Modulated structures of homologous compounds InMO3(ZnO)m (M = In, Ga; m = integer) described by four-dimensional superspace group

The modulated structures appearing in the homologous compounds InMO3(ZnO)(m) (M = In, Ga; m = integer) were observed by using a high-resoultion transmission electron microscope and are described based on a four-dimensional superspace group, The electron diffraction patterns for compounds with m larger than 6 reveal extra spots, indicating the formation of a modulated structure. The subcell structures for m = odd and even numbers are assigned to be either monoclinic or orthorhombic, respectively, On the other hand, extra spots can be indexed by one-dimensional modulated structure, The possible space groups for the subcell structure are Cm, C2, and C2/m for m = odd numbers, while those for m = even numbers are Ccm2(1) and Ccmm, respectively, Then, corresponding possible superspace groups are assigned to be P-s(C2), P-(1 over bar)(Cm), and P-s (1 over bar)(C2/m) for odd rn numbers and P(<1(11)over bar>)(Ccm21) and P-1(1 over bar 1)(Ccmm) for even m numbers, Based on the superspace group determination, a structure model for a one-dimensional modulated structure is proposed. (C) 1998 Academic Press.