Rotational Degrees of Freedom of Molecules in Solids. I. The Cyanide Ion in Alkali Halides

By means of infrared-absorption, thermal-conductivity, and specific-heat measurements at low temperatures, the problem of rotational motion of molecules in solids has been studied using ${\mathrm{CN}}^{-}$ ions substituted for the halogen in KCl, KBr, KI, RbCl, NaCl, and NaBr. Energy levels associated with the ion performing free rotation, hindered rotation, oscillation, and tunneling motion were observed. It was found that a simple 3-dimensional potential for a linear diatomic molecule developed by Devonshire based on a 2-dimensional cosine potential first proposed by Pauling explained all of our observations. For the potassium halides the barrier height is 0.003 eV; in RbCl it is 0.0075 eV, and in the sodium halides it is >0.015 eV. Stress experiments show that the ion has 6 equilibrium orientations along the 〈100〉 directions. Strong phonon scattering by tunneling states and rotational states is observed. The scattering can be quantitatively described with a Lorentzian resonance cross section.