^{1}

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.

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 [

The issue of solid solution instability under irradiation has been addressed by several researchers in the past. These investigations may be broadly categorized into two major themes. In one class of investigation, the state of the material under irradiation is represented by a coupled system of reaction-diffusion equations in defect and material component fields. In these formulations, the origin and subsequent growth of the instability have been attributed to the presence of vacancy-interstitial recombination reactions, assisted by off-diagonal terms of the diffusion matrix [

In the present study, the instability of a solid solution under irradiation has been investigated. For a binary system under irradiation, there are six species in the model: three off-lattice dumbbell interstitials, vacancy, and two material components. All the defect species diffuse either by vacancy mechanism or by interstitialcy mechanism. The diffusion of material components is coupled to the diffusion of the defects. The defects participate in two types of reactions: vacancy-interstitial recombination and change in dumbbell type when a dumbbell interstitial encounters a lattice atom of different type. The defect production has been considered uniform in space and time. The model consists of a set of six coupled nonlinear reaction-diffusion equations with uniform source. For a miscible system (Cu-Au) under irradiation, the linear stability analysis of the reaction-diffusion equations shows that the solid solution indeed becomes unstable when a set of control parameters (temperature, defect production rate, and initial alloy composition) is varied in a certain way.

Section

We consider an ideal, concentrated binary solid solution, AB, under irradiation. There are six species in the model: three types of dumbbell interstitials (AA, BB, and AB), vacancy, and A and B lattice atoms. Under operating temperatures of nuclear reactors, the defects are sufficiently mobile. All the defect species diffuse either via vacancy mechanism or via interstitialcy mechanism. The diffusion of the material components is mediated by the defects. In addition to diffusion, defects also participate in two types of reactions: vacancy-interstitial recombination and change in the dumbbell-type reactions. Change in the dumbbell type happens when a dumbbell encounters a lattice atom of different type than its constituents. In this formulation, A is a faster diffusing species both by vacancy and interstitialcy mechanism, whereas B is the slower diffusing species. Evolution of all the species is governed by reaction-diffusion type dynamics with uniform defect generation term,

Before performing linear stability analysis, the system of reaction-diffusion equations has been nondimensionalized with respect to the intrinsic length and time scales of the system. This has been achieved by the following transformations:

The concentrations

The perturbations grow in space and time as follows:

Considering Cu-Au as the system of interest [

Stable (^{−6}

Stability of a binary solid solution under irradiation has been studied. There are six species in the model: three dumbbells as off-lattice species, vacancies, and two material components as on-lattice species. The temporal evolution of the solid solution is described by a set of coupled nonlinear reaction-diffusion equations in all the species concentration. Defects diffuse either by vacancy mechanism (vacancies) or by interstitialcy mechanism (dumbbells). The diffusive flux of the defects has been derived in the Fickian framework by considering the solid solution to be isotropic and ideal. The correlation effects in the defect jumps have also been neglected. The flux of the atomic species is coupled to the defect fluxes. Defects also participate in two types of reactions: recombination and change in the dumbbell type. Stability of the solid solution has been investigated by performing linear stability analysis of the set of six reaction-diffusion equations with respect to the uniform state of the binary solid solution under quasi-static approximation [

The authors declare that there is no conflict of interests regarding the publication of this paper.

^{+}irradiated metals