DIFFUSION AND TUNNELING OF HYDROGEN IN VANADIUM, NIOBIUM AND TANTALUM

Literature data for diffusion, internal friction, inelastic neutron scattering and specific heat for hydrogen in V, Nb and Ta are correlated with simple models for tunnelling. Tunnelling motion can occur through interference of tunnel-split excited state, or through two-phonon transitions via virtual states. Energy asymmetry between neighboring hydrogen sites will block the tunnelling motion, so then only classical hopping over the barrier is possible. Hence both rapid tunnelling and slow classical hopping can be observed for hydrogen bound to impurities. The only adjustable parameters in our model are the magnitude of the assumed sinusoidal potential, and the deformation potential for the coupling to the phonons. We neglect the hydrogen self-trapping in the calculations of the tunnelling rates, but it makes the fitted potential barriers for the isotopes D and T about 20% and 30% less than barrier for H in the same metal.