Emre S. Tasci

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.

Brillouin-zone database on the Bilbao Crystallographic Server.

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.

AN ALGORITHM TO GENERATE TOROIDAL AND HELICAL CAGE STRUCTURES USING PENTAGONS, HEXAGONS AND HEPTAGONS

An algorithm to generate toroidal or helical cage structures has been developed. Any toroidal or helical structure can be generated following four stages. In the first stage a Fonseca type unit cell and its symmetrical counterpart is formed which represents one-fifth of a toroid. In the second stage one-fifth fragment of the torus is fully obtained by applying geometry optimization to the structure obtained in the first stage. In the third stage the torus fragment obtained in the second stage is reproduced five times and connected to each other to generate either toroidal or helical structure. In the last stage a final optimization process is reapplied to get the complete structure desired.

A survey of the structural models proposed for PbZr1−xTixO3 using mode analysis

The numerous structures that have been reported for the different phases of the lead zirconate titanate system, PbZr1−xTixO3 (PZT), are analysed by means of a systematic symmetry-mode analysis. The distortion corresponding to the order parameter has been separated out and expressed in all phases in a comparable form. The fact that the physical origin of the PZT phases is an unstable threefold degenerate polar mode, plus in some cases an unstable octahedral tilting mode, produces structural correlations between the different phases. These correlations had remained unnoticed until now but are directly observable in a mode parameterization. They can be used both to characterize the evolution of the order parameters through the phase diagram and as a stringent test of the reported structural models. It is further shown that the activity of a single polar mode yields a specific feature in the mode decomposition of the monoclinic phases. This single-mode signature can be observed in the majority of the monoclinic structures proposed, making the others questionable. In fact, this internal constraint is satisfied by PZT to such a high degree that it drastically reduces the number of effective structural degrees of freedom. It is conjectured that this type of structural constraint beyond space-group symmetry can be a rather general property of low-symmetry distorted structures. As shown here, its existence can be detected and assessed by a symmetry-mode analysis, if considered in relation to the single underlying multidimensional order parameter.

Stability of Carbon Nanotori under Heat Treatment: Molecular‐Dynamics Simulations

Abstract The structural stability of carbon nanotori have been investigated by performing molecular‐dynamics simulations. The systems considered are C170, C250, C360, C520 and C750 tori, which have been constructed using a recently developed algorithm based on the idea of Fonseca et al. Calculations, have been realized by using an empirical many‐body potential energy function for carbon. It has been found that all the nanotori considered are stable under heat treatment.

Symmetry conditions for type II multiferroicity in commensurate magnetic structures

Type II multiferroics are magnetically ordered phases that exhibit ferroelectricity as a magnetic induced effect. We show that in single-k magnetic phases the presence in the paramagnetic phase of non-symmorphic symmetry combined with some specific type of magnetic propagation vector can be sufficient for the occurrence of this type of multiferroic behaviour. Other symmetry scenarios especially favourable for spin driven multiferroicity are also presented. We review and classify known type II multiferroics under this viewpoint. In addition, some other magnetic phases which due to their symmetry properties can exhibit type II multiferroicity are pointed out.

JUNCTION FORMATION IN CROSSED NANOTUBES UNDER PRESSURE: MOLECULAR-DYNAMICS SIMULATIONS

Junction formation in crossed C(10,0) single wall carbon nanotubes under pressure has been investigated, using classical molecular-dynamics simulations at 1 K. It has been found that a stable mechanical junction was formed by means of placing two crossed single wall carbon nanotubes between two rigid graphene layers which move toward each other.

Materials studies by the Bilbao Crystallographic Server

The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with an access to crystallographic data of space and point groups, magnetic space groups, subperiodic groups, their representations and group-subgroup relations [1]. Wide range of complex solid-state physics and structure-chemistry aspects of materials studies are facilitated by the specialized software provided by the server. The server offers a set of structure-utility programs including basic tools for transformations between different structure descriptions or transformations compatible with a specific symmetry reduction. There is an online tool (COMPSTRU) for a quantitative analysis of the similarity of two structure models, also helpful for the recognition of identical or nearly identical atomic arrangements of different compounds. The program STRUCTURE RELATIONS for the analysis of structure relations between two phases of the same compound with group-subgroup related space groups is of great utility for the construction of family trees of homeotypic crystal structures, known as Baernighausen trees.
 The program AMPLIMODES performs the decomposition of the global distortion into symmetry-mode contributions and classifies the correlated atomic displacements separating the so-called primary modes (fundamental for the phase stability), from the weaker distortions of limited relevance for the transition mechanism [2]. 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, which could serve as a powerful method for the prediction of new ferroic materials. Of special interest is the program SUBGROUPS which extends further the capabilities of the server in the symmetry characterization of distorted structures by providing their possible subgroup symmetries given the relationship of the distorted to the parent undistorted lattice. Recently implemented computational tools and databases in the server allow the systematic application of symmetry arguments in the study of magnetic structures [3]. There is an online access to basic crystallographic data of magnetic space groups in different settings (MGENPOS, MWYCKPOS), to the systematic absences for non-polarized neutron magnetic diffraction and also to the symmetry-adapted forms of the corresponding structure factors (MAGNEXT). The user can identify a magnetic space group from its symmetry operations given in an arbitrary setting (IDENTIFY MAGNETIC GROUP), derive the possible magnetic space groups for a given set of propagation vectors (MAXMAGN, k-SUBGROUPSMAG) or generate a magnetic structure model complying with a chosen magnetic space group (MAGMODELIZE). The server offers an access to a database of more than 400 published magnetic structures (MAGNDATA) described using magnetic space groups for commensurate structures, and magnetic superspace groups for incommensurate structures. The presentation of the databases and programs offered by the Bilbao Crystallographic Server will be accompanied by case studies illustrating the capacity and efficiency of the online tools in material studies.

Crystallography online by the Bilbao Crystallographic Server

Received January 7, 2011; Revised April 19, 2011 The Bilbao Crystallographic Server is a web site with crystallographic databases and programs available online (www.cryst.ehu.es). It has been operating for more than ten 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 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. There are also software package studying specific problems of solid-state physics, structural chemistry and crystallography.

Structural properties of indium phosphide nanorods: molecular dynamics simulations

We study the structural properties of the indium phosphide nanorods of different thickness in zinc blende and wurtzite phases by performing classical molecular dynamics simulations using an inter-atomic potential. In addition to different temperatures, the nanorods are also investigated under strain and compression. When the stretch is applied, simulations reveal that the sequence of the irreversible structural transformation for the zinc blende nanorods is zinc blende → rock salt → wurtzite and the wurtzite nanorods follow the sequence of wurtzite → rock salt. After the wurtzite nanorods are compressed and stretched back, the thinner nanorods recover their initial non-deformed structure. Upon heating without stretching, the zinc blende nanorods undergo a transition from the zinc blende phase to the rock salt formation and the wurtzite phase is not observed, whereas the wurtzite nanorods transform from the wurtzite to the rock salt phases. For the wurtzite nanorods, a heating procedure is also carried out at a constant temperature to observe the annealing effect. The wurtzite nanorods are subjected to two approaches processes to observe if the transition processes are reversible: in the first process, the heated wurtzite nanorods are cooled down; in the second process, the cooled nanorods are put under strain. It has been observed that the transition is always irreversible for the nanorods once they are completely transformed into the rock salt phase whereas it is usually reversible for the nanorods before the complete transition into the rock salt phase has occurred. The reversible transition is also observed as the cooled nanorod is stretched back.