EQUILIBRIUM PROPERTIES OF A QUADRUPOLAR GLASS

We introduce a semimicroscopic discrete-state model appropriate to the orientational glass phase in mixed alkali halide cyanides with [111] equilibrium orientations of the CN- ions, such as K(CN)xBr1-x. The ord er-parameter fields are defined as symmetry adapted combinations of th e occupation number operators along the cubic body diagonals, which tr ansform according to the T2g representation of the cubic group. These interact via an infinite-range random interaction in the presence of q uenched local random strains. We then use the replica formalism to der ive a replica-symmetric solution for the components of the orientation al-glass order parameter, the linear susceptibilities, and the elastic compliances. The high-temperature orientational-glass phase is charac terized by an isotropic order-parameter matrix with only the diagonal elements q(mu) being nonzero. At high temperatures, the behavior of th e order parameter q = SIGMA(mu) q(mu)/3 is similar to that of an Ising spin glass, however, at intermediate and low temperatures the two mod els differ significantly. We also derive the instability line T(f)(DEL TA) separating the replica-symmetric isotropic phase from the low-temp erature anisotropic orientational glass phase, which is characterized by broken replica symmetry. In contrast to the random-bond-random-fiel d model of an Ising spin glass, the instability temperature increases with random-field variance, implying that in quadrupolar glasses repli ca-symmetry breaking may be relevant already at relatively high temper atures. Finally, an expression for the distribution of local strains r elated to the NMR line shape is derived. It is also shown that the qua drupolar glass order parameter can be determined by NMR.