TheThe 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

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.

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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.

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