Conjecture on the Rate of Vibrational Relaxation of a Diatomic Molecule in a Monatomic Lattice

In this paper we use a simple model—a substitutional diatomic molecule in a linear monatomic chain—to examine the problem of intermolecular vibrational relaxation in the solid phase. A binary collision theory of vibrational deactivation is proposed for the relaxation process, with the motion of the collision partners governed by the normal modes of the lattice. The collision frequency is calculated by using an analysis similar to that of the Slater theory of unimolecular reactions. The model calculations predict the relaxation time to be very long compared with the vibrational period of the diatomic molecule. We thus conclude that, in a molecular crystal composed of polyatomic molecules, the excitation energy will be removed by the surrounding medium, not by the transformation of internal energy into lattice modes, but rather by other processes such as the formation of vibration excitons etc.