Phase-field simulations of gas density within bubbles in metals under irradiation

Phase-field simulations are used to study the evolution of gas density within irradiation-induced bubbles in solids. In our simulations, which use copper as a model material, the dpa rate, gas production rate, and defect diffusivities are systematically varied to understand their effect on bubble nucleation rates, bubble densities, and the distribution of gas concentration within bubbles and in the solid regions. We find that gas densities within bubbles fluctuate drastically in the early nucleation stages, when growth rates are highest, but converge to steady-state values during the later coarsening stages. The steady-state gas densities within bubbles correspond with the ratio of total accumulated vacancy content divided by the total accumulated gas content, in agreement with a thermodynamic analysis concerning free-energy minimization.