AN INTRODUCTION TO ROTATIONAL DEGREES OF FREEDOM OF SOLID MOLECULES

Recently many interests have been shown to study the rotational motion of molecules in solids of alkali halide crystals doped with polar impurities which shows pronounced effects on optical, thermal and electrical properties of the host crystals, playing a dominant role in science and technology.

A free molecule containing N atoms has 3N-6 degree of vibrational freedom, three degree of translational freedom and three degrees of rotational freedom. When a molecule is introduced substitutionally into a lattice, the vibrational degrees of freedom are usually changed relatively small by the matrix. The translational degrees of freedom of the molecules are the same as the translational degrees of freedom of an impurity atom, i.e., they manifest themselves as impurity modes. We have considered the third group of degree of freedom, those connected with the rotational inertia of the molecule.

Low temperature infra-red absorption, thermal conductivity and specific heat measurements have shown a better agreement with the theoretical one by optical spectroscopy method on Devonshire model. This model explains gross features of the IR data except the tunneling translations which were not observed in optical measurements that have been discussed in details.

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 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.