Wyckoff Positions Splitting
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.
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.
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.
After all of the necessary input data has been given, you go to a page that
- the transformation matrix and the index of the subgroup in the group,
- three fields for a coordinates of a specific point in the supergroup, if
you want to find the splitting of a given orbit.
- a list with the Wyckoff positions of the group and the subgroup, from
which you should select the positions for which the splitting should be found by
marking the checkbox corresponding to each one of these positions. To find the
splitting for all of the Wyckoff positions of the group G, mark the checkbox
When you have selected the positions, click on [Splitting]
to see the result from the splitting.
The result from the splitting is represented as a table which contains:
- the group Wyckoff position multiplicity and letter,
- the suborbits given as
- a button Relations which will show the
relations between the representatives of the group Wyckoff position and its
suborbits in the subgroup.
To select other Wyckoff positions to split, click on
[Group - Subgroup Data].
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:
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.
- group Wyckoff position in the basis of the group and in the basis of the
- the subgroup Wyckoff positions represented as
<multiplicity><letter> which correspond to the
suborbits of the group Wyckoff position,
- the representatives of the subgroup Wyckoff positions
The transformation matrix, also should relate the non conventional settings of
NOTE, that the result will be shown in the non conventional setting of the subgroup.
More about the program