Model of quadrupolar glass of mixed alkali cyanide crystals

Abstract

A model of the transition from the orientationally disordered to the quadrupolar-glass (QG) phase of mixed alkali cyanide crystals is proposed. Starting from the semimicroscopic Hamiltonian constructed by Vollmayr, Kree, and Zippelius the effective Hamiltonian containing random long-ranged orientational interactions between ${\mathrm{CN}}^{\mathrm{\ensuremath{-}}}$ ions and their orientational coupling to the random local strain field has been obtained. The ${\mathrm{CN}}^{\mathrm{\ensuremath{-}}}$ ion is treated as a quadrupolar molecule and no restriction has been made to a finite number of spatial orientations of it. With the Sherington-Kirkpatrick approach the formula for the free energy has been derived. In the framework of the replica-symmetric theory the Landau expansion of the free energy up to third order in the QG Edwards-Anderson parameter has been performed in the absence of the random local strain field. This predicts a continuous QG transition. However, it is smeared out due to the influence of the random local strains, which in fact have a nonzero value. The elastic compliance has been calculated and it has been shown, that ${\mathit{T}}_{2\mathit{g}}$ orientational modes govern the softening of the elastic constant ${\mathit{C}}_{44}$ on approaching the QG transition point, whereas ${\mathit{E}}_{2\mathit{g}}$ modes are responsible for the much less pronounced temperature dependence of ${\mathit{C}}_{11}$ and ${\mathit{C}}_{12}$. This is in agreement with experimental data.