A priori calculation of rate of dissociation of a molecule in an ionic lattice assuming a phonon relaxation process

Abstract

The rate of dissociation of the rectangular N₄ ⁻ ion into two diatomic molecules has been calculated in the ionic KN₃ lattice assuming the initial step is the transfer of three lattice phonons to the internal vibrational states of the molecule causing an internal vibrational excitation of the N₄ ⁻. The rate of dissociation of the molecule is then calculated using a stochastic random walk approach which enables a determination of the mean time for the molecule to be vibrationally excited to the dissociative state. The results are in order of magnitude agreement with the measured reaction rates at a number of temperatures suggesting the possible role of phonon relaxation processes in unimolecular chemical reactions in the bulk solid state.