Self-consistent phonon studies of a model diatomic ferroelectric

A model of a diatomic crystal loosely patterned on tin telluride is developed. The crystal has the sodium chloride structure at high temperatures, but displays a soft-mode instability as the temperature is lowered. The lattice dynamics of the model is treated in the self-consistent phonon approximation. The free energy is found to show the behaviour characteristic of a second-order phase transition, but the temperature of the transition is not the same as the temperature at which the frequency of the soft mode becomes zero. Additional contributions to the anharmonic frequency shift, the bubble diagrams, are shown to shift the frequency of the soft mode so that it does go to zero at the transition temperature