The stability of a binary solid solution under irradiation has been studied. This has been done by performing linear stability analysis of a set of nonlinear reaction-diffusion equations under uniform irradiation. Owing to the complexity of the resulting system of eigenvalue equations, a numerical solution has been attempted to calculate the dispersion relations. The set of reaction-diffusion equations represent the coupled dynamics of vacancies, dumbbell-type interstitials, and lattice atoms. For a miscible system (Cu-Au) under uniform irradiation, the initiation and growth of the instability have been studied as a function of various control parameters. 1. Introduction Materials under irradiation are a class of dissipative systems driven far away from the equilibrium state due to production of high densities of defects. These systems decay to lower energy metastable states by the process of phase transformation, microstructure evolution, spatial organization of compositional fluctuations and microstructural elements, and so forth [1]. The spatial organization of compositional fluctuations and microstructural elements happens when the material becomes unstable to infinitesimal perturbations in the order parameter characterizing the pattern: for example, in the case of compositional fluctuations, the order parameter is the composition, whereas, in the case of microstructural elements, the order parameter is the density of these elements. Well known examples of spatial organization of microstructural elements are voids [2–4] and bubble lattices [5, 6], precipitate ordering [7], and ordering of vacancy dislocation loops [8]. On the other hand, spatial organization of compositional fluctuations has been observed in two types of material systems. In thermodynamically unstable systems (e.g., Fe-35%Ni-Cr), the spatial organization of compositional fluctuations takes place when a sluggish long wavelength spinodal-type instability in the composition is accelerated under irradiation, which lead to decomposition of the solid solution; long-term thermal annealing of the irradiated specimen has no effect on the state of the material [9]. On the other hand, in thermodynamically stable systems (e.g., Fe-15%Ni-Cr), the origin of compositional fluctuations is solely due to irradiation. When irradiation is turned off and irradiated sample is annealed for long time, the material attains its homogeneous state [10]. The presence of spatial structures with definite characteristics has strong influence on the physical and mechanical properties of the materials. Therefore, it
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