## 3 Results
### Structural Effects
RDF there are some atoms from the 1 nn and 2 nn shell that have relaxed from the lattice site due to this distortion (Figure 5). When the mono-vacancy is located at 2 nn from the Ga atom, the formation energy increases to 1.48 eV, and then farther away at 6 nn, the formation energy decreases to 1.25 eV, which is similar in energy to the tetragonal distortion calculated in the pure system with no Ga. The distortion is similar to the tetragonal distortion as shown in the RDF plot in Figure 5.  
Figure 4: Distortion induced by a mono-vacancy at first nearest neighbor to a Ga atom for **(a)** 0.926, **(b)** 1.852, and **(c)** 2.778 at. % Ga, and **(d)** when the mono-vacancy is located at fourth nearest neighboring distance from the Ga for the 2.778 at. % Ga. For **(a)** and **(b)** only the distortion is shown, and the entire structure is shown for **(c)** and **(d)**. Yellow and purple atoms are the Pu and Ga atoms, respectively, and Pu-Pu bonds >3.0 Å are shown in black. Figure 5: Radial distribution function (RDF) of a mono-vacancy from first (1 nn), second (2 nn), and sixth (6 nn) nearest neighboring distance from the Ga atom for 0.926 at. % Ga. RDF is calculated from the perspective of the Ga atom. For the 1.852 at. % Ga structures with a mono-vacancy, there are two Ga atoms in the cell, and we begin to observe competing effects. When the mono-vacancy is 1 nn distance from only one Ga atom, the formation energy increases to 1.49 eV as compared to the 0.926 at. %, and the monoclinic distortion is still present, even though the second Ga atom is at 3 nn distance away from the vacancy [Figure 4b]. The RDF is similar to the 0.926 at. % Ga case when the vacancy is 1 nn to the Ga (Figure 6). The formation energy remains the same at 2 nn distance (1.50 eV) and then decreases to a similar formation energy as observed in the pure and 0.926 at. % Ga results to 1.22 eV when the vacancy is located at 7 nn distance from the Ga. When the mono-vacancy is interacting with both Ga atoms at either 1 nn or 2 nn, the formation energy increases even more to 1.58 eV and 1.61 eV, respectively. It is evident from the RDF plot (Figure 5) that even though the formation energy is the highest among mono-vacancy structures that were investigated in this work, the stability of the fcc crystal is the highest (Figure 6), i.e., least distorted fcc lattice. The mono-vacancy at 1 nn shows the local instability of the fcc lattice in the RDF (Figure 6), while when located at 7 nn, we observe a similar tetragonal distortion as the 0.926 at. % Ga case. With an increase in Ga to 2.778 at. %, the trend remains the same as the 1.852 at. % Ga results, such as the formation energy increases at 2 nn distance (1.44 eV) and then decreases when the mono-vacancy is the farthest away at 7 nn distance (1.17 eV). The local monoclinic distortion that was observed when the mono-vacancy was 1 nn to the Ga in the 0.926 and 1.852 at. % Ga structures is no longer present for the 2.778 at. % Ga concentration [Figure 4c], but is a tetragonal distortion in nature (Figure 7). The highest stability least distorted fcc lattice from the RDF in Figure 7 occurs when the mono-vacancy is 2 nn between three Ga atoms, but with a significant increase of formation energy of 1.75 eV. As the mono-vacancy is further away from the Ga, the monoclinic distortion reappears at 4 nn distance away from the Ga as shown in Figure 4d with a significant drop in formation energy to 1.10 eV. This is very close in energy to the monoclinic distortion induced by a mono-vacancy calculated in pure \(\delta\)-Pu with formation energy of 1.08 eV [38]. The RDF also indicates this instability of the structure as  
Figure 6: Radial distribution function (RDF) of a mono-vacancy from first (1 nn), first in between two Ga atoms (1 nn bw 2 Ga), second in between two Ga atoms (2 nn bw 2 Ga), and seventh (7 nn) nearest neighboring distance from the Ga atom for 1.852 at. % Ga. RDF is calculated from the perspective of the Ga atom.