## 4 Discussion
For example, the corrected relaxation volume of \(-3.28\) A\({}^{3}\) for the charged (2\(-\)) oxygen interstitial (overall neutral i.e., the oxygen interstitial with respect to doubly charged bulk UO\({}_{2}\)) compares very well with the volume of \(-3.20\) A\({}^{3}\) of the reaction involving charged (2\(-\)) oxygen interstitial with two holes. Similar comparisons for other point defects in UO\({}_{2}\) are also very good, because as can be seen in Figure 9, the slopes of change in volume of defects with charge are almost parallel to the slope of change in volume of bulk with charge. However, for Si and GaAs we observe that different defects have different slopes, suggesting that the effect of electrons and holes present in different defects leads to different strains and volume changes. We also acknowledge that the difference in the dependence of the change in volume on charge between different charged defects can originate due to the deep (localized) vs. the shallow (delocalized) nature of the defect [15]. However, in this work we do not assess the impact of deep vs. shallow nature of the defect on defect relaxation volumes because in both cases the relaxation volumes show strong sensitivity to the charged state. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Defect Reaction**} & \multicolumn{4}{c}{**Individual Defect**} \\ \hline
**Defects** & \(\mathbf{\Sigma\ \Delta\Omega^{r}}\) & **Defect** & \(\mathbf{\Delta\Omega^{r}}\)**–\(\mathbf{q\Delta\Omega^{r\theta}}\)** & **Defect** & \(\mathbf{\Delta\Omega^{r}}\)**–\(\mathbf{q\Delta\Omega^{r\theta}}\)** \\ \hline \(V^{r\prime\prime}_{\mathrm{U}}+4h\): & \(-6.26\) & \(V^{r\prime\prime}_{\mathrm{U}}\) & \(-6.02\) & \(V^{r\prime}_{\mathrm{U}}\) & \(-9.07\) \\ \(\Omega^{r}_{\mathrm{f}}+2h^{\Delta}\) & \(-3.20\) & \(\Omega^{r}_{\mathrm{i}}\) & \(-3.28\) & \(\Omega^{r}_{\mathrm{i}}\) & \(-3.38\) \\ \(V^{r}_{\mathrm{O}}+2e^{\prime}\) & \(6.52\) & \(V^{r}_{\mathrm{O}}\) & \(6.54\) & \(V^{r}_{\mathrm{O}}\) & \(0.56\) \\ \(V^{r}_{\mathrm{Ga}}+3h^{\Delta}\) & \(-33.83\) & \(V^{r}_{\mathrm{Ga}}\) & \(-36.07\) & \(V^{r}_{\mathrm{Ga}}\) & \(-26.29\) \\ \(V^{r}_{\mathrm{Si}}+2e^{\prime}\) & \(-12.39\) & \(V^{r}_{\mathrm{Si}}\) & \(-10.57\) & \(V^{r}_{\mathrm{Si}}\) & \(-14.69\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the corrected defect relaxation volume [\(\Delta\Omega^{r}-q\Delta\Omega^{ref}\)] (Å\({}^{3}\)) of neutral and charged individual defects, with the sum of defect relaxation volumes of individual charge defects computed in separate supercells under the defect reaction approach. Some of these values appeared in Table 6 but are reproduced here for convenience. Computing the dipole tensor (Equation (17)) of charged defects from the corrected relaxation volumes does result in physically reasonable magnitudes in the change in defect formation energy of the charged point defect upon interaction with external strains. Accounting for the change in volume of the electron reservoir with net charge in the definition of the defect formation volume and elastic dipole tensor allows us to reconcile these two perspectives: that defect behavior not only has meaning via reactions but that isolated defects in an overall neutral lattice (which requires the reservoir) also have unique properties that determine how they behave within the lattice. Finally, returning to Figure 4 and the associated discussion, there is an interesting parallel in the concept of the charge reservoir highlighted in Figure 9 and the corrections described in Figure 4. In Figure 4, we decomposed the potential alignment correction into two parts, one due to the net charge introduced into the cell and another due to the defect itself. On the other hand, as highlighted by Figure 9 and Table 8, the largest component of the absolute relaxation volume is due to the net charge, not the defect.