Bilbao Crystallographic Server is an open access website offering online crystallographic database and programs aimed at analyzing, calculating and visualizing problems of structural and mathematical crystallography, solid state physics and structural chemistry. Initiated in 1997 by the Materials Laboratory of the Department of Condensed Matter Physics at the

University of the Basque Country The University of the Basque Country ( eu, Euskal Herriko Unibertsitatea, ''EHU''; es, Universidad del País Vasco, ''UPV''; UPV/EHU) is a Spanish public university of the Basque Autonomous Community. Heir of the University of Bilbao, initiall ...

, Bilbao, Spain, the Bilbao Crystallographic Server is developed and maintained by academics.

Information on contents and an overview of tools hosted

Focusing on crystallographic data and applications of the group theory in solid state physics, the server is built on a core of databases and contains different shells.

Space Groups Retrieval Tools

The set of databases includes data from ''International Tables of Crystallography, Vol. A: Space-Group Symmetry'', and the data of maximal subgroups of space groups as listed in ''International Tables of Crystallography, Vol. A1: Symmetry relations between space groups''. A k-vector database with

Brillouin zone In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice ...

figures and classification tables of the k-vectors for space groups is also available via th
KVEC
tool.

Magnetic Space Groups

In 2011, the Magnetic Space Groups data compiled from H.T. Stokes & B.J. Campbell's and D. Litvin's's works

general position In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are ...

symmetry operation In group theory, geometry, representation theory and molecular symmetry, a symmetry operation is a transformation of an object that leaves an object looking the same after it has been carried out. For example, as transformations of an object in spac ...

s and

Wyckoff positions In crystallography, a Wyckoff position is a point belonging to a set of points for which site symmetry groups are conjugate subgroups of the space group. Crystallography tables give the Wyckoff positions for different space groups. For any point i ...

for different settings, along with systematic absence rules have also been incorporated into the server and a new shell has been dedicated to the related tools
MGENPOSMWYCKPOS
.

Group-Subgroup Relations of Space Groups

This shell contains applications which are essential for problems involving group-subgroup relations between space groups. Given the space group types of G and H and their index, the progra
SUBGROUPGRAPH
provides graphs of

maximal subgroup In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' ...

s for a group-subgroup pair G > H, all the different subgroups H and their distribution into

conjugacy class In mathematics, especially group theory, two elements a and b of a group are conjugate if there is an element g in the group such that b = gag^. This is an equivalence relation whose equivalence classes are called conjugacy classes. In other wo ...

es. The Wyckoff position splitting rules for a group-subgroup pair are calculated by the progra
WYCKSPLIT

Representation Theory Applications

The fourth shell includes programs on

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...

and point groups
REPRES
constructs

little group In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism g ...

and full group irreducible representations for a given space group and a k-vector
CORREL
deals with the correlations between the irreducible representations of group-subgroup related space groups. The progra

lists

character table In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group elements. The entries consist of character ...

s of crystallographic point groups, Kronecker multiplication tables of their irreducible representations and further useful symmetry information.

Solid State Theory Applications

This shell is related to solid state physics and structural chemistry. The progra
PSEUDO
performs an evaluation of the ''pseudosymmetry'' of a given structure with respect to supergroups of its space group

performs the 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 low symmetry structures, the program calculates the amplitudes and polarization vectors of the distortion modes of different symmetry frozen in the structure. The progra

calculates symmetry-adapted modes for the centre of the Brillouin zone and classifies them according to their

infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...

and Raman activity
NEUTRON
computes the phonon extinction rules in inelastic

neutron scattering Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. Th ...

. Its results are also relevant for diffuse-scattering experiments.

Structure Utilities

A set of structure utilities has been included for various applications such as: the transformation of

unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...

s
CELLTRAN
or complete structures

;

strain tensor In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimal ...

calculation
STRAIN
; assignment of

Wyckoff Positions In crystallography, a Wyckoff position is a point belonging to a set of points for which site symmetry groups are conjugate subgroups of the space group. Crystallography tables give the Wyckoff positions for different space groups. For any point i ...

