# Phonon Scattering and Thermal Conductivity of Actinide Oxides with Defects
## 3 Results and Discussion
### The Effect of Fission Gases on Thermal Transport in Actinide Oxides  
Figure 8 shows the temperature profile for the stoichiometric UO\({}_{2}\) and the UO\({}_{2}\) with two fission gas bubbles. For the case of UO\({}_{2}\) structures with point defects, temperature slips are observed at the hot bath and the two cold baths when the defect concentrations are low (Figure 4). In the UO\({}_{2}\) structure with fission gas bubbles, however, the temperature slip is not clearly seen at the hot bath or the cold baths, indicating the diffusive nature of the thermal transport (Figure 8a). As stated in the previous section (Section 3.1) and the authors' previous research [3], this diffusive thermal transport is observed in actinide oxides with uniformly distributed point defects. Considering that the simulation structure in Figure 8 contains only two fission gas bubbles, it is interesting that these two fission gas bubbles (two phonon scattering sources) make the thermal transport across the entire structure highly diffusive. In another thermal transport study that simulated a nanostructure with two interfacial thermal resistance sites, [PERSON] et al. [41] observed that thermal transport still maintains a ballistic transport nature, showing temperature slips at the hot bath and the cold baths when only a few interfaces are present. As can be seen in Figure 8b, fission gas bubbles distort the lattice structure of actinide oxides and become the sources of enormous phonon scattering; they correspond to a large number of point defects that are uniformly distributed across the whole simulation structure. Figure 7: Thermal conductivity of UO\({}_{2}\)/PuO\({}_{2}\) with oxygen interstitials as a function of temperature. Using RNEMD, thermal conductivities are estimated for pristine UO\({}_{2}\) with \(N_{x}\) = 50 and UO\({}_{2}\) with a fission gas bubble, and results are plotted in Figure 9a. A significant decrease (approximately 78% decrease) in thermal conductivity is observed in all structures with fission gas bubbles. In their previous study [2], the authors observed that 2% of oxygen vacancy in the UO\({}_{2}\) structure decreases its thermal conductivity by 77%. Considering that the number of Kr and/or Xe atoms in the present study is only 30 atoms, and the number of point defects that correspond to 2% is 150 atoms, one may come to the conclusion that fission gas bubbles have a more disastrous effect on thermal conductivity when compared to point defects. To examine the effect of the composition in a fission gas bubble to the thermal transport in UO\({}_{2}\), interfacial thermal resistances across fission gas bubbles are estimated for UO\({}_{2}\) with fission gases of different Kr/Xe compositions (Figure 9a). The composition of a fission gas bubble does not seem to make a meaningful difference in interfacial thermal resistance across the fission gas bubble. Both Kr and Xe are large atoms; the atomic mass of Kr is 83.798 u and the atomic mass of Xe is 131.293 u. When these large atoms are present in the middle of a UO\({}_{2}\) crystal structure, they are expected to alter the lattice vibration of UO\({}_{2}\) significantly. It is interesting that the number of Kr/Xe atoms in a fission gas bubble does not alter the interfacial thermal resistance across the fission gas bubble much. In the present study, we created the same amount of empty space (that corresponds to \(3\times 3\times 3\) unit cells of UO\({}_{2}\)) to place a fission gas bubble. Therefore, when the number of Kr/Xe atoms in a fission gas bubble is decreased, the density of the fission gas bubble is decreased at the same time. This could increase the gap between the fission gas bubble and surrounding UO\({}_{2}\) crystals, giving rise to further phonon scattering. In their previous study [2], the authors observed a similar phenomenon for UO\({}_{2}\) with vacancy defects.