A combined rate theory-population balance model of the evolution of irradiation-induced helium bubbles in metals during annealing.

• A multiscale model describing the evolution of helium bubbles is established based on the rate equations and the population balance equation. • The model can effectively describe the nucleation and evolution of helium bubbles. • The model contains bubble evolution mechanisms including "migration and coalescence (MC)" and "Ostwald ripening (OR)". • The model allows for independent statistics on the contribution of MC and OR, as well as an explanation of their coupling effects. A multiscale model describing the evolution of helium bubbles in the irradiated materials is established based on the rate equations and the population balance equation. The size distribution of the helium bubbles and the evolution law of the statistical average size and number density of the bubbles with time changing predicted by the model are in good agreement with the experimental statistics. The influence of annealing temperature, annealing time, irradiation energy, irradiation flux, and coarsening mechanisms on the evolution of helium bubbles are numerically simulated and discussed, taking FeCrAl alloy as the irradiated material. The results show that the bubble evolution is dominated by the Ostwald ripening mechanism under high temperature annealing conditions (≥ 1073 K), and the time dependence of the average size and density of helium bubbles is consistent with the existing theoretical results. And the number of shrinking helium bubbles caused by Ostwald ripening is effectively reduced by the bubble coalescence effect, leading to further growth of the proportion of large-sized helium bubbles. Consequently, a Gaussian bubble size distribution has been obtained modeling the coupling of the Ostwald ripening mechanism and the bubble coalescence mechanism. The generation rates of helium and vacancy in the material during irradiation, as well as their ratio, are significant factors that can affect the nucleation and evolution of helium bubbles. [ABSTRACT FROM AUTHOR]