Phase transitions in polytypic substances can display a rich structure. A polytypic material, being formed from stacked layers, each layer having freedom of orientation, has an infinite number of possible structures. Thus a phase transition between two simple structures could occur directly, or via an infinite sequence of intermediate phases. Such a sequence, called a `devil's staircase', can arise from simple and general 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, and . 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 alternating sign. Although no staircase results from this interaction, one intermediate phase does arise, and others are barely unstable.