Homogenization of reconstructed crystal surfaces: Fick's law of diffusion.

Fick's law for the diffusion of adsorbed atoms (adatoms) on crystal surfaces below roughening is generalized to account for surface reconstruction. In this case, material parameters vary spatially at the microscale, and the coarse graining for crystal steps via Taylor expansions is not strictly applicable. By invoking elements of the theory of composites in one independent space dimension, we homogenize the microscale description to derive the macroscopic adatom flux from step kinetics. This approach relies on a multiscale expansion for the adatom density. The effective surface diffusivity is determined through appropriate discrete averages of microscale kinetic parameters.