Quantum and Anharmonic Effects on the Temperature and Mass Dependence of Rate Processes in Solids

摘要

The contributions to the temperature and mass dependence by quantum statistical effects in the harmonic approximation are shown to give rise to terms proportional toTminus;2nandmminus;n, respectively, wherenequals;1,2,middot; middot; middot;.It is shown, explicitly, that anharmonic terms make no contribution to the mass dependence in the classical case, except in second order. An analysis of the temperature dependence of the prehyphen;exponential part of the diffusivity, for one atomic mechanism, including anharmonic effects, reveals, for Cu, that deviations from a constant value occur only at high temperatures in the classical case. On the other hand, quantum effects cause a positive curvature at low temperatures. The very small variation ofD0with temperature provides a proof that Arrheniushyphen;type behavior is nearly correct in the classical case despite anharmonic contributions toD0.