Quantum theory of diffusion: temperature dependence of diffusion of light interstitials in Debye solids

The temperature dependence of the motion of light interstitials is calculated using the quantum theory of Flynn and Stoneham (1970). The results are compared with the asymptotic expressions given previously. They show that the high temperature asymptotic is accurate over a wider range of temperature than expected, whereas the low temperature form is of very restricted application. Deviations from the asymptote depend both on the temperature and on the ratio of the activation energy to the Debye energy. Results for protons in Ta agree remarkably well with the theory for an activation energy 0.188 eV and for a hopping integral J of 29% of the Debye energy.