Predicting trends in rate parameters for self-diffusion on FCC metal surfaces

The hopping self diffusion coefficient of an adatom on the (1 0 0), (1 1 0) and (1 1 1) surfaces of nine FCC metals have been investigated using Monte Carlo variational transition state theory and the Lennard-Jones (L-J) interactions. The metals that have been studied are Ag, Al, Au, Cu, Ir, Ni, Pd, Pt and Rh. The potential parameters for the L-J interactions have been determined from the known experimental values of cohesive energies and lattice constants. The ratio, R, of the cohesive energy to the activation energy for diffusive hopping on the (1 1 1) and (1 0 0) surfaces are found to be 30 and 6, respectively. For diffusive hopping on the (1 1 0) surface, R depends on the direction of diffusion: R is 5 and 2.8 along the [1 1 0] and [0 0 1] directions, respectively. The pre-exponential factor, D 0, for these metals is found to vary within a factor of three from the corresponding average value, ( D 0) av for a given surface and diffusion channel. Also, the pre-exponential factors corresponding to diffusion on the (1 1 1), (1 0 0), (1 1 0) [1 1 0] and (1 1 0)[0 0 1] surfaces are found to satisfy an empirical expression in terms of R, lattice constant, and the distance between the two nearest binding sites. The results on the activation energies and pre-exponential factors are compared with other experimental and theoretical data.