Phonon free energy and devil's staircases in the origin of
polytypes
MJ Rutter, V Heine, J.Phys.:Cond. Matt. (1997) Vol. 9 Pg 2009
Abstract
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, CdI2 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
alternating sign. Although no staircase results from this interaction, one
intermediate phase does arise, and others are barely unstable.
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