1.18.1 Introduction

Irradiation creates excess point defects in materials (vacancies and self-interstitial atoms), which can be eliminated by mutual recombination, clustering, or annihilation of preexisting defects in the micro­structure, such as surfaces, grain boundaries, or dis­locations. As a result, permanent irradiation sustains fluxes of point defects toward these point defect sinks and, in case of any preferential transport of one of the alloy components, leads to a local chemical redistribution. These radiation-induced segregation (RIS) phenomena are very common in alloys under irradiation and have important technological implica­tions. Specifically in the case of austenitic steels, because Cr depletion at the grain boundary is sus­pected to be responsible for irradiation-assisted stress corrosion, a large number of experiments have been conducted on the RIS dependence on alloy composi­tion, impurity additions, irradiation flux and time, irradiation particles (electrons, ions, or neutrons), annealing treatment before irradiation, and nature of grain boundaries.1-5

The first RIS models generally consisted of appli­cation of Fick’s laws to reproduce two specific effects of irradiation: diffusion enhancement due to the increase ofpoint defect concentration, and the driving forces associated with point defect concentration gra­dients. According to these models, RIS is controlled by kinetic coefficients D or L (defined below) relating atomic fluxes to gradients of concentration or chemi­cal potentials. It was shown that these coefficients are best defined in the framework of the thermodynamics of irreversible processes (TIPs) within the linear response theory. RIS models were then separated into two categories: models restricted to dilute alloys, and models developed for concentrated alloys.

From the beginning until now, the dilute alloy models have benefited from progress made in the diffusion theory.6 The explicit relations between the phenomenological coefficients L and the atomic jump frequencies have been established, at least for alloys with first nearest neighbor (nn) interactions. In principle, such relations allow the immediate use of ab initio atomic jump frequencies and lead to pre­dictive RIS models.7

While the progress of RIS models of dilute alloys is closely related to that of diffusion theory, most segregation models for concentrated alloys still use oversimplified diffusion models based on Manning’s relations.8 This is mainly because the jump sequences of the atoms are particularly complex in a multicomponent alloy on account of the multiple jump frequencies and correlation effects that are involved. Only very recently has an interstitial diffu­sion model been developed that could account for short-range order effects, including binding energies with point defects.9, Emphasis has so far been

placed on comparisons with experimental observations. The continuous RIS models have been modified to include the effect of vacancy trapping by a large-sized impurity or the nature and displacement of a specific grain boundary. Most of the diffusivity coefficients of Fick’s laws are adjusted on the basis of tracer diffusion data. Paradoxically, the first RIS models were more rigorous11 than the present ones in which thermody­namic activities, particularly some of the cross-terms, are oversimplified. In this review, we go back to the first models starting from the linear response theory, albeit slightly modified, to be able to reproduce the main characteristics of an irradiated alloy. It is then possible to rely on the diffusion theories developed for concen­trated alloys.

Then again, lattice rate kinetic techniques12-14 and atomic kinetic Monte Carlo (AKMC) methods15-17
have become efficient tools to simulate RIS. Thanks to a better knowledge of jump frequencies due to the recent developments of ab initio calculations, these simulations provide a fine description of the thermo­dynamics as well as the kinetics of a specific alloy. Moreover, information at the atomic scale is precious when RIS profiles exhibit oscillating behavior and spread over a few tens of nanometers.

Discoveries and typical observations of RIS are illustrated in the first section. In the second section, the formalism of TIP is used to write the alloy flux couplings. It is explained that fluxes can be estimated only partially from diffusion experiments and ther­modynamic data. An alternative approach is the cal­culation of fluxes from the atomic jump frequencies. The third section presents more specifically the con­tinuous RIS models separated into the dilute and concentrated alloy approaches. The last section intro­duces the atomic-scale simulation techniques.