EFFECT OF THE HEAT BATH ON ACTIVATED RATE PROCESSES IN SOLIDS

Abstract
The effect of heat-bath coupling on the conditions of access to saddle-point configurations of vacancy jumps in solid-state diffusion is investigated by analysing, in the framework of quantum statistics, the interplay between i) the rate of phonon-phonon collisions caused by anharmonicity, representing the bath rate, ii) the resonant mode of the defect and its lifetime determined by the additional anharmonicity caused by the defect, and iii) the rate of barrier relaxation of the multivariate deformable barrier. At low temperature where damping is small, the resulting jump rate closely approaches the rate law of Vineyard (1957) characterized by the fully relaxed saddle point. With increasing temperature, damping of the resonant mode increases, allowing but for a partial relaxation ; jumps occur at reduced rate over non-equilibrium configurations of the saddle point with increased migration enthalpy and, caused by large spatial gradients of the energy, with enlarged values of migration entropy and activation volume. The typical non-Arrhenius form of the rate resulting from temperature-dependent damping allows to interpret self-diffusion in many metals by jumps of monovacancies only. Anharmonic damping of the resonant mode involves essentially low-frequency phonons not contained in the spectrum of crystallites with up to 1000 atoms. Computer modelling of jump rates thus underestimates the relevant damping and yields always the low-temperature approximation, that is the Vineyard rate.