Determination of Krypton Diffusion Coefficients in Uranium Dioxide Using Atomic Scale Calculations

We present a study of the diffusion of krypton in UO₂ using atomic scale calculations combined with diffusion models adapted to the system studied. The migration barriers of the elementary mechanisms for interstitial or vacancy assisted migration are calculated in the DFT+U framework using the nudged elastic band method. The attempt frequencies are obtained from the phonon modes of the defect at the initial and saddle points using empirical potential methods. The diffusion coefficients of Kr in UO₂ are then calculated by combining this data with diffusion models accounting for the concentration of vacancies and the interaction of vacancies with Kr atoms. We determined the preferred mechanism for Kr migration and the corresponding diffusion coefficient as a function of the oxygen chemical potential μ_O or nonstoichiometry. For very hypostoichiometric (or U-rich) conditions, the most favorable mechanism is interstitial migration. For hypostoichiometric UO₂, migration is assisted by the bound Schottky defect and the charged uranium vacancy, V_U^4-. Around stoichiometry, migration assisted by the charged uranium-oxygen divacancy (V_UO^2-) and V_U^4- is the favored mechanism. Finally, for hyperstoichiometric or O-rich conditions, the migration assisted by two V_U^4- dominates. Kr migration is enhanced at higher μ_O, and in this regime, the activation energy will be between 4.09 and 0.73 eV depending on nonstoichiometry. The experimental values available are in the latter interval. Since it is very probable that these values were obtained for at least slightly hyperstoichiometric samples, our activation energies are consistent with the experimental data, even if further experiments with precisely controlled stoichiometry are needed to confirm these results. The mechanisms and trends with nonstoichiometry established for Kr are similar to those found in previous studies of Xe.