WPASSIGN
; equivalent descriptions of a given structure

; comparison of different structures with support for the affine

normalizer In mathematics, especially group theory, the centralizer (also called commutant) of a subset ''S'' in a group ''G'' is the set of elements \mathrm_G(S) of ''G'' such that each member g \in \mathrm_G(S) commutes with each element of ''S'', o ...

s of

monoclinic In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic s ...

space groups
STRUCTURE RELATIONS
calculates the possible transformation matrices for a given pair of group-subgroup related structures.

Incommensurate Crystal Structures Database

The Bilbao Crystallographic Server also hosts th
B-IncStrDB: Bilbao Incommensurate Crystal Structures Database
a database for incommensurately modulated and composite structures.

Scientific Research

In addition to receiving citations from scientific articles and theses, the Bilbao Crystallographic Server also actively publishes research reports in internationally reviewed articles, as well as hosting/participating in international workshops, summer schools and conferences. A list of these publications and events are accessible from th

Development History and People

The Bilbao Crystallographic Server came to life in 1997 as a scientific project by th
Departments of Condensed Matter Physics and Applied Physics II
of the

(EHU) under the supervision of J. Manuel Perez-Mato (EHU) and Mois I. Aroyo (EHU), in coordination with Gotzon Madariaga (EHU) and Hans Wondratschek ( Karlsruhe Institute of Technology, Germany) with funding from the Basque government and several ministries of the Spanish government. The initial code was written by then Ph.D. students Eli Kroumova (EHU) and Svet Ivantchev (EHU) and the very first shells related to retrieval tools, group-subgroup relations and space group representations have soon appeared online. Afterwards, in collaboration with Harold T. Stokes and Dorian M. Hatch from

Brigham Young University Brigham Young University (BYU, sometimes referred to colloquially as The Y) is a private research university in Provo, Utah. It was founded in 1875 by religious leader Brigham Young and is sponsored by the Church of Jesus Christ of Latter-d ...

, USA, the server extended its services to include symmetry modes analysis. Asen K. Kirov, a Ph.D. student from

Sofia University Sofia University, "St. Kliment Ohridski" at the University of Sofia, ( bg, Софийски университет „Св. Климент Охридски“, ''Sofijski universitet „Sv. Kliment Ohridski“'') is the oldest higher education i ...

, Bulgaria contributed to the server, working on programs dedicated to

irreducible representations In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero representation that has no proper nontrivial subrepresentation (\rho, _W,W ...

and extinction rules. In 2001, Ph.D. student Cesar Capillas began his research on the server and became the main developer and system administrator focusing on structure relations, such as pseudosymmetry and

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states o ...

s. Danel Orobengoa, also a Ph.D. student, joined the developer team in 2005 and worked mainly on symmetry modes, k-vector classification tables and non-characteristic orbits (in collaboration with Massimo Nespolo of the

Nancy-Université Nancy-Université federated the three principal institutes of higher education of Nancy, France, Nancy, in Lorraine (region), Lorraine, France before their merger into the University of Lorraine: * Henri Poincaré University (UHP, also known as ...

, France), writing his Ph.D. thesis on the applications of the server for ferroic materials. In 2009, Ph.D. student Gemma de la Flor and post-doc Emre S. Tasci were recruited for the development team: de la Flor working mainly on the identification and interpretation of

s, structure comparison and Tasci becoming the new system administrator and main developer, focusing in the structure relations concerning phase transitions. The Bilbao Crystallographic Server team took its current (2012) line-up in 2010 with the addition of Ph.D. student Samuel Vidal Gallego, his main research field being the magnetic space groups."About the Bilbao Crystallographic Server", Bilbao Crystallographic Server's official wiki entry.
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References

External links

* {{Official website, www.cryst.ehu.es Crystallography Science software Crystallographic databases Scientific databases