Most of the RIS models for concentrated alloys were devoted to the ternary Fe-Cr-Ni system, which is a model alloy of austenitic steels. The diffusion ratios used in the fitting process are the ones extracted from the tracer diffusion coefficients measured by Rothman et al. (referenced in Perks and Murphy104 and Allen and Was11 ). In most of the studies, the input parameters are taken from Perks model.104 The more recent MIK model, which was initially based on the Perks model, used the CALPHAD database to fit its concentration-dependent migration energy model.11 A significant improvement in the predictive cap­abilities of RIS modeling was concluded after a sys­tematic comparison with RIS, observed by Auger spectroscopy in Fe-Cr-Ni as a function of tempera­ture, nominal composition, and irradiation dose.1 However, all the models were proved to be powerful enough to reproduce the correct tendencies of RIS in austenitic steels: a depletion of Cr and an enrich­ment of Ni near a grain boundary. When the binding energies of point defects with atoms are not so strong and the ratios between the tracer diffusion coefficients of the major elements are large enough (larger than 2-3), a rough estimation of the partial diffusion coefficients from tracer diffusion coefficients seems to be sufficient to reproduce the main tendencies.

The interstitial contribution to RIS is usually neglected due to the lack of diffusion data. Stepanov eta/.120 observed an electron-irradiated foil at a tem­perature low enough so that only interstitials con­tributed to the RIS. Segregation profiles were similar to the typical ones at higher temperature. Parameters of the interstitial diffusion model were estimated in such a way that the experimental RIS was repro­duced. The migration energy of interstitials was assumed to be equal to 0.2 eV, which is quite low in comparison with the effective migration energy deduced from recovery resistivity measurements.121

The attempts of the MIK model to reproduce the characteristic ‘W-shaped’ Cr profiles observed at intermediate doses were not conclusive36; transitory profiles disappeared after a dose of 0.001 dpa, while the experimental threshold value was around 1 dpa. A possible explanation may be the approximation used to calculate the chemical driving force. Indeed, a thermodynamic factor equal to 1 pushes the system to flatten the concentration profile in reaction to the formation of the RIS profile. A study based on a lattice rate theory pointed out that an oscillating profile was the signature of a local equilibrium estab­lished between the surface plane and the next plane.13 This kind of mean-field model predicts that the local enrichment of Cr at a surface persists at larger irradiation dose (0.1 dpa), though not as large as the experimental value.

The role of impurities as point defect traps has been explored since the 1970s.122 In those models, impurities do not contribute to fluxes but to the sink population as immobile sinks with an attachment parameter depending on an impurity-point defect binding energy.123 Other models account for immo­bile vacancy traps by renormalizing the recombina­tion coefficient with a vacancy-impurity binding energy. Whether by vacancy or by interstitial trapping, the result is a recombination enhancement and a decrease of point defect concentrations, leading to a reduction of RIS and swelling. Hackett et a/.12 estimated some binding energies between a vacancy and impurities, such as Pt, Ti, Zr, and Hf in fcc Fe, using ab initio calculations. The energy calculations seem to have been performed without relaxing the structure, probably because fcc Fe is not stable at 0 K. Although the absolute values of the binding energies should be used with caution, one can expect the strong difference between the bind­ing energies of a vacancy with Zr (1.08 eV) and Hf (0.71 eV) to persist after a relaxation of atomic posi­tions. In a more rigorous way, the trapping of dumb­bells could be modeled using the high migration energy associated with dumbbells bound to an impu — rity.12 Such a model would allow the impurity to migrate and change the sink density with dose. The same model could explain the recent experimental results observing that, after a few dpa, RIS of the major elements starts again.123

RIS in austenitic steels was observed to be strongly affected by the nature of the grain boundary, that is, by the misorientation angle and the S value.40 Differences between the observed RIS are explained by a so-called grain boundary efficiency, introduced in a modified rate equation model.40,109,114,124 Calcu­lations of vacancy formation energies at different grain boundaries, for example, in nickel in which atomic interactions are described by an embedded atom method, have been used to model sink strength as a function of misorientation angle. The resulting RIS predictions around several tilt grain boundaries were found to be in good agreement with RIS data.124 Grain boundary displacement and its effect on RIS were considered too. Grain boundary displacement was explained by an atomic rearrangement process due to recombination of excess point defects at the interface. New kinetic equations including an atomic rearrangement process after recombination of point defects at the interface predict asymmetrical concen­tration profiles, in agreement with experiments.114