On the application of mean-field and landau theory to displacive phase transitions

Abstract

It is commonly observed that displacive phase transitions, including ferroelectric phase transitions, can be accurately described by mean-field theory and hence Landau theory. In same cases the reasons why can be deduced by renormalisation group theory, but there are many other cases where the reasons are less clear. We have developed a model for displacive phase transitions in silicates, called the rigid unit mode model, in which it is assumed that any change in the structure does not involve distortion of the SiO₄ tetrahedra. This model can explain a wide range of phenomena associated with phase transitions in silicates, such as why phase transitions are so common, why they have their particular transition temperatures, and why they can be described by Landau theory over a wide range of temperatures including close to the transition temperature. The model can be generalised to a model of a crystal of atoms with nearly-constant contact distances, a rigid bond model. This is then applied to the phase transitions in HCN and Na₂CO₃, where the predictions of the model are found to be in agreement with experiment.

Keywords:

• displacive phase transitions
• Landau theory
• rigid unit modes