Kramers’ turnover theory for diffusion of Na atoms on a Cu(001) surface measured by He scattering

The diffusion of adatoms and molecules on a surface at low coverage can be measured by helium scattering. The experimental observable is the dynamic structure factor. In this article, we show how Kramers’ turnover theory can be used to infer physical properties of the diffusing particle from the experiment. Previously, Chudley and Elliot showed, under reasonable assumptions, that the dynamic structure factor is determined by the hopping distribution of the adsorbed particle. Kramers’ theory determines the hopping distribution in terms of two parameters only. These are an effective frequency and the energy loss of the particle to the bath as it traverses from one barrier to the next. Kramers’ theory, including finite barrier corrections, is tested successfully against numerical Langevin equation simulations, using both separable and nonseparable interaction potentials. Kramers’ approach, which really is a steepest descent estimate for the rate, based on the Langevin equation, involves closed analytical expressions and so is relatively easy to implement. Diffusion of Na atoms on a Cu(001) surface has been chosen as an example to illustrate the application of Kramers’ theory.