A general theory was presented for the spatial ordering of immobile clustered defects in irradiated materials. A vectorial form was derived for the Fourier transforms of perturbations in the concentrations of point and clustered defects. A linear stability analysis indicated that, under suitable conditions (high temperatures) for void growth, instabilities which led to spatially ordered microstructures were driven by vacancy cluster density fluctuations. This extended the range of validity of previous conclusions for low-temperature microstructures without voids. It was shown that collision cascade-induced vacancy cluster formation was crucially important. Amplitude equations of Ginzburg-Landau type were derived, and were used to analyze the qualitative features of microstructure pattern formation in the post-bifurcation regime. This was combined with numerical analysis of the space-time rate equations in order to test the validity of the weakly non-linear analysis. The evolution of 1-dimensional and 2-dimensional patterns in a microstructure was illustrated by using examples of reactor and accelerator irradiation. The quasi-static approximation which was used in the weakly non-linear analysis was shown to be adequate only for short irradiation doses. At longer times, higher-mode generation led to a wavelength selection that was rather insensitive to the dose; as observed experimentally. The role of interstitial diffusion anisotropy was shown to be significant with regard to the alignment of microstructural patterns in orientations that were parallel to directions of high interstitial mobility; again in agreement with experiment.

D.Walgraef, J.Lauzeral, N.M.Ghoniem: Physical Review B, 1996, 53[22], 14782-94