where ∇ ∥ J i (γ) is the gradient for surface diffusion flux, ρ i is the surface density, c i (γ) is the surface mass fraction of the k-component and Jn e (γ) is related to species arriving at a surface state characterized by γ. The stoichiometric coefficients vkr of species k in reaction r of the adsorption process leads to the correspondence: