Control of the defect chemistry in $\mathrm{U}{\mathrm{O}}_{2\pm x}$ is important for manipulating nuclear fuel properties and fuel performance. For example, the uranium vacancy concentration is critical for fission gas release and sintering, while all oxygen and uranium defects are known to strongly influence thermal conductivity. Here the point defect concentrations in thermal equilibrium are predicted using defect energies from density functional theory (DFT) and vibrational entropies calculated using empirical potentials. Electrons and holes have been treated in a similar fashion to other charged defects allowing for structural relaxation around the localized electronic defects. Predictions are made for the defect concentrations and non-stoichiometry of $\mathrm{U}{\mathrm{O}}_{2\pm x}$ as a function of oxygen partial pressure and temperature. If vibrational entropy is omitted, oxygen interstitials are predicted to be the dominant mechanism of excess oxygen accommodation over only a small temperature range (1265 K–1350 K), in contrast to experimental observation. Conversely, if vibrational entropy is included oxygen interstitials dominate from 1165 K to 1680 K (Busker potential) or from 1275 K to 1630 K (CRG potential). Below these temperature ranges, excess oxygen is predicted to be accommodated by uranium vacancies, while above them the system is hypo-stoichiometric with oxygen deficiency accommodated by oxygen vacancies. Our results are discussed in the context of oxygen clustering, formation of U₄O₉, and issues for fuel behavior. In particular, the variation of the uranium vacancy concentrations as a function of temperature and oxygen partial pressure will underpin future studies into fission gas diffusivity and broaden the understanding of $\mathrm{U}{\mathrm{O}}_{2\pm x}$ sintering.

缺陷化学的控制 $\mathrm{ü}{\mathrm{Ø}}_{\mathrm{2个}\pm X}$对于操纵核燃料特性和燃料性能非常重要。例如，铀空位浓度对于裂变气体的释放和烧结至关重要，而已知所有的氧气和铀缺陷都会严重影响导热率。在这里，利用密度泛函理论（DFT）的缺陷能量和使用经验势计算出的振动熵来预测热平衡中的点缺陷浓度。电子和空穴的处理方式与其他带电缺陷类似，可以使局部电子缺陷周围的结构松弛。预测缺陷浓度和非化学计量$\mathrm{ü}{\mathrm{Ø}}_{\mathrm{2个}\pm X}$作为氧气分压和温度的函数。如果省略振动熵，则与实验观察相反，氧气间隙被预测为仅在一个较小的温度范围（1265 K–1350 K）内过量氧气容纳的主要机制。相反，如果包括振动熵，则氧间隙在1165 K至1680 K（Busker势）或1275 K至1630 K（CRG势）中占主导地位。在这些温度范围以下，铀空位可容纳过量的氧气，而在这些温度之上，系统是化学计量不足的，而空位可容纳缺氧。在氧簇聚，U ₄ O ₉形成的背景下讨论了我们的结果，以及燃油行为问题。特别是，铀空位浓度随温度和氧分压的变化将为裂变气体扩散率的未来研究奠定基础，并拓宽对裂变气体扩散性的认识。$\mathrm{ü}{\mathrm{Ø}}_{\mathrm{2个}\pm X}$ 烧结。