Density functional theory (DFT) calculations of the thermodynamic and kinetic properties of point defects in the $\beta$ phase of uranium are reported. Defect energies and entropies were calculated using $2\times 2\times 2$ supercells and the Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation potential. Due to computational cost, calculations of the vibrational properties governing entropies were performed by only displacing atoms within (roughly) the 3rd or 4th nearest neighbor shell of the defect, which implicitly assumes that atoms beyond this distance are unaffected by the defect. Migration barriers were estimated by nudged elastic band (NEB) calculations. The low symmetry of the $\beta$-U phase (the unit cell is tetragonal and contains 30 atoms) results in many point defect configurations and even more migration pathways. A connectivity map, starting from the most stable point defects, was developed in order to identify the rate-limiting step controlling the net diffusion rate in each crystallographic direction. The uranium self-diffusivity tensor was calculated by combining the defect formation energies, entropies, migration barriers and attempt frequencies. The fastest diffusion rate was determined to be a vacancy mechanism in the z crystallographic direction. The predicted uranium self-diffusivity for this mechanism agrees well with available experimental data. The diffusion mechanisms and rates identified in this study will inform fuel performance models of swelling and gas evolution.

点缺陷的热力学和动力学特性的密度泛函理论 (DFT) 计算 $\beta$铀的阶段报告。缺陷能量和熵的计算方法是$2\times 2\times 2$超胞和 Perdew-Burke-Ernzerhof (PBE) 的广义梯度近似 (GGA) 用于交换相关势。由于计算成本，控制熵的振动特性的计算仅通过在（大致）缺陷的第 3 或第 4 个最近邻壳内置换原子来执行，这隐含地假设超出此距离的原子不受缺陷影响。通过轻推弹性带 (NEB) 计算估计迁移障碍。低对称性$\beta$-U 相（晶胞是四方的，包含 30 个原子）导致许多点缺陷配置和更多的迁移路径。从最稳定的点缺陷开始，开发了连接图，以确定控制每个结晶方向净扩散速率的限速步骤。铀的自扩散张量是通过结合缺陷形成能量、熵、迁移势垒和尝试频率来计算的。最快的扩散速率被确定为 z 结晶方向上的空位机制。这种机制的预测铀自扩散率与可用的实验数据非常吻合。本研究中确定的扩散机制和速率将为膨胀和气体演化的燃料性能模型提供信息。