Model for the kinetics of cluster nucleation in irradiated materials

The development of materials microstructures during the initial stages of irradiation is important in the overall irradiation performance of the material. The incubation dose to the onset of measurable void swelling is critical for assessing the material's useful life in design situations. Several numerical models, based on void and interstitial loop nucleation and early growth theories, have been developed to predict experimental observations of void and interstitial loop number densities and size distributions evolved during irradiation. These models are complicated and difficult to implement. In this paper, a model describing interstitial dislocation loop nucleation and growth kinetics is presented. The model involves the solution of the Fokker-Planck equation which represents a continuum description of the process. The solution is found through an eigenfunction expansion after applying a suitable transformation to the equation. Boundary values are chosen to properly represent the physical problem. An approximation for the point defect agglomeration is necessary to pose the problem for solution. This model is applied to materials and irradiation conditions that represent those of the first wall of a fusion reactor.