Phase stability under irradiation: Ballistic effects

Abstract

We propose a simple mean-field description of solid solutions in the presence of irradiation-induced atomic mixing. The equilibrium configuration of the system is described by a concentration profile which is a steady-state solution of the appropriate diffusion equation. For clustering solid solutions, we show that a Lyapunov functional may be built, the minimum of which yields the equilibrium configuration. In a simple case (regular solution in the Bragg-Williams approximation together with simplifying assumptions on the concentration dependence of the diffusion coefficients), a law of corresponding states is found: The equilibrium configuration of the solid under irradiation flux $\phi$ and temperature $T$ is identical to the configuration at $\phi =0\mathrm{}$ and $T^{\prime }=T(1+\Delta )$ where $\Delta$ has a simple expression in terms of the irradiation parameters and of material characteristics. As a prototype of ordering solid solutions, the Bragg-Williams approximation of the $B2\mathrm{}$ structure is treated. A Lyapunov function is found; the above law of corresponding configurations is checked numerically and found to be obeyed fairly precisely. With the above law taken as a guide, interesting features are anticipated. In particular, we speculate on the possibility for obtaining equilibrium between an amorphous and a crystalline phase, the latter being a long-range-ordered or random solid solution.