A phase-field model for void and gas bubble superlattice formation in irradiated solids

Abstract

A phase-field model to simulate the formation of both void and gas bubble superlattices is derived from a grand potential functional, assuming 1D diffusion of self-interstitial atoms. The model is capable of accounting for superlattice formation by either a nucleation and growth or spinodal decomposition mechanism; in this work, we focus on the nucleation and growth mechanism, using a discrete nucleation approach in the phase-field model. In simulations of void formation, short aligned rows of voids were initially formed, followed by growth in the size of the aligned rows, and finally leading to superlattice formation, consistent with experimental observations. Void superlattice spacing as a function of model parameters was quantified. Increased nucleation rates led to smaller superlattice spacing, while increased vacancy diffusivity led to larger superlattice spacing. In simulations of gas bubble superlattice formation, superlattice spacing decreased with increasing gas atom flux, consistent with experimental observations. Simulations with increasing ratio of gas atom flux to vacancy–interstitial pair production led to increased superlattice spacing, which is inconsistent with experimental observations at high gas atom flux rates; this discrepancy is attributed to the fact that the model does not account for bound gas atom–vacancy pairs that may dominate at high gas flux rates.