INFORMATION ON SYMMETRY IN POWDER DIFFRACTION DATA. M. Ohmasa¹, K. Ohsumi² and H. Toraya³. ¹Department of Life Science, Himeji Institute of Technology, Japan; ²Photon Factory, National Laboratory for High Energy Physics, Japan; ³Ceramics Research Laboratory, Nagoya Institute of Technology, Japan.

Since each crystal family except triclinic, monoclinic and orthorhombic ones doesn't correspond to a Laue class uniquely (: holohedral and hemihedral Laue classes) and no method to identify Laue classes of those families had been presented for powder specimens, their space groups had been assigned only with crystal family and reflection conditions. Because summed intensities are measured by powder diffraction methods and they are not separable to individual intensities. Recently Ohmasa & Ohsumi (1995) indicated that weighted reciprocal lattices named composite reciprocal lattices are constructed from powder diffraction data in such a way that summed intensities are distributed to reciprocal lattice points to hold holohedral symmetry and indicated that information on Laue classes can be obtained from concentrations of interatomic vectors in Patterson functions evaluated with intensities at the composite reciprocal lattice points (composite Patterson functions). For hemihedral Laue classes, a composite reciprocal lattices is regarded as a superposed record of weighted reciprocal-lattice points of a single crystal. In this case the superposition yields new symmetry generators (extra generators) which are not intrinsic to the Laue class of the single crystal. The same generators as the extra ones are included in holohedral symmetry and the distribution of the points and their relative weights in the composite Patterson function coincide with those in the Patterson function of the real structure. The same generators as the extra ones are not included in the symmetry generators of the real structure with hemihedral Laue symmetry but the apparent symmetry of the composite Patterson functions is enhanced to holohedral one by the extra generators. However the distribution of the peaks and their relative weights in the composite Patterson functions are not perturbed by the extra generators and the feature of the concentration of the peaks related to interatomic vectors in the real structure is retained. Consequently, distinction of space groups should in principle be possible by interpretation of composite Patterson functions. Composite Patterson functions of some materials will be indicated as examples.

Ohmasa, M. and Ohsumi, K. (1995). Acta Cryst. A51, 87-91.