Theory and numerical simulations of defect ordering in irradiated materials

Abstract

A general theory for the spatial ordering of immobile clustered defects 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), instabilities leading to spatially ordered microstructure are driven by vacancy cluster density fluctuations, which extends the range of validity of previous conclusions for microstructure with no void present (e.g., low temperature). The crucial importance of collision-cascade-induced vacancy cluster formation is clearly shown. Amplitude equations of the Ginzburg-Landau type are derived and used to discuss the qualitative features of microstructure pattern formation in the post-bifurcation 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 irradiation conditions. The quasistatic approximation used in the weakly nonlinear analysis is shown to be adequate only for short irradiation doses. At larger times, higher mode generation leads to a wavelength selection that is somewhat insensitive to the dose, as observed experimentally. The role of interstitial diffusion anisotropy is shown to be significant in the alignment of microstructural patterns in parallel orientation to the directions of high interstitial mobility, in agreement with experiments. @S0163- 1829~96!03722-8#