THEORY OF DISPLACIVE PHASE-TRANSITIONS IN MINERALS

A lattice-dynamical treatment of displacive phase transitions leads na turally to the soft-mode model, in which the phase-transition mechanis m involves a phonon frequency that falls to zero at the transition tem perature. The basic ideas of this approach are reviewed in relation to displacive phase transitions in silicates. A simple free-energy model is used to demonstrate that Landau theory gives a good approximation to the free energy of the transition, provided that the entropy is pri marily produced by the phonons rather than any configurational disorde r. The ''rigid unit mode'' model provides a physical link between the theory and the chemical bonds in silicates and this allows us to under stand the origin of the transition temperature and also validates the application of the soft-mode model. The model is also used to reapprai se the nature of the structures of high-temperature phases. Several is sues that remain open, such as the origin of first-order phase transit ions and the thermodynamics of pressure-induced phase transitions, are discussed.