## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Defect Reaction**} & \multicolumn{4}{c}{**Individual Defects**} \\ \hline
**Defects** & \(\Delta\Omega^{ref}\) & **Defect** & \(\Delta\Omega^{f}\) & **Defect** & \(\Delta\Omega^{f}\) \\ \hline \(V_{\text{U}}^{\prime\prime\prime\prime}\) (Equation (14)) & \(-\)10.84 & \(V_{\text{U}}^{\prime\prime\prime\prime}\) & \(-\)10.8 & \(V_{\text{U}}^{\times}\) & \(-\)13.97 \\ \(\text{O}_{i}^{r}\) (Equation (12)) & \(-\)25.8 & \(\text{O}_{i}^{r}\) & \(-\)25.83 & \(\text{O}_{i}^{\times}\) & \(-\)26.01 \\ \(V_{\text{O}}^{\prime}\) & 29.15 & \(V_{\text{O}}^{\prime}\) & 29.13 & \(V_{\text{O}}^{\prime}\) & 23.19 \\ \(V_{\text{Ga}}^{\times}\) & \(-\)13.49 & \(V_{\text{Ga}}^{\times}\) & \(-\)16.26 & \(V_{\text{Ga}}^{\times}\) & \(-\)5.95 \\ \(V_{\text{Si}}^{\times}\) & 8.05 & \(V_{\text{Si}}^{\times}\) & 9.92 & \(V_{\text{Si}}^{\times}\) & 5.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the corrected defect formation volumes \(\Delta\Omega^{f}\) (Å\({}^{3}\)) of neutral and charged individual defects, with the defect relaxation volumes \(\Delta\Omega^{ref}\). Figure 9: Defect relaxation volume as a function of the overall charge on the DFT supercell for point defects and bulk in (**a**) UO\({}_{2}\), (**b**) GaAs, and (**c**) Si. significantly affect the final defect relaxation volumes. Corrections based on potential alignment with respect to pristine bulk (Figure 3b) agree with the conclusions made in Reference [13], where potential alignment correction was shown to have a huge volume contribution to the charged defects relaxation volumes and likely provide a different viewpoint of correcting charged defect relaxation volumes. The charged defect elastic dipole tensor is theoretically computed from its relaxation volume (Equation (1)), and experimental works often report it as chemical strain [7; 22; 75], estimated by measuring the change in the lattice parameter as a function of deviation from the stoichiometric chemical formula. The apparent question that comes next is should the charged defect relaxation volume be corrected to account for the volume associated with the electron/hole reservoir. The change in the volume of the bulk with charge (volume associated with the electron/hole reservoir) as given by \(\Delta\Omega^{ref}\) can be understood as the lattice perturbation associated with excess electron and/or holes in the bulk, as described in Section 3.2.1. We reason that charged defects are individual entities that are present in an overall charge neutral system. Both their elastic dipole tensor and relaxation volumes are meaningful when defined with respect to the electron/hole reservoir in order to keep the overall system charge neutral, as one would expect when measuring these defect properties from experiments. Traditionally, when one calculates the elastic dipole tensor and relaxation volume of a charged defect, it is relative to the neutral bulk. Perhaps the correct reference for a charged atomic defect in a lattice is not the neutral bulk, but the charged bulk, so that the defect represents a perturbation of the charged lattice only, and not the neutral lattice. The elastic dipole tensor \(G_{ij}\) for a charged defect when defined in an overall neutral (with respect to the electron or hole reservoir) but locally charged lattice is then given as:  
\[G_{ij}=C_{ijkl}\Big{[}\Delta\Omega^{r}_{kl}-q\Delta\Omega^{ref}\Big{]} \tag{17}\]  
where, \(\Big{[}\Delta\Omega^{r}_{kl}-q\Delta\Omega^{ref}\Big{]}\) represents the corrected relaxation volume. As listed in Table 8, the corrected relaxation volumes of charged defects are more reasonable in magnitude when compared to relaxation volumes for both the neutral individual defects and those of defect reactions.