Conduction-electron effect in quantum tunneling diffusion of hydrogen on metal surfaces

The effective-medium theory of electrons by Norskov and Lang suggests that hydrogen adsorbed on transition metals is affected by only one-third of the electron densities when compared with interstitial hydrogen in the metals. As an important consequence, we show that the hydrogen-electron coupling parameter κ (as defined by Kondo) on W and Ni surfaces is close to 1/2 as opposed to 0.2 for interstitial hydrogen and positive muons in metals. It means that the electron-controlled under-barrier tunneling rate of hydrogen on W and Ni, proportional to T^2κ-1, varies weakly with temperature. Our numerical calculation shows that the over-barrier hopping can directly cross over to electron-controlled tunneling. We thus believe that the conduction-electron mechanism is a strong candidate to explain the weakly temperature-dependent tunneling of hydrogen on W and Ni.