Phonon induced tunneling of ions in solids

A quantum mechanical analysis is given of the change of position or orientation of an atom, ion or molecule in a crystal as it occurs e.g. in the processes of diffusion or hindered rotation. One-phonon processes, Raman processes and indirect processes are discussed. The limits of applicability of the classical rate theory are given. Specifically, the analysis is applied to the reorientation of the O₂- center in alkali halides under the influence of external mechanical stresses at low temperatures, which has been investigated experimentally byKänzig. The measured dependence of the reorientation time upon temperature and applied stress can be explained by one-phonon processes. Random internal strains in the crystal are shown to play an important part. As further application of the theory the proton motions in ice and in iron are elucidated. Finally, an estimate is given of the effect of direct processes involving imperfections on the thermal conductivity of alkali halides.