Order-disorder structural phase transitions described by the three-states potts model

Abstract

Orientational ordering of spontaneously distorted building blocks of a crystal is a mechanism for order-disorder structural phase transitions. We study as a model substance the case of a simple cubic array of tetragonally deformed octahedral complexes. The three equivalent tetragonal deformations along the cube axes are taken as the three states of the Potts model. We investigate the various structures which can appear depending on the type of interaction between the complexes. The phase diagram, the stability of the various phases, the type of transitions, and the temperature dependence of the order parameter are studied in mean-field approximation. We further show that piezodistortive coupling to the elastic strain may stabilize different low-temperature structures, and that it gives rise to a renormalization of elastic constants and to acoustic anomalies.