Phase-transition studies at the Bilbao Crystallographic Server

The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with crystallographic databases and programs. The server is built on a core of databases that contain crystallographic data of space groups, magnetic space groups, subperiodic groups and their symmetry relations. Parallel to the crystallographic software we have developed specialized tools for the analysis of complex solid-state physics and structural chemistry problems. The aim of this contribution is to report on databases and computer programs of the server that facilitate complete and thorough phase-transition studies. Starting from the experimental structures of the high- and low-symmetry phases the program STRUCTURE RELATIONS studies the crystal-structure relationship between two phases. It is characterized by a global distortion that, in general, can be decomposed into homogeneous strain and atomic displacement field. The program AMPLIMODES [2] performs the decomposition of the global distortion into symmetry-mode contributions, and the determination of the corresponding polarization vectors. This type of analysis separates the correlated atomic displacements that are fundamental for the phase stability, the so-called primary modes, from the weaker distortions of limited relevance for the transition mechanism. The server also offers online tools for the evaluation of the pseudosymmetry of a given structure with respect to a supergroup of its space group [3]. The detection of structural pseudosymmetry as the consequence of a small distortion of a higher symmetry is a powerful method for the prediction of new ferroic materials. Recently, computer databases and tools for the analysis of magnetic phase transitions have been implemented. Case studies will accompany the presentation of the programs offered by the Bilbao Crystallographic Server and will illustrate their capacities and efficiency in phase-transition studies.

Mode parameterization of structures with very low symmetry: PZT and magnetite

The parameterization of distorted structures in terms of symmetry modes is an effective and efficient method for both their description and refinement [1]. A basis of symmetry-adapted modes transforming according to irreducible representations not only provides a hierarchical division of the degrees of freedom consistent with the mechanism at the origin of the distorted phase, but it allows the avoidance of false refinement minima, typical of highly pseudo-symmetric phases. A reduction of the number of free parameters by setting to zero negligible marginal modes is also possible. The mode description is nowadays easily applicable through freely available programs [2,3], while direct single crystal and powder diffraction refinements under this parameterization are possible combining these programs with some of the most popular refinement codes. The mode description is especially effective when dealing with distorted structures of very low symmetry compared with that of the parent phase. In these cases, the hierarchy between strong primary modes and weak marginal ones is specially pronounced, minimizing the role of many secondary modes. The physical origin of each primary distortion is usually a set of unstable degenerate normal modes. This introduces correlations among the different phases in the phase diagram that become patent in a mode description and can be used both to characterize the evolution of the relevant order parameters and as a stringent test of proposed structural models. Furthermore, the fact that each of the primary mode distortions is basically associated with the activity (instability) of a single normal mode can yield a "single mode" signature in the mode decomposition, which represents a set of subtle additional structural constrains beyond conventional crystallography. We will illustrate these considerations using the examples of the monoclinic phases of ferroelectric PbZr1-xTixO3 (PZT) and the Verwey phase of magnetite.

A collection of magnetic structures with cif-like files as a database seed

We report the release within the Bilbao Crystallographic server [1] of a webpage providing detailed quantitative information on a representative set of published magnetic structures. Under the name of MAGNDATA (www.cryst.ehu.es/magndata) more than 140 entries are available. Each magnetic structure has been saved making use of magnetic symmetry, i.e. Shubnikov magnetic groups for commensurate structures, and magnetic superspace groups for incommensurate ones. This ensures a unified communication method and a robust and unambiguous description of both atomic positions and magnetic moments. The origin and main crystallographic axes of the parent phase are usually kept, with the cost of often using a non-standard setting for the magnetic symmetry. The magnetic point group is also given, so that the allowed macroscopic tensor properties can be derived. The fact that magnetic structures are being described according to various methods, often with ambiguous information, has forced an elaborate interpretation and transformation of the original data. For this purpose the freely available internet tools MAXMAGN [1] and ISODISTORT [2] have been our essential tools. Most of the analyzed structures happen to possess maximal magnetic symmetries within the constraints imposed by the magnetic propagation vector, and the relevant model could be derived in a straightforward manner using MAXMAGN [1]. In a few cases a lower symmetry is realized, but then it corresponded to one isotropy subgroup of one or several irreducible representations (irreps) of the paramagnetic grey space group, and ISODISTORT [2] could be applied to model the structure. Although the structure description is done using magnetic groups, the active irrep(s) are also given in most cases. The entries of the collection can be retrieved in a cif-like format, which is supported by internet tools as STRCONVERT [1] and ISOCIF [2], the visualization program VESTA [3], and some refinement programs (JANA2006, FULLPROF). Each entry also includes Vesta files that allow the visualization of a single magnetic unit cell.