# 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
In most of the experiments, researchers simply control the oxygen-to-metal ratio of oxide fuels, and thus, they cannot control the amount of oxygen vacancies and oxygen interstitials independently. For example, if the oxide fuel is missing with 10% of oxygen, it could mean that the fuel has 20% oxygen interstitials and 30% oxygen vacancies (\(+20\%-30\%=-10\%\)). Or, it could mean that the fuel has 10% oxygen interstitials and 20% oxygen vacancies (\(+10\%-20\%=-10\%\)). In both cases, the total deficit in oxygen is the same (\(-10\%\)), while the actual amount of oxygen interstitials is different. Therefore, more experimental efforts are required to examine the results obtained in the present research. For example, instead of the traditional thermogravimetry method (widely used in experimentalists), more advanced methods that utilize nanoscale characterization along with nanoscale imaging should provide a breakthrough. It should be noted that the charge imbalance is ignored throughout this research because the defect concentrations are relatively small. UO\({}_{2}\) can be charged with a \(-2\) for oxygen interstitial, \(-4\) for uranium vacancy, and \(+2\) for oxygen vacancy. Researchers [30; 31] reported that \(-2\) charged oxygen interstitial is expected to be stable over a wide range of compositions, while \(+2\) charged oxygen vacancy is more stable in the Fermi level close to the valence band. Therefore, further study is required to clearly understand the effect of charge imbalance on the thermal transport property of oxide fuels. For example, the effect of charge imbalance can be more systemically studied by introducing the corresponding charge while compensating for defects in the other regions of the simulation structure. Figure 6a illustrates the change in the thermal conductivity of PuO\({}_{2}\) as a function of defect concentration. The effect of uranium/plutonium vacancy defects is notably greater than that of oxygen vacancies and interstitials. The addition or subtraction of larger atoms is expected to cause a greater change in phonon transport in crystalline structures, because it alters the lattice vibration in the simulation structure more abruptly. The authors have identified the same results in their previous research study [3] that investigated thorium vacancies and oxygen vacancies in ThO\({}_{2}\). Other researchers [22; 32; 33] also reported the same observations in nanostructured crystalline solids. For the case of PuO\({}_{2}\) with \(N_{x}=100\), 0.5% plutonium vacancy shows a 61% decrease in the thermal conductivity  
when compared to its stoichiometric structure, while 0.5% oxygen interstitials cause a 45% decrease in the thermal conductivity when compared to its stoichiometric sample. Phonon density of states (PDOS) is plotted for PuO\({}_{2}\) with different point defects in Figure 6b. PDOS is obtained directly from MD simulations through velocity auto-correlation using the same potential field at 300K [34]. The shaded area represents the PDOS of stoichiometric PuO\({}_{2}\). The locations of the transverse acoustic (TA) peak (near 12 meV) and longitudinal acoustic (LA) peak are consistent with the results by other researchers [35; 36; 37], while the location of high-frequency optical phonon peak (near 75 meV) is slightly different from the previous results. By calculating phonon spectra using the DMFT, [PERSON] et al. [38] showed that the LA phonon mode dominates the thermal transport because of its high group velocity and small anharmonicity implied by its Gruneisen constant, while the contribution of high frequency optical phonons to the thermal conductivity of PuO\({}_{2}\) is negligible.