Interplay of defect cluster and the stability of xenon in uranium dioxide from density functional calculations

Self-defect clusters in bulk matrix might affect the thermodynamic behavior of fission gases in nuclear fuel such as uranium dioxide. With first-principles local spin-density approximation plus $U$ calculations and taking xenon as a prototype, we find that the influence of oxygen defect clusters on the thermodynamics of gas atoms is prominent, which increases the solution energy of xenon by a magnitude of 0.5 eV, about 43% of the energy difference between the two lowest lying states at 700 K. Calculation also reveals a thermodynamic competition between the uranium vacancy and trivacancy sites to incorporate xenon in hyperstoichiometric regime at high temperatures. The results show that in hypostoichiometric regime neutral trivacancy sites are the most favored position for diluted xenon gas, whereas in hyperstoichiometric condition they prefer to uranium vacancies even after taking oxygen self-defect clusters into account at low temperatures, which not only confirms previous studies but also extends the conclusion to more realistic fuel operating conditions. The observation that gas atoms are ionized to a charge state of ${\text{Xe}}^{+}$ when at a uranium vacancy site due to strong Madelung potential implies that one can control temperature to tune the preferred site of gas atoms and then the bubble growth rate. A solution to the notorious metastable states difficulty that frequently encountered in density functional theory plus $U$ applications, namely, the quasiannealing procedure, is also discussed.