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SYMMODES - Symmetry Modes

Online Help

The software package SYMMODES (Symmetry Modes) provides the necessary tools for a group-theoretical analysis of a structural phase transition characterized by a symmetry change G-H, with G > H. The package combines modules of the programs SUBGROUPGRAPH, WYCKSPLIT and the program SOPD (Subgroup Graph Order-Parameter Displacements). The latter has been developed by H. Stokes and D. Hatch (Brigham Young University, Utah, USA) and is a dedicated segment of the package ISOTROPY.

Input Data

Examples and screenshots

Step 1:Identification of the group-subgroup pair.

Example: (option 1)

Supergroup Number62
Subgroup Number33

This is the look and feel of the first form in the option 1. The user must specify the supergroup(G) and subgroup(H) numbers and the index [i].

Given the space groups G, H and their index, the program returns a list of all possible subgroups Hj (of the space group type H) with this index. Each subgroup is specified by the transformation matrix relating its basis to that of G. Different transformation matrices leading to the same subgroup Hj are listed under 'Identical'. The subgroups Hj are distributed into classes of conjugate subgroups. The user is expected to check from the list the relevant subgroup Hj.

Example: (option 2)

Supergroup Number62
Subgroup Number33
Transformation Matrix
 1  0  0   0
 0  0  1   0
 0 -1  0   0

This is the look and feel of the first form in option 2. The user must specify the supergroup(G) and subgroup(H) ITA numbers and the transformation matrix that relates the bases of G and H.

Step 2: Wyckoff Positions of the high-symmetry structure

Given the group-subgroup pair G > H, the program returns a list of the Wyckoff positions of G. The user is expected those Wyckoff positions which correspond to the occupied orbits of G.


G = Pnma and occupied Wyckoff positions 8d and 4c.

Output Data

The results of the symmetry analysis can be summarized as follows:

  1. Given the space-group types of G and H, and their index(in the option 1), the program constructs the lattice of maximal subgroups relating G and H and provides:

    Example: To see the results for the symmetry break Pnma > Pna21 with index 2, click here.

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

    Example: Splitting scheme of the Wyckoff position 8d for the symmetry break Pnma > Pna21.

    Representative Subgroup Wyckoff position
    No group basis subgroup basis name[n] representative
    1 (x, y, z ) (x, y, z ) 4a1 (x1, y1, z1 )
    2 (-x, y+1/2, -z ) (-x, -y, z+1/2 ) (-x1, -y1, z1+1/2 )
    3 (x+1/2, y, -z-1/2 ) (x+1/2, -y+1/2, z ) (x1+1/2, -y1+1/2, z1 )
    4 (-x+1/2, y+1/2, z-1/2 ) (-x+1/2, y+1/2, z+1/2 ) (-x1+1/2, y1+1/2, z1+1/2 )
    5 (-x+1/2, -y, z-1/2 ) (-x+1/2, y+1/2, -z ) 4a2 (x2, y2, z2 )
    6 (x+1/2, -y+1/2, -z-1/2 ) (x+1/2, -y+1/2, -z+1/2 ) (-x2, -y2, z2+1/2 )
    7 (-x, -y, -z ) (-x, -y, -z ) (x2+1/2, -y2+1/2, z2 )
    8 (x, -y+1/2, z ) (x, y, -z+1/2 ) (-x2+1/2, y2+1/2, z2+1/2 )

More about the program

[*] Miller, S.C., Love, W.F. (1967). Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups. Boulder: Prett.

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