Non-equilibrium agglomeration of helium-vacancy clusters in irradiated materials

Abstract

Time evolution of non-equilibrium systems, where the probability density is described by a continuum Fokker-Planck (F-P) equation, is a central area of interest in stochastic processes. In this paper, a numerical solution of a two-dimensional (2-D) F-P equation describing the growth of helium-vacancy clusters (HeVCs) in metals under irradiation is given. First, nucleation rates and regions of stability of HeVCs in the appropriate phase space for fission and fusion devices are established. This is accomplished by solving a detailed set of cluster kinetic rate equations. A nodal line analysis is used to map spontaneous and stochastic nucleation regimes in the helium-vacancy (h-v) phase space. Growth trajectories of HeVCs are then used to evaluate the average HeVC size and helium content during the growth phase of HeVCs in typical growth instability regions.

The growth phase of HeVCs is modeled by a continuum 2-D, time-dependent F-P equation. Growth trajectories are used to define a finite solution space in the h-v phase space. A highly efficient dynamic remeshing scheme is developed to solve the F-P equation. As a demonstration, typical HFIR irradiation conditions are chosen. Good agreement between the computed size distributions and those measured experimentally are obtained.