Kinematical diffraction from solid solutions with short-range order and size effect

A new approach to the kinematical theory has been developed for the case of binary alloy solid solutions with short-range ordering of the atoms and displacements of the atoms from the average lattice sites due to departures of the effective atomic radii from the average for the alloy. Both the pseudo-temperature factor on the Bragg reflexions and the diffuse scattering intensity are shown to depend on summations over higher-order correlation parameters, defined in terms of the probabilities that groups of three, four or more sites should be occupied in specific ways. Expressions involving these parameters, and the usual short-range order parameters, α_i, are derived with terms of up to the second order in the displacement parameters for the Huang scattering around the fundamental Bragg reflexions, for the short-range order diffuse peaks, and for additional diffuse scattering depending on higher-order correlation parameters only. Special cases of practical significance are explored, and some estimates are made of the relative magnitudes of the terms not included in previous treatments of this problem.