## 3 Results  
### Structural Effects  
Before we discuss the structural effects due to a defect, we would like to first note the structural effects due to Ga alloying. Table 1 shows a summary of the equilibrium lattice constants and formation energies for the \(\delta\)-Pu-Ga structures investigated in this study. The formation energies are exothermic and the equilibrium lattice constant decreases with increasing Ga concentrations, which agrees with experimental results, but with a consistent contraction of \(\sim\)2.6% difference (Figure 2) [3,47]. Formation energies also follow a similar trend as calculated with previous DFT studies [25,26,48]. In a pure \(\delta\)-Pu fcc lattice with no Ga, there are no structural effects locally, but the presence of a substitutional Ga induces a tetragonal distortion along the spin axis (100) plane. This is evident in the 1 nn radial distribution functions (RDF) shown in Figure 3. For the 0.926 at. % Ga structure four Pu atoms decrease inward by 0.13 A and the remaining eight Pu atoms decrease inward by 0.06 A. This tetragonal distortion due to the Ga transmits through the 2 nn shell but is minimal with only a 0.04 A decrease. As the Ga concentration increases, this tetragonal distortion becomes more evident due to the competing interactions of the Ga within the cell and the increase of short-range disorder [25,48]. This varying distances from the Ga was observed via EXAFS in Pu-Ga alloys, which was also dependent on the proximity to the Ga atoms [27,49]. EXAFS data has found overlapping Ga-centered 3 nn shells influences the local environment around all Pu atoms [27], and this effect increases at higher Ga concentrations [49]. The magnitude of the Pu-Ga bond length contractions within the supercell are in reasonable agreement with EXAFS observations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\% at. Ga** & \begin{tabular}{c} **a\({}_{0}\)** \\ **(Å)** \\ \end{tabular} & \
\begin{tabular}{c} \(E_{f}^{\wp_{u}-Ga}\) **(eV/atom)** \\ \end{tabular} &
\begin{tabular}{c} \(E_{f}^{\wp_{u}-Ga}\) **(kJ/mol)** \\ \end{tabular} \\ \hline
0 & 4.524 & - & - \\
0.926 & 4.520 & \(-\)0.010 & \(-\)0.944 \\
1.852 & 4.515 & \(-\)0.019 & \(-\)1.807 \\
2.778 & 4.501 & \(-\)0.030 & \(-\)2.867 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equilibrium lattice constants and formation energies (\(E_{f}^{\wp_{u}-Ga}\)) in eV/atom and kJ/mol for 0.926, 1.852, and 2.778 at. % Ga \(\delta\)-Pu structures. The effects of Ga on the local distortion induced by the mono-vacancy is evident. In the 0.926 at. % Ga structure, depending on the distance from the Ga, the distortion either is tetragonal or monoclinic, similar to what was calculated in the pure \(\delta\)-Pu [38]. The formation energy increases as compared to a mono-vacancy in pure \(\delta\)-Pu (1.23 eV for tetragonal distortion and 1.08 eV for monoclinic distortion [38]) when the mono-vacancy is 1 nn to the Ga. Other DFT calculations that used an AFM or disordered local moment configuration for a mono-vacancy in \(\delta\)-Pu calculated 1.34 eV and 1.07 eV [42], respectively, which are similar to our previously calculated values [38]. Surprisingly, a mono-vacancy at 1 nn to the Ga formed a monoclinic local distortion in the \(<\)100\(>\) direction away from the Ga atom with formation energy of 1.39 eV (Figure 4a). The Ga atom shares four nearest neighboring bonds that comprise atoms within the one mirror symmetry plane for the monoclinic distortion due to the vacancy and from the  
Figure 3: Radial distribution functions (RDF) for 0 (pure), 0.926, 1.852, and 2.778 at. % Ga \(\delta\)-Pu structures from the perspective of the Ga atom when applicable. Nearest neighboring shells include first, second, third, fourth, fifth, sixth, seventh, ninth, and tenth. Figure 2: Experimental and density functional theory (DFT) calculated lattice parameters as a function of Ga dependency. Experimental data is from [PERSON] et al. [3].