The first mean-field lattice rate models included two thermally activated jump frequencies, one for the vacancy and the other for the interstitial. A direct interstitial diffusion mechanism14 and later a dumb­bell diffusion mechanism1 have been modeled in detail. The vacancy jump frequency parameters are fitted to available thermodynamic and tracer dif­fusion data, and the interstitial parameters are fitted to effective migration energies derived from resistiv­ity recovery measurements.121 The resulting local — concentration-dependent jump frequencies describe both the kinetics of thermal alloys toward equilib­rium and irradiation-induced surface segregation in concentrated alloys. The surface and its vicinity are modeled by the stacking of N parallel atomic planes perpendicular to the diffusion axis, which is taken to be a [100] direction of an fcc alloy. A mirror bound­ary condition is used at one end, and a free surface, which can act as both a source and sink for point defects at the other end. Above the surface, a buffer plane almost full of vacancies is added. Fluxes between the buffer plane and vacuum are forbidden. The resulting equilibrium segregation profiles are controlled by the nominal composition, temperature, and two interaction contributions, the first one expressed in terms of the surface tensions and the second in terms of the ordering energies. Note, that the predicted equilibrium vacancy concentration at the surface is much higher than in the bulk.

Time dependence of mean occupations in an atomic plane of point defects and atoms results from a balance between averaged incoming and out­going fluxes. Fluxes are written within a mean-field approximation, decoupling the statistical averages into a product of mean occupations and mean jump frequencies for which the occupation numbers in the exponential argument are replaced by the corresponding mean occupations. The resulting first order differential kinetic equations are integrated using a predictor corrector variable time step algo­rithm because of the high jump frequency disparities between vacancies and interstitials.

It is observed that interstitial contribution to RIS is of the same order as that of the vacancy. The predicted formation of a ‘W-shaped’ profile as a tran­sient state from the preirradiated enrichment to the strong depletion of Cr is shown to be governed by both thermodynamic properties and the relative values of the transport coefficients between Fe, Cr, and Ni (Figure 9). Thermodynamics not only plays a part in the transport coefficients but also arises in the establishment of a local equilibrium between the surface and the adjacent plane, explaining the oscil­latory behavior of the Cr profile: an equilibrium tendency toward an enrichment of Cr at the grain boundary plane, which competes with a Cr depletion tendency under irradiation. However, the predicted profile is not as wide as the experimental one.

What needs to be improved is the interstitial dif­fusion model. The lack of experimental and ab initio data leads to approximate interstitial jump frequen­cies. Coupling between fluxes is described partially as correlation effects are not accounted for. The recent mean-field developments98 should be integrated in this type of simulation.