Continuous displacement cluster variation method and diffuse scattering intensity calculation

Continuous Displacement Cluster Variation Method within the pair approximation is combined with Lennard-Jones type potential and we investigate local atomic displacements for a binary ordering system in the two dimensional square lattice at 1:1 stoichiometry. The order-disorder transition temperature is reduced by the introduction of the local atomic displacement, while the second order nature of the transition is conserved. The distribution of unlike pair is localized in the vicinity of the rigid lattice points, which is explained as the deepest pair potential characteristic for the ordering system. The obtained information of atomic displacements in the real space is Fourier transformed to calculate diffuse scattering intensity spectrum in k-space. The maximum intensity contribution from the linear term is attained at (k_x*, k_y*) with k_x* = k_y* < 0.5 in k-space, while the maxima of the short range order diffuse intensity appears at (0.5, 0.5). This is interpreted based on the concept of displacement wave.