Spatially ordered void ensemble states at high irradiation temperatures

Abstract

The physical mechanism of the spatially homogeneous void ensemble state instability with respect to small void size deviations induced by vacancy emission from voids is demonstrated by means of both the exact diffusion and chemical rate equations for the point defect concentrations in a volume containing voids. As it was shown in previous papers the corresponding instability conditions can be valid at rather high irradiation temperatures (higher than the swelling maximum). Here the nonlinear analysis of the void system response to small void size variations is carried out to obtain the qualitative characteristics of spatially ordered void distribution when the instability concerned takes place. Void ordering is the result of the spatially homogeneous void shrinkage after the completion of void nucleation process. Only “ordered” voids survive. The mathematical investigation is based on the conception of slowly and rapidly varying distributions, which is used to describe in unified fashion a spontaneous formation of ordered structures in a large class of nonequilibrium physical systems, whose properties depend on the parameters that differ in their spatial dispersion. In the case under consideration the spatial diffusion lengths of point defects and voids are such parameters. It is shown that the constructed periodical void distribution is stable in time with respect to small void size deviations. The roles of the anisotropic transport of self-interstitials in the void spatial ordering and the stochastic fluctuations of void growth rate in the expansion of the temperature range of the nonequilibrium phase transition from a spatially disordered to an ordered void system state are also discussed.