Diffusion of hydrogen interstitials in the near-surface region of Pd(111) under the influence of surface coverage and external static electric fields

Past scanning tunneling microscopy (STM) experiments of H manipulation on Pd(111), at low temperature, have shown that it is possible to induce diffusion of surface species as well as of those deeply buried under the surface. Several questions remain open regarding the role of subsurface site occupancies. In the present work, the interaction potential of H atoms with Pd(111) under various H coverage conditions is determined by means of density functional theory calculations in order to provide an answer to two of these questions: (i) whether subsurface sites are the final locations for the H impurities that attempt to emerge from bulk regions, and (ii) whether penetration of the surface is a competing route of on-surface diffusion during depletion of surface H on densely covered Pd(111). We find that a high H coverage has the effect of blocking resurfacing of H atoms travelling from below, which would otherwise reach the surface fcc sites, but it hardly alters deeper diffusion energy barriers. Penetration is unlikely and restricted to high occupancies of hcp hollows. In agreement with experiments, the Pd lattice expands vertically as a consequence of H atoms being blocked at subsurface sites, and surface H enhances this expansion. STM tip effects are included in the calculations self-consistently as an external static electric field. The main contribution to the induced surface electric dipoles originates from the Pd substrate polarisability. We find that the electric field has a non- negligible effect on the H-Pd potential in the vicinity of the topmost Pd atomic layer, yet typical STM intensities of 1-2 VÅ−1 are insufficient to invert the stabilities of the surface and subsurface equilibrium sites