The formation ofvoids in irradiated solids results from the clustering of vacancies, which can be assisted by vacancy clusters produced directly in displacement cascades and by the presence of gas atoms. Vacancy supersaturation under irradiation may locally reach a level large enough to trigger clustering owing to the biased elimination of interstitials on sinks, especially since interstitial atoms and small interstitial clusters usually migrate much faster than vacancies. Evans134 discovered in 1971 that under irradiation voids may self-organize into a mesoscopic lattice. The symmetry of the void lattice is identical to that of the underlying crystal, but with a void lattice parameter about two orders of magnitude larger than the crystalline lattice parameter (see also the reviews by Jager and Trin — kaus135 and Ghoniem et al.136 for irradiation-induced patterning reactions). It has been suggested that the formation of the void lattice results from the 1D migra­tion of self-interstitial atoms (SIAs) and of clusters of SIAs, although elastic interactions between voids could also contribute to self-organization.137 This 1D migra­tion of SIAs would stabilize the formation of voids along directions of the SIAs migration by a shadowing
effect.138-140 The model proposed by Woo141 indicates, in particular, that the mean free path of SIAs needs to exceed a critical value for a void lattice to be stable. Atomistic KMC simulations have been performed142 to evaluate the dynamics of void formation, shrinkage, and organization during irradiation. Due to the large difference in mobility of vacancies and interstitials, the slow evolution of the microstructure, and the large range of length scales, assumptions had to be used, in particular, regarding the void position and size. Recently, Hu and Henager143 have approached the problem of void lattice formation in a pure metal using a PFM. Their model relies on the traditional approach presented in Section 1.15.2 for the evolution of the vacancy field, but it makes use of continuum­time random-walk kinetics for modeling the fast transport of interstitials. 2D simulations indicate that irradiation can stabilize a void lattice if the ratio of SIA to vacancy diffusion coefficients is large enough (see Figure 12) and if the defect production rate is not too large (see Figure 13). It would be interesting to extend this first model to include interstitial clusters. The model lacks an absolute length scale, for the rea­sons discussed in Section 1.15.2, and thus nucleation of new voids is treated in a deterministic and phenomeno­logical manner based on the local vacancy concentra­tion. It would clearly be beneficial to use a quantitative PFM of the type presented in Section 1.15.3 to treat void nucleation. This would also then make it possible to directly compare the void size stabilized by irradia­tion with experimental observations.

We note also that Rokkam et al.144 recently intro­duced a simple PFM for void nucleation and coarsen­ing in a pure element subjected to irradiation-induced vacancy production. In addition to the local vacancy concentration, these authors introduced a noncon­served order parameter to model the matrix-void interface, similar to the nonconserved order parameter

used for solid-liquid interfaces. It is shown144’145 that this model reproduces many known phenomena, such as nucleation, growth, coarsening of voids, as well as the formation of denuded zones near sinks such as free surfaces and grain boundaries. This phe­nomenological model is currently limited by the absence of interstitial atoms in the description. It may also suffer from the fact that the void-matrix interfaces are intrinsically treated as diffuse, whereas real void-matrix interfaces are essentially atom­ically sharp. This problem is further discussed in the following section.