THEORY AND NUMERICAL SIMULATIONS OF DEFECT ORDERING IN IRRADIATED MATERIALS

A general theory for the spatial ordering of immobile clustered defect s in irradiated materials is presented here. A vectorial form for the Fourier transforms of perturbations in the concentration of point and clustered defects is derived. Linear stability analysis indicates that , under conditions appropriate for void growth (high temperature), ins tabilities leading to spatially ordered microstructure are driven by v acancy cluster density fluctuations, which extends the range of validi ty of previous conclusions for microstructure with no void present (e. g., low temperature). The crucial importance of collision-cascade-indu ced vacancy cluster formation is clearly shown. Amplitude equations of the Ginzburg-Landau type are derived and used to discuss the qualitat ive features of microstructure pattern formation in the post-bifurcati on regime. This is accompanied by numerical analysis of the space-time rate equations to test the validity of the weakly nonlinear analysis. Evolution of one- and two-dimensional patterns of the microstructure is illustrated by examples of typical reactor and accelerator irradiat ion conditions. The quasistatic approximation used in the weakly nonli near analysis is shown to be adequate only for short irradiation doses . At larger times, higher mode generation leads to a wavelength select ion that is somewhat insensitive to the dose, as observed experimental ly. The role of interstitial diffusion anisotropy is shown to be signi ficant in the alignment of microstructural patterns in parallel orient ation to the directions of high interstitial mobility, in agreement wi th experiments.