1.13.1 Introduction

The study of radiation effects on the structure and properties of materials started more than a century ago,1 but gained momentum from the development of fission reactors in the 1940s. In 1946, Wigner2 pointed out the possibility of a deleterious effect on material properties at high neutron fluxes, which was then confirmed experimentally.3 A decade later, Konobeevsky et al4 discovered irradiation creep in fissile metallic uranium, which was then observed in stainless steel.5 The discovery of void swelling in neutron-irradiated stainless steels in 1966 by Cawthorne and Fulton6 demonstrated that radiation effects severely restrict the lifetime ofreactor materials and that they had to be systematically studied.

The 1950s and early 1960s were very productive in studying crystalline defects. It was recognized that atoms in solids migrate via vacancies under thermal — equilibrium conditions and via vacancies and self­interstitial atoms (SIAs) under irradiation; also that the bombardment with energetic particles generates high concentrations of defects compared to equilib­rium values, giving rise to radiation-enhanced diffu­sion. Numerous studies revealed the properties of point defects (PDs) in various crystals. In particular, extensive studies of annealing of irradiated samples resulted in categorizing the so-called ‘recovery stages’ (e. g., Seeger7), which comprised a solid basis for understanding microstructure evolution under irradiation.

Already by this time, which was well before the discovery of void swelling in 1966, the process of interaction of various energetic particles with solid

targets had been understood rather well (e. g., Kinchin and Pease8 for a review). However, the primary dam­age produced was wrongly believed to consist of Frenkel pairs (FPs) only. In addition, it was com­monly believed that this damage would not have serious long-term consequences in irradiated materi­als. The reasoning was correct to a certain extent; as they are mobile at temperatures of practical interest, the irradiation-produced vacancies and SIAs should move and recombine, thus restoring the original crys­tal structure. Experiments largely confirmed this sce­nario, most defects did recombine, while only about 1% or an even smaller fraction survived and formed vacancy and SIA-type loops and other defects. How­ever small, this fraction had a dramatic impact on the microstructure of materials, as demonstrated by Cawthorne and Fulton.6 This discovery initiated extensive experimental and theoretical studies of radiation effects in reactor materials which are still in progress today.

After the discovery of swelling in stainless steels, it was found to be a general phenomenon in both pure metals and alloys. It was also found that the damage accumulation takes place under irradiation with any particle, provided that the recoil energy is higher than some displacement threshold value, £d, (^30-40 eV in metallic crystals). In addition, the microstructure of different materials after irradiation was found to be quite similar, consisting of voids and dislocation loops. Most surprisingly, it was found that the microstructure developed under irradiation with ~1 MeV electrons, which produces FPs only, is similar to that formed under irradiation with fast neutrons or heavy-ions, which produce more compli­cated primary damage (see Singh et a/.1). All this created an illusion that three-dimensional migrating (3D) PDs are the main mobile defects under any type of irradiation, an assumption that is the foundation of the initial kinetic models based on reaction rate the­ory (RT). Such models are based on a mean-field approximation (MFA) of reaction kinetics with the production of only 3D migrating FPs. For conve­nience, we will refer to these models as FP produc­tion 3D diffusion model (FP3DM) and henceforth this abbreviation will be used. This model was devel­oped in an attempt to explain the variety of phenom­ena observed: radiation-induced hardening, creep, swelling, radiation-induced segregation (RIS), and sec­ond phase precipitation. A good introduction to this theory can be found, for example, in the paper by Sizmann,9 while a comprehensive overview was pro­duced by Mansur,10 when its development was already completed. The theory is rather simple, but its general methodology can be useful in the further development of radiation damage theory (RDT). It is valid for ^1MeV electron irradiation and is also a good introduction to the modern RDT, see Section

1.13.5.

