PHONON FREE-ENERGY AND DEVILS STAIRCASES IN THE ORIGIN OF POLYTYPES

Phase transitions in polytypic substances can display a rich structure . A polytypic material, being formed from stacked layers, each layer h aving freedom of orientation, has an infinite number of possible struc tures. Thus a phase transition between two simple structures could occ ur directly, or via an infinite sequence of intermediate phases. Such a sequence, called a 'devil's staircase', can arise from simple and ge neral mathematical models. This paper presents a simple model in which the phonon free energy drives a temperature-induced phase transition, the mechanism which is believed to cause phase transitions in SiC, Cd l(2) and PbI2. The form of interaction between changes in the stacking orientation caused by the phonon free energy is found to be inversely proportional to the square of the separation of the changes, but of a lternating sign. Although no staircase results from this interaction, one intermediate phase does arise, and others are barely unstable.