Wyckoff Positions in Alternate Settings of Space Groups. Y. Le Page1,4, Toshihiro Ashino2, Stéphane Raymond1, E.J. Gabe1,4, P.S. White3,4 and J.R. Rodgers4, 1. National Research Council of Canada, Ottawa, CANADA, 2. RACE, The University of Tokyo, JAPAN, 3. University of North Carolina, Chapel Hill, NC , USA, 4. Toth Information Systems Inc., CANADA
International Tables for Crystallography, Vol. A (IT) print over 1,000 different symbols to designate space groups (SG), but list the general position and Wyckoff positions for about 300 symbols only. The reader is therefore left with the problem of deriving general positions and Wyckoff positions for over 700 remaining symbols.
Wyckoff positions for alternate settings are fully defined by the axial setting with respect to the standard one. Some space group symbols, including "standard" ones can exist in several possible settings, with same sets of Wyckoff positions, but with possible swaps among Wyckoff letters corresponding to some sets of coordinate triplets.
We have developed the program ALTWYK which lists the general position and Wyckoff positions for all SG symbols printed in IT, even unusual notations like F41/ddc referred to origin 1. If full information is printed in IT, the general position is listed in the same order as in IT. Values listed for the first position corresponding to each Wyckoff letter are identical with those in IT. Otherwise, the standard SG and a new axial setting are indicated. The first position corresponding to each Wyckoff letter is then the first such position in IT expressed in the new setting. Variable coordinates may involve reparametrization. ALTWYK can also produce letters and numerical values of variables in Wyckoff expressions from numerical triplets of coordinates.
The ALTWYK program can be accessed, free of charge, at web address http://ylp.icpet.nrc.ca/altwyk/.