Soon after the discovery of void swelling, a number of important observations were made, for example, the void super-lattice formation11-14 and the microm­eter-scale regions of the enhanced swelling near grain boundaries (GBs).15 These demonstrated that under neutron or heavy-ion irradiation, the material micro­structure evolves differently from that predicted by the FP3DM. First, the spatial arrangement of irradia­tion defects voids, dislocations, second phase particles, etc. is not random. Second, the existence of the micrometer-scale heterogeneities in the microstruc­ture does not correlate with the length scales accounted for in the FP3DM, which are an order of magnitude smaller. Already, Cawthorne and Fulton6 in their first publication on the void swelling had reported a nonrandomness of spatial arrangement of voids that were associated with second phase precipi­tate particles. All this indicated that the mechanisms operating under cascade damage conditions (fast neu­tron and heavy-ion irradiations) are different from those assumed in the FP3DM. This evidence was ignored until the beginning of the 1990s, when the production bias model (PBM) was put forward by Woo and Singh.16,17 The initial model has been changed and developed significantly since then18-2 and explained successfully such phenomena as high swelling rates at low dislocation density (Section

1.13.6.2.2) , grain boundary and grain-size effects in void swelling, and void lattice formation (Section

1.13.6.2.3) . An essential advantage of the PBM over the FP3DM is the two features of the cascade dam­age: (1) the production of PD clusters, in addition to single PDs, directly in displacement cascades, and (2) the 1D diffusion of the SIA clusters, in addition to the 3D diffusion of PDs (Section 1.13.3). The PBM is, thus, a generalization of the FP3DM (and the idea of intracascade defect clustering intro­duced in the model by Bullough et a/. (BEK29)). A short overview of the PBM was published about 10 years ago.1 Here, it will be described somewhat differently, as a result of better understanding of what is crucial and what is not, see Section 1.13.6.

From a critical point of view, it should be noted that successful applications of the PBM have been limited to low irradiation doses (< 1 dpa) and pure metals (e. g., copper). There are two problems that prevent it from being used at higher doses. First, the PBM in its present form1 predicts a saturation of void size (see, e. g., Trinkaus et at19 and Barashev and Golubov30 and Section 1.13.6.3.1). This originates from the mixture of 1D and 3D diffusion-reaction kinetics under cascade damage conditions, hence from the assumption lying at the heart of the model. In contrast, experiments demonstrate unlimited void growth at high doses in the majority of materials and conditions (see, e. g., Singh et at.,31 Garner,32 Garner et at.,33 and Matsui et at.34). An attempt to resolve this contradiction was undertaken23,25,27 by including thermally activated rotations of the SIA-cluster Burgers vector; but it has been shown25 that this does not solve the problem. Thus, the PBM in its present form fails to account for the important and common observation: the indefinite void growth under cascade irradiation. The second problem of the PBM is that it fails to explain the swelling satura­tion observed in void lattices (see, e. g., Kulchinski et at.13). In contrast, it predicts even higher swelling rates in void lattices than in random void arrange — ments.25 This is because of free channels between voids along close-packed directions, which are formed during void ordering and provide escape routes for 1D migrating SIA clusters to dislocations and GBs, thus allowing 3D migrating vacancies to be stored in voids.

Resolving these two problems would make PBM self-consistent and complete its development. A solu­tion to the first problem has recently been proposed by Barashev and Golubov35,36 (see Section 1.13.7). It has been suggested that one of the basic assumptions of all current models, including the PBM, that a random arrangement of immobile defects exists in the material, is correct at low and incorrect at high doses. The analysis includes discussion of the role of RIS and provides a solution to the problem, making the PBM capable of describing swelling in both pure metals and alloys at high irradiation doses. The solu­tion for the second problem of the PBM mentioned above is the main focus of a forthcoming publication by Golubov et at.37

Because of limitations of space, we only give a short guide to the main concepts of both old and more recent models and the framework within which radiation effects, such as void swelling, and hardening and creep, can be rationalized. For the same reason, the impact of radiation on reactor fuel materials is not considered here, despite a large body of relevant experimental data and theoretical results collected in this area.