Bilbao Crystallographic Server SYMMODES Documentation Help

A software package for group-theoretical analysis of structural phase transitions

C.Capillas, E.Kroumova, M.I. Aroyo, J. M. Pérez-Mato, H.T. Stokes and D. Hatch

Dept. Física de la Materia Condensada , Universidad del País Vasco, Apdo 644, 48080 Bilbao, Spain
Dept. of Physics and Astronomy, Brigham Young University, Provo, Utah 84602 USA.

Keywords: Phase transitions, symmetry break, primary and secondary modes.

The problem

The analysis of symmetry break in a structural phase transition.

The method

Consider a structural phase transition with a symmetry change G > H, where the low-symmetry space group H is a subgroup of the high-symmetry group G. The main steps of the symmetry analysis carried out by SYMMODES can be summarized as follows:

  1. Given the space-group types of G and H, and their index, the SUBGROUPGRAPH module constructs the lattice of maximal subgroup s relating G and H. All possible subgroups Hj of the type of H are listed, and their distribution into classes of conjugate subgroups is indicated. In addition, the program also supplies the corresponding transformation matrices relating the (conventional) bases of G to each of the subgroups Hj. By specifying the relevant subgroup Hj of G the module returns the particular graph of maximal subgroups for G > Hj. The results on the group-subgroup relations for the chain G > H obtained by the program SUBGROUPGRAPH are based on the data of maximal subgroups of space groups available in International Tables for Crystallography, vol.A1 (2003).

  2. For a given symmetry break G > Hj and a crystal structure specified by the Wyckoff positions of the occupied atomic orbits, the program calculates:

The program

Input Data

  1. The space groups ITA numbers.
  2. The index of the transformation and the subgroup type or the matrix transformation that relates both space groups.
  3. Wyckoff Positions of the atoms.

Output data

  1. Group - Subgroup relations, matrix transformations and classification.
  2. Order parameters, isotropy groups and k - vectors.
  3. The primary and secondary modes according to the irreps of G for each of the Wyckoff positions.
  4. Wyckoff positions splitting.


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