Bilbao Crystallographic Server WYCKSPLIT Help

Wyckoff Positions Splitting

Online Help

The program WYCKSPLIT calculates the splitting of the Wyckoff positions for a group-subgroup pair G > H and a transformation matrix that relates the basis of the group G with that of the subgroup H. The program uses as an input data the numbers of the groups and the transformation matrix. The positions to split are selected from the list with the Wyckoff positions of the group. The result contains the splitting of the selected positions and a link to a page with the correspondence between the representatives of the group Wyckoff positions and those of the suborbits in the subgroup.

Also, a non-conventional setting can be used for the group and/or the subgroup basis.

NOTE, that the result is given in the basis of the subgroup.

Input Data

The program needs as an input information the numbers of the space groups G and H as given in the International Tables for Crystallography, vol.A, and the transformation matrix relating these groups.

If you do not know the numbers of the group you can select them from a table.

The rotational part of the transformation matrix should be given as 3x3 matrix, and the translational part as a vector. If you do not now the transformation you can use the link to the other programs available on the Bilbao Crystallographic Server to find it.

To go to the page with the list with the group Wyckoff positions, click on [Show group-subgroup data].

Also, a non conventional setting for the space groups can be used. To do that click on [Non conventional Setting]. In this case, the transformation matrices that relate the conventional with non conventional bases of both groups should be provided.

Select Groups

All of the programs need as an input the number of one or two space groups as given in International Tables for Crystallography, vol.A. If you do not know these numbers, you can select them from the Table of Space Group Symbols.

Select Wyckoff Positions

After all of the necessary input data has been given, you go to a page that contains:

When you have selected the positions, click on [Splitting] to see the result from the splitting.

Wyckoff Positions Splitting

The result from the splitting is represented as a table which contains:

To select other Wyckoff positions to split, click on [Group - Subgroup Data].

Wyckoff Positions Relations

For each one of the Wyckoff positions for which the splitting has been found you can see the correspondence between the representatives of the Wyckoff position and the representatives of its suborbits. This information is represented as a table which contains:

Non-conventional Settings

If you want to use a non-conventional setting for the group and/or the subgroup you should click on the button [Non conventional Setting] on the main page. This will show you a form with two buttons [Supergroup Non conventional Setting] and [Subgroup Non conventional Setting] which you can use to give the transformation matrix that relates the conventional setting of the group or subgroup with the non conventional one you want to use.

The transformation matrix, also should relate the non conventional settings of both groups.

NOTE, that the result will be shown in the non conventional setting of the subgroup.

More about the program

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