Soft-modes in displacive transitions

Abstract

Displacive phase transitions which do not change the size of the unit cell may be classified under two types depending on their order parameter : in the elastic transitions, this is the amplitude of an elastic strain ; it is the amplitude of a relative displacement of the atoms in an optic transition. In this last case, we prove that there always exists at least a whole plane of optical phonons, which are Raman inactive in the high temperature phase, and the frequency of which goes to zero at the transition temperature. These soft modes become Raman active in the low temperature phase. Should these phonons be Raman active in the high temperature phase, they would induce an elastic transition as shown by Miller and Axe : an elastic constant will pass through zero for a still finite frequency of the optical phonon. In the case of an elastic transition, if the Landau theory allows it to be second order, we show by group theory that there always exists at least one sound velocity which passes through zero at the critical temperature. We also prove that the optical or elastic soft mode never carries an electric field with it. Nevertheless the dielectric constant becomes infinite at the transition temperature, and at low temperature is polar, either if the optical soft mode is infrared active or if the elastic mode induces a piezoelectric strain. The damping effect associated with such transitions is not taken into account in this paper.