Discrete-state models of orientational glasses.

Abstract

We construct and study a class of models for crystalline systems which undergo structural changes due to the cooperative freezing of orientable defects. The defects are assumed to possess uniaxial symmetry and are located on randomly chosen sites of a deformable cubic lattice. The orientations of the defects are restricted by lattice anisotropies. We consider three possibilities with discrete sets of allowed orientations. The defect axis may be parallel to (a) the cubic axes, (b) the space diagonals of the cube, or (c) the face diagonals of the cube. For quadrupolar defects the phase diagram and the elastic properties of the emerging three-state (case a), four-state (case b), and six-state (case c) model are studied, with the coupling between defects in mean-field approximation. In addition, we obtain results for a model of dipolar defects with three orientations, which is related to the six-state model. Depending on the degree of disorder, we find either states with long-range orientational order and uniform lattice distortions or glassy states. The freezing of defect orientations into a homogeneously ordered state is accompanied by enhanced fluctuations and a pronouced softening of the lattice in symmetry directions, which are determined by the lattice-anisotropy fields. We conclude that the models correctly describe essential experimental findings for orientational glasses.