Bilbao Crystallographic Server arrow Subgroups Help

Subgroups: Subgroups compatible with a given supercell or some propagation vector(s).

The program Subgroups provides the possible subgroups of a space group which are possible for a given supercell. The program provides a list of the set of space groups or a graph showing the group-subgroup hierarchy, grouped into conjugacy classes. More optional information about the classes or subgroups is also given.

Other alternatives for the input of the program:

  • Instead of the whole set of subgroups, the output can be limited to subgroups having a chosen common subgroup of lowest symmetry, common point group of lowest symmetry, or groups which belong to a specific crystal class.
  • Instead of a supercell, a set of modulation wave vectors can be given, including complete or partial wave-vectors stars.
  • The subgroups compatible with intermediate unit cells between the unit cell of the parent space group and the given supercell (or the supercell determined by the given wave vector(s) when the previous option is used) can be included.
  • When a set of wave-vectors is used as input, the output can be further refined introducing the Wyckoff positions of the atoms and/or a set of irreducible representations.

  • Tutorial_SUBGROUPS: download

    See the Help for details.
    Enter the serial number of the space group:

    Introduce the supercell

    +++The supercell is centred:

    Include the subgroups compatible with intermediate cells.
    (It is not applied when only the maximal subgroups are calculated)

    Optional: refine further the subgroups of the output giving the Wyckoff positions of the atoms
    Give the Wyckoff positions

    Optional: Show only subgroups that can be the result of a Landau-type transition (single irrep order parameter).

    Possible limitations of the subgroup list.

    (Check only one option on the left and the specific value on the right)
    (Check only one option on the left and the specific value on the right)
    Lowest space group to consider
    Lowest point group to consider
    Lowest crystal system to consider
    Only maximal subgroups

    Further limitations considering physical properties of the point groups

  • Only centrosymmetric/non centrosymmetric groups
  • Only polar/non polar groups
  • Only proper ferroelastic phase transitions
  • List of subgroups Graph of subgroups

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