Xe gas bubbles evolution in UO₂ fuels - A phase field simulation

Owing to the large formation energy of vacancies and inert gas atoms (Xe and Kr) in nuclear fuel (UO₂), the thermodynamic equilibrium concentrations of these species are extremely low in the UO₂ matrix, which makes it extremely difficult to conduct quantitative study of gas bubbles evolution by phase-field method (PFM). In this study, a more physics based quantitative phase-field model has been proposed. The free energy density of the system was derived according to the principles of thermodynamics and KKS model, the UO₂ tri-vacancy, Xe gas atoms and gas bubbles were considered in the system. This model enables one to study the gas bubble growth with extremely low concentrations of vacancy and Xe gas atom in the UO₂ matrix. The influence of temperature, vacancy and Xe gas atom generation rates on single and multi-gas bubbles evolution were studied. At high temperature and with high generation rates of vacancies and Xe gas atoms, the gas bubbles had higher growth rate. In addition, the effect of temperature gradient on gas bubble migration was also studied by adding a temperature gradient term in the Cahn-Hillard equations. The gas bubble preferred to migrate to high temperature area. Their shape changed from initial circular shape to a prolate shape along the direction of temperature gradient, which is consistent with the experimental results. The simulation results confirmed the formation of center cavity in the nuclear fuel pellet. The simulation results are consistent with the classical rate theory and experimental observations.