A quantitative phase-field model of gas bubble evolution in UO₂

Due to the large formation energy of vacancies and noble gas atoms at interstitial and/or substitutional sites in nuclear fuel (UO₂), the thermodynamic equilibrium concentrations of these species are very low in the nuclear fuel matrix even at very high temperature, which imposes difficulties upon the quantitative study of bubble evolution via the phase-field method. In this study, a quantitative phase-field model is proposed to deal with this problem. The free energy density of the system is derived according to the principles of thermodynamics, with consideration of the elastic interaction and internal pressure of each gas bubble, and with the use of material parameters from experiments. The model enables one to study the kinetics of gas bubble growth with very dilute concentrations of vacancy and gas atoms in the matrix. With this model, the growth of a single bubble and multiple bubbles were simulated under different concentrations of vacancy and gas atoms and at different temperatures. The effect of elastic interaction energy and the generation rate of vacancies and gas atoms on bubble growth are analyzed.