Theory of elastic and phonon softening in ionic molecular solids. Application to alkali cyanides

We have carried out a theoretical study of the effect of coupling between rotational and translational degrees of freedom first proposed by Michel and Naudts on the elastic constants and phonon frequencies of ionic molecular solids. We have applied our theory to the high-temperature plastic phase of alkali cyanides NaCN, KCN, and RbCN. We find that the competition between short-range repulsion and the interaction of the electric quadrupole moment of the C${\mathrm{N}}^{-}$ ion with the fluctuating electric field gradient strongly influences the elastic softening and ferroelastic instabilities in these systems. The effect of direct intermolecular interaction and anharmonicity is found to be significant in some cases. The ferroelastic transition temperatures for the above three compounds are found to be 337.5, 190, and 179 K which compare favorably with the experimental values 255.4, 156, and 130 K if we note the mean-field nature of our theory. Within our model we can understand the qualitative differences between the cyanides and the superoxides, a similar class of compounds showing drastically different ferroelastic behavior. Our calculations provide a microscopic justification for the use of certain phenomenological parameters by Strauch et al. in their calculation of phonon frequencies in NaCN and KCN at 300 K.