The effect of elastic anisotropy on the symmetry selection of irradiation-induced void superlattices in cubic metals

Self-organized microstructures and patterns have been widely observed in non-equilibrium physical systems. In particular, irradiation in metals creates far-from-equilibrium environments, in which the competing dynamics of defect production and annihilation can lead to unique self-organized superlattice structures, e.g., void and gas bubble superlattices. From a physical point of view, the superlattice structures are dictated by the intrinsic symmetry breaking in the metals, i.e., anisotropy caused by the breaking of continuous rotational symmetry. In the literature, two distinctive anisotropies, elastic anisotropy and diffusion anisotropy of interstitials, have been proposed to be the origins of superlattice formation. However, it is still unclear which anisotropy dominates the symmetry selection of superlattice structures. In this paper, we study elastic anisotropy and its effect on the symmetry of void superlattices. By using theoretical analyses and phase field simulations, we show that elastic anisotropy in cubic metals can lead to either face-centered cubic or simple cubic superlattices depending on the Zener anisotropy ratio. The superlattices formed under this elastic anisotropy mechanism must form under the influence of spinodal decomposition, as the mechanism requires perturbations in the vacancy concentration field to develop into spatially-static concentration waves. We compare to existing work on symmetry selection in superlattices via diffusion anisotropy and to experimental observations, and we suggest that concentration wave development under the influence of elastic anisotropy is not the mechanism for symmetry selection during the formation of irradiation-induced void superlattices, but that diffusion anisotropy could be the dominant mechanism.