Prediction of diffuse intensity surfaces in short-range-ordered ternary derivative structures based on SnS, NaCl, CsCl and other structures

The atom arrangement in ternary and quaternary ionic long-range-ordered derivative structures of ZnS, NaCI, CsCI and others is governed by a principle which is known as Pauling's electrostatic valence rule. This valence rule is actually part of a more general ordering principle for derivative structures, which is not restricted to ionic compounds and requires that the smallest building blocks of the structure (centred tetrahedra, octahedra or cubes) have as far as possible a composition identical with the overall composition of the compound. Depending on the type of polyhedron, this rule can be fulfilled only for a limited number of overall compositions. In this case it is possible to produce an analytical formulation of the general ordering principle giving relations amongst the Warren short-range-order parameters. Use of these relations in a structure-factor formula of the binary base structure permits the derivation of the general location (lines, planes or a general surface) of superstructure reflexions or diffuse intensity in reciprocal space for the cases of long-range order or short-range order respectively. With this method it is possible not only to explain the experimentally determined diffuse intensity shapes due to short-range order in NaCl-related structures, but also to predict the diffuse intensity shape for ZnS and CsCl-related structures and others for which no experimental data are yet available.