## 3 Results  
The computed values of the relaxation volumes of point defects in both neutral and fully charged states are listed in Table 2. The lattice relaxation and its symmetry around a defect are quantified by the relaxation volume tensor, \(\Delta\Omega_{ij}^{r}\) (Equation (7)), which in turn determines the defect dipole tensor, \(G_{ij}\) (Equation (1)), listed in Table 3. The relaxation volumes are relatively large for charged defects compared to their neutral counterpart and, interestingly, the sign of the relaxation volume is sensitive to the charge state of the defect. The relaxation volumes are computed using Equation (6) (when relaxing cell shape, volume and ionic positions), and Equation (7) (when keeping volume and cell shape fixed, relaxing only ionic positions). The agreement in computed relaxation volumes calculated through the two approaches is between 0.5-2 A\({}^{3}\); the differences in total energies is 50-100 meV, a similar range to that reported by [PERSON] et al. [52]. As discussed above, the dipole tensor is used to compute the change in defect formation energy upon interaction with strains in the material [11; 24]. We find that the changes in the formation energy differ significantly between the charged and neutral states for a given defect. For example, for a fully charged (2-) oxygen interstitial under 1% compressive strain the change in formation energy is about 277.4 meV, which is 6 times larger than the \(-\)46.4 meV change in energy for a neutral oxygen interstitial under the same strain state. Similarly, the segregation energy of a fully charged oxygen interstitial in UO\({}_{2}\) under the strain field of edge dislocation [60] is computed to be \(-\)8.3 eV, much larger than the \(-\)1.2 eV segregation energy of the neutral oxygen interstitial. The differences in formation energies [29] and the analyzed local lattice distortions (see Section 3.2) between the neutral and charged defects are, however, not so large. Therefore, this extremely large change in segregation energies (which depend on the value of the relaxation volumes) between a charged and a neutral defect interacting with the same strain field seems unphysical and suggests that something is amiss with the volumes calculated for the charged defects. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**System** & **Defect** & \(\Delta\Omega^{\prime}\) & \(\frac{\Delta\Omega^{\prime}}{\Omega_{\text{unit}}}\) \\ \hline \multirow{4}{*}{\(\text{UO}_{2}\)} & \(V_{\text{U}}^{0}\) & \(-9.1\) & \(-0.22\) \\  & \(V_{\text{U}}^{0}\) & \(40.5\) & \(1.05\) \\  & \(V_{\text{O}}^{0}\) & \(0.56\) & \(0.01\) \\  & \(V_{\text{O}}^{2+}\) & \(-16.7\) & \(-0.41\) \\  & \(V_{\text{O}}^{0}\) & \(-3.38\) & \(-0.08\) \\  & \(\text{O}_{i}^{2-}\) & \(20.0\) & \(0.49\) \\ \hline \multirow{4}{*}{GaAs} & \(V_{\text{Ga}}^{0}\) & \(-26.3\) & \(-1.12\) \\  & \(V_{\text{Ga}}^{0}\) & \(31.2\) & \(1.42\) \\  & \(V_{\text{Ga}}^{0}\) & \(-24.4\) & \(-1.09\) \\  & \(V_{\text{As}}^{\text{As}}\) & \(-73.5\) & \(-3.3\) \\ \hline \multirow{4}{*}{Si} & \(V_{\text{Si}}^{0}\) & \(-14.7\) & \(-0.72\) \\  & \(V_{\text{Si}}^{2+}\) & \(-42.8\) & \(-2.1\) \\ \cline{1-1}  & \(V_{\text{Si}}^{2-}\) & \(28.1\) & \(1.38\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computed defect relaxation volumes, \(\Delta\Omega^{\prime}\) (Å\({}^{3}\)), normalized relaxation volume, \(\Delta\Omega^{\prime}/\Omega_{\text{unit}}\), for charged and neutral point defects calculated from DFT calculations. For reference, for \(\text{UO}_{2}\) and GaAs, the volume per formula unit (\(\Omega_{\text{unit}}\)) is 40.3 Å\({}^{3}\) (\(\Omega_{\text{UO2}}\)), and 44.6 Å\({}^{3}\) (\(\Omega_{\text{GaAs}}\)) respectively, and for Si the atomic volume is 20.4 Å\({}^{3}\) (\(\Omega_{\text{Si}}\)). The values are obtained from 144 atom supercells for \(\text{UO}_{2}\), and 216 atom supercells for Si and GaAs.