Computer simulation of Bragg and diffuse scattering intensities against temperature for a structural phase transition

Molecular dynamics has been used to estimate the properties of a two-dimensional crystal exhibiting a second-order soft-mode phase transition. Using a vibrational potential for the crystal which is temperature independent, the essential features observed experimentally in the coherent scattering from analogous real systems are reproduced in the computer simulation. The potential consists of an effective one-particle component with multiple minima and a harmonic nearest-neighbour coupling component. It is emphasized that the coupling component is essential to reproduce correctly the qualitative features not only of the diffuse scattering, but also of the mean-square displacements as a function of temperature. The condition for appearance of a cusp at T_C in the mean-square displacement versus temperature curve is discussed and the formation of superlattice peaks in the diffuse scattering is demonstrated.