A comprehensive investigation on point defects and their clustering behavior in nonstoichiometric uranium dioxide $\mathrm{U}{\mathrm{O}}_{2\pm x}$ is carried out using the $\mathrm{LSDA}+\mathrm{U}$ method based on density functional theory. Accurate energetic information and charge transfers available so far are obtained. With these energies that have improved more than 50% over that of pure generalized gradient approximation and local density approximation, we show that the density functional theory predicts the predominance of oxygen defects over uranium ones at any compositions, which is possible only after properly treating the localized $5f$ electrons. Calculations also suggest an upper bound of $x\sim 0.03$ for oxygen clusters to start off. The volume change induced by point uranium defects is monotonic but nonlinear, whereas for oxygen defects, increasing $x$ always reduces the system volume linearly, except dimers that require extra space for accommodation, which has been identified as a metastable ionic molecule. Though oxygen dimers usually occupy Willis ${\mathrm{O}}^{″}$ sites and mimic a single oxygen in energetics and charge state, they are rare at ambient conditions. Its decomposition process and vibrational properties have been studied carefully. To a general clustering mechanism in anion-excess fluorites systematically obtain, we also analyze the local stabilities of possible basic clustering modes of oxygen defects. The result shows a unified way to understand the structure of Willis-type and cuboctahedral clusters in $\mathrm{U}{\mathrm{O}}_{2+x}$ and $\beta \text{−}{\mathrm{U}}_4{\mathrm{O}}_9$. Finally, we generalize the point defect model to the independent cluster approximation to include clustering effects; the impact on defect populations is discussed.

The structural behavior of $\mathrm{U}{\mathrm{O}}_2$ under high pressure up to $300\mathrm{GPa}$ has been studied by first-principles calculations with $\mathrm{LSDA}+\mathrm{U}$ approximation. The results show that a pressure-induced structural transition to the cotunnite-type (orthorhombic $Pnma$) phase occurs at $38\mathrm{GPa}$. It agrees well with the experimentally observed $\sim 42\mathrm{GPa}$. An isostructural transition following that is also predicted to take place from $80\text{to}130\mathrm{GPa}$, which has not yet been observed in experiments. Further high compression beyond $226\mathrm{GPa}$ will result in a metallic and paramagnetic transition. It corresponds to a volume of $90{\mathrm{\AA }}^3$ per cell, in good agreement with a previous theoretical analysis in the reduction of volume required to delocalize $5f$ states.

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 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.