Incommensurate crystal phases in mean-field approximation

Abstract

A model for structural phase transitions in crystals in three dimensions is studied in a mean-field approximation. The forces between the particles are short-range (up to second neighbours) and non-linear. Contrary to formerly studied models the temperature dependence is explicitly taken into account in this way. The phase diagram shows incommensurate phases as well as superstructures. The form and properties of the states in this phase are discussed. It is found that in the incommensurate phase two regions can be distinguished, characterised by the form of the modulation. In one the modulation is smooth and nearly sinusoidal; in the other there are discommensurations and chaotic states. The dynamic properties are studied with an effective Hamiltonian which extends the mean-field approach. It is shown that the vibrations in the two incommensurate regions are qualitatively different: in one region there is a zero-frequency phason, whereas in the discommensuration regime the phason is pinned and localised states occur.