SPGR4D: A COMPUTER PROGRAM FOR DERIVING SYMMETRY OPERATIONS OF THE (3+1)-DIMENSIONAL SUPERSPACE GROUPS FROM THE TWO-LINE SYMBOLS. Zhengqing Fu* and Haifu Fan, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China

A computer program was written for deriving the symmetry operations of the (3+1)-dimensional superspace groups from their two-line symbols. The (3+1)-dimensional superspace groups, which are denoted by the two-line symbols, were first introduced by P.M.de Wolff (Acta Cryst. A30, 777-785,1974; A33, 493-497, 1977) and A. Janner & T. Janssen (Phys.Rev.B15,643-658, 1977) to describe the symmetry of one-dimensional incommensurate modulated structures. At present, the superspace-group formalism has been widely accepted and used in both classification and structure determination. Up to now, however, most structure-analusis program systems for incommensurate crystals require the input of multi-dimensional symmetry operations. This is much inconvenient and could easily bring errors. To avoid this disadvantage it is desirable to have a computer program providing the symmetry operations. In this paper, an approach is proposed for automatically deriving the (3+1)-dimensional superspace-group symmetric operations. The derivation is based on the concept of generators {R(i),e(i),s(i),t(i),q with i=1,NG} , in which {R(i),s(i)} denotes the set of generators of the basic space group represented by the upper line. The program, named SPGR4D, is written in Fortran77 and designed as a subroutine such that it can be easily used in further program systems. In SPGR4D, the program developed by H. Burzlaff & A. Hountas [J.Appl.Cryst. 15,464-467, 1982] is adopted for the derivation of symmetric operations of basic space groups. SPGR4D has been incorporated into a new version of the direct-method program DIMS (Z.Q. Fu & H.F. Fan, J.Appl.Cryst. 27,124-127, 1994) for solving incommensurate modulated structures. The detailed information about the approach and SPGR4D will be published elsewhere (Z.Q. Fu & H.F. Fan, to be published, 1996).