a computer program for determination of the relations of Wyckoff positions 
for a group - subgroup pair

The program

Consider group-subgroup related space groups G > H. Atoms which are symmetrically equivalent under G, i.e. belong to the same orbit of G, may become non equivalent under H, (i.e. the orbit splits) and/or their site-symmetries can be reduced. The structural relation between the group-subgroup related phases follows from the relations of the occupied orbits, and this behavior is the same for all orbits belonging to a Wyckoff position. The aim of the program is the determination of the relations of the Wyckoff positions (known as splitting of Wyckoff positions) for a group-subgroup symmetry break G > H.

Input Information

1. Specification of the group-subgroup chain G > H

(i) The groups G and H specified either by their sequential numbers, as listed in International Tables for Crystallography, vol.A. You can specify the origin choice, rhombohedral or hexagonal axes and the unique axis.

Default values are:

If your group or subgroup data are in unconventional settings, you can give the transformation matrices to the corresponding conventional settings by clicking over "Unconventional settings".

(ii) A transformation matrix relating the bases of the group and the subgroup.

The elements of the matrix can be given either as decimals or fractions.

If you don't know the transformation matrix click here for more information about "How to find the correct transformation?"

By clicking over the button "Show Group-Subgroup Data" you see:

At this step the transformation matrix is checked. If it does not correspond to the chosen group-subgroup chain, then the user is given the possibility to correct it.

2. Specification of the orbit of G

The orbits of G are selected either from a list with Wyckoff positions of G, or by the coordinate triplet of any point of the orbit of G.

To study the behavior of some of the Wyckoff positions of G:

If you want to obtain the behavior of a particular orbit:

To view the behavior of the chosen orbit of G for the symmetry break G > H

Output Information

The output file contains the following data:

Group Subgroup Data

Characteristics of the group-subgroup chain:

Splitting of the chosen orbit of G (or the corresponding Wyckoff position)
The result from the splitting is shown in table-form with the following columns: The distribution of the representatives of the G-orbit into H-orbits

There is a link to the file with the full information for the splitting. This file contains:

There is a possibility to specify another orbit of the group G, by clicking over the button "Group-subgroup data".