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

The contributions to the temperature and mass dependence by quantum statistical effects in the harmonic approximation are shown to give rise to terms proportional to T⁻²ⁿ and m⁻ⁿ, respectively, where $\text{n=1,2,· · ·.}$ 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 pre‐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 of D₀ with temperature provides a proof that Arrhenius‐type behavior is nearly correct in the classical case despite anharmonic contributions to D₀.