THE THERMAL PHASE OF FAST PROTON EQUILIBRATION IN METALS - HYDROGEN-ATOM DIFFUSION

A fast proton passing through a metal slows down and captures an electron to form a hydrogen atom. Subsequent equilibration of the spatial location of the hydrogen atom proceeds by diffusion amongst interstitial sites in the crystal lattice of the metal. The diffusion coefficient is a strong function of both temperature and the isotopic mass of the H-atom. Using a quantum barrier crossing model, we have computed the Arrhenius activation energy, E(j), for diffusion where j = 1, 2, 3 runs over the mass numbers of the three isotopes, H-1, H-2, H-3, respectively. At sufficiently low temperatures, we find a ''normal'' isotope effect, where E(1) < E(2) < E(3) (as in the case of H-atoms diffusing through Fe, V, Nb, and Ta), while at sufficiently high temperatures, we find an ''inverse'' isotope effect, where E(3) < E(2) < E(1) (as in the case of H-atoms diffusing through Cu, Ni, and Pd). Between these two extremes, we find temperature ''cross-over'' regions where E(1) < E(3) < E(2) and E(3) < E(1) < E(2).