A simple hopping model for the diffusion of an adsorbed species, from the surface and into the bulk of a material, was developed and analyzed mathematically. The difference in the energy barriers for an atom moving between atomic layers at the surface and in the bulk was considered. The model was also capable of describing the initial stages of diffusion. It was noted that conventional solutions of the continuum diffusion equation could not handle this situation. Auger electron spectroscopy was used to measure the dissolution rate of O from Zr(00•1) and Zr(10•0) surfaces and into the bulk (table 280). Satisfactory results were obtained by applying the present model to diffusion data for these Zr surfaces under various heating conditions. These were a rapid temperature ramp-and-hold, or continuous linear heating as a function of time. The associated Arrhenius expressions were:

[00•1]     D (cm2/s) = 0.115 exp[-44.45(kcal)/RT]

[10•0]     D (cm2/s) = 1.07 exp[-46.18(kcal)/RT]

B.Li, A.R.Allnatt, C.S.Zhang, P.R.Norton: Surface Science, 1995, 330, 276-88