Abstract

First principles calculations of adatom potential energy surfaces using density functional theory are being performed with ever more accuracy with the aim of achieving ‘chemical accuracy’ in the prediction of rates of surface processes. For activated diffusion in the quantum case, relatively little attention has been given as to how to actually use these potential energy landscapes to predict diffusion rates with corresponding accuracy: typically the rate for activated diffusion is given by the product of a Boltzmann factor and the barrier energy, and the classical pre-exponential value kBT/h (see for example [1]). The advent of helium spin-echo (HeSE) quasielastic scattering experiments makes possible measurements on atomic length scales, guaranteeing that terrace, as opposed to over-step-edge, diffusion is being measured. The measurements are at a sufficiently short timescale (typically 1ps to 1ns) to require little extrapolation in the evaluation of the pre-exponential factor and so deliver diffusion measurements in equilibrium situations of unparalleled accuracy and reliability. Calculations of the momentum dependence of hydrogen atom energy states in the atom-surface potential (atomic band structures) have been used for some time in the interpretation of the vibrational spectra of surface adsorbed hydrogen [2]. Here we extend this concept and use these band structures to determine the rate of hydrogen diffusion with a formalism that does not make the arbitrary distinction between ‘over the barrier’ and tunnelling states. We compare HeSE data and published field emission fluctuation data with predictions for the Cu(111), Pt(111), Ru(001) and Ni(111). The high temperature, activated diffusion is predicted with remarkable accuracy, but at low temperatures significant discrepancies are found due to the transition to incoherent atom wave propagation. I show, however, how the bandstructure formalism gives a good framework in which to discuss and include calculations of such effects.

[1] P.G. Sundell and G. Wahnström, Phys. Rev. B 70 , 081303 (2004) [2] M.J. Puska and R.M. Nieminen, Surf. Sci. 157, 413 (1985) [3] T.-S. Lin and R. Gomer, Surf. Sci. 255 41 (1991)