server provides access to general information related to space groups (generators, general positions, Wyckoff positions and representations of crystallographic groups). Computer programs for the analysis of group–subgroup or group–supergroup relations of space groups and for the study of specific problems related to solid-state physics, structural chemistry and crystallography also form part of the Bilbao Crystallographic Server. The server has been operating since 1998 and new applications are being added regularly. The aim of the present chapter is to report on the different databases and programs of the server related to the subject of this volume. Section 1.7.2 presents the relevant databases and retrieval tools that access the stored symmetry information. The crystallographic computing programs related to group–subgroup and group–supergroup relations between space groups are presented in Section 1.7.3. A computer tool for the analysis of the relations of Wyckoff positions for a group–subgroup pair of space groups is introduced in Section 1.7.4. The group-theoretical background of the programs that have been developed is briefly explained and details of the necessary input data and the output results are given. Illustrative examples demonstrate the use of the programs. Keywords: Bilbao Crystallographic Server

Search for New Pna21 Ferroelectrics

Two different pseudosymmetry-search methods are compared and applied in the search for new ferroelectrics among the binary, ternary and quaternary compounds of Pna21 symmetry. Among the 322 compounds with this symmetry, 18 candidates for ferroelectrics are detected.