Wyckoff Position Types

In PowderCell a procedure for an identification of special positions — the so-called Wyckoff positions — has been implemented. This supports the user to check imported data or to understand the interaction between space-group and local symmetry: On the other hand the program uses the Wyckoff notation for an optimized generation of atomic positions. This is very useful, especially for a structure manipulation — the aim of this program. It is planned to fix the local symmetry for selected atoms/ions or molecules. Currently you must be careful of this by yourself.
In the description of all space-group types and their settings (more than 745) a total of 208 different types of special positions have been extracted. They will be used to encode the special-position types in the symmetry file pcwspgr.dat. There each special position is characterized by two numbers: the encoded Wyckoff-position type and its generator sequence.
However, the extracted types of special positions classify the first coordinate only, but not all symmetry-equivalents. This is the reason that the number of different types is relative small.
The disadvantage of this classification is, that all atomic coordinates must be transformed to the condition of the identified Wyckoff-position type. Using the generators selected, only with the transformed coordinates the generation of atomic positions will be carried out correctly.

The procedure can be described shortly in the following manner: At first PowderCell creates the atomic positions using all generators. The comparision between all locations generated and the possible Wyckoff-position types for the actual space-group number supplies the Wyckoff letters wanted. In this part of procedure a multiple generation is allowed and in general necessary. But if the program has been allocated the Wyckoff-position types the following structure manipulation or generation of atomic positions will be used the Wyckoff-specific generation.

For a better classification it is recommendable to split the position types into a group with no, one or two degrees of freedom. The following tables show all types of special positions used in PowderCell. With the help of the given code number it is possible to translate the Wyckoff-position data from the symmetry file pcwspgr.dat.