The isotope and temperature dependence of self-diffusion for hydrogen, deuterium, and tritium on Cu(100) in the 100–1000 K range

Abstract

The quantum mechanical contributions to the diffusion of H, D, and T on the Cu(100) surface are investigated as a function of temperature. The results proceed from a transition state theory calculation of the barrier crossing rate using an anharmonic, temperature-dependent potential between the adatom and the static Cu surface. The temperature-dependent potential is derived from path integral considerations. At room temperature, the present calculations indicate a 0.6, 0.3, and 0.2 kcal/mol decrease in the effective activation energy for H, D, and T, respectively. However, at 100 K, the analogous decreases become 1.8, 1.0, and 0.7 kcal/mol. These values may be compared to the classical activation energy of 11.6 kcal/mol. Note that these corrections qualitatively conform to a 1/ m mass dependence in the effective activation energy which is predicted by a harmonic model also presented below. One of the goals of this work is to provide some preliminary framework by which the results of electronic structure calculations may be adjusted for quantum mechanical contributions so as to facilitate comparison with experiment.0