# Phonon Scattering and Thermal Conductivity of Actinide Oxides with Defects
## 3 Results and Discussion  
### The Effect of Point Defects on Thermal Transport in Actinide Oxides  
Representative temperature profiles after RNEMD are shown in Figure 4. A temperature gradient is estimated directly from the temperature profile after 2 ns of RNEMD using linear regression function in MATLAB. As can be seen in the temperature profile, temperature profiles are not linear near the hot bath and cold baths. This is a result of the unphysical manner during the energy exchange between the hot bath and the cold baths; the frequency of energy swap between the hot bath and the cold baths seems to be faster than the diffusion of thermal energy across imaginary bins during RNEMD. To obtain a more statistically reliable temperature gradient, linear regression is performed six times graphically on the temperature profile plots. Error bars in Figure 5 are obtained from the combination of these multiple attempts of linear regression and the intrinsic statistical errors in the linear regression function. Figure 5 shows the thermal conductivities of UO\({}_{2}\) and PuO\({}_{2}\) with various point defects at room temperature. The most significant finding is that oxygen interstitials have a detrimental effect on the thermal conductivity of UO\({}_{2}\) and PuO\({}_{2}\) comparable to oxygen vacancy defects; a 0.1% interstitial defect decreases thermal conductivity for UO\({}_{2}\) by 18.6% (14.99 W/m-K \(\to\) 12.19 W/m-K), and PuO  
Figure 4: Representative temperature profiles during RNEMD. (**a**) The temperature profiles of UO\({}_{2}\) with 0.1% and 5% oxygen interstitials. The black line on the temperature profile of 5% interstitial defects indicates the linear regression line used for determining the temperature gradient for the thermal conductivity calculation. (**b**) The temperature profiles of UO\({}_{2}\) with 0.1% and 5% oxygen vacancy defects. Figure 3: (**a**) The schematic of a simulation structure with fission gas bubbles. \(\Delta\)T indicates the temperature jump across the fission gas bubble. (**b**) Fission gas unit with 30 Kr, (**c**) 20 Kr/10 Xe, (**d**) 15 Kr/15 Xe, (**e**) 10 Kr/20 Xe, and (**f**) 30 Xe. by 17.9% (17.15 W/m-K \(\rightarrow\) 14.08 W/m-K) when compared to the respective stoichiometric structures for the simulation structures with 100 unit cells in the direction of thermal conductivity calculation (\(N_{x}=100\)). Any perturbations to the lattice structures of crystalline solids are expected to disturb phonon transport in the structures. In this regards, [PERSON] et al. [22] showed that the thermal transport is affected by a defect site, exhibiting interfacial thermal resistance across the defect. In all structures simulated, thermal conductivities are increased with an increase in sample length. This indicates that the thermal transport in actinide oxides is still ballistic, even when they contain point defects. When the sample is larger than its intrinsic phonon mean free path, the thermal conductivity begins to reach the plateau and finally approaches its bulk thermal conductivity. However, this ballistic thermal transport is not observed when the sample contains a large number of defects; the thermal conductivity is not increased with an increase in the sample length when the concentration of point defects is 5%. The same phenomenon can be observed in the temperature profiles in Figure 4; temperature slips near hot baths, and cold baths that are observed in the simulation structure with low (0.1%) defect concentration are not observed in the simulation structure with high (5%) defect concentration. This indicates that the thermal transport in structures with high defect concentrations is readily diffusive even when the sample size is smaller than its phonon mean free path.