Linear stability analysis of helium-filled cavities in SiC

Abstract

In this paper, we present a theoretical analysis of the stability of cavities in SiC under fusion irradiation conditions. Nucleation and growth of helium-filled cavities is modeled by dynamical equations, The growth/shrinkage of a cavity is given in terms of two equations representing the rates of change of the net number of vacancies and helium atoms inside the cavity. The equations describe the drift motion of cavities in a two-dimensional phase under the influence of point defect and helium absorption. First the linear stability of these equations is performed to identify the nature of singular points in phase space. The directions of trajectories around the saddle point are also found. The effects of dislocation density and void density on the nature of the singular points are considered. The effect of helium atom generation rate is also investigated. It is found that in the case of high helium generation, as in SiC under fusion conditions, the critical cavity size is relatively small (about 30 A), and one saddle point is found between two stable critical points. This is shown to correspond to a bimodal cavity distribution.