First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ${\mathrm{ThO}}_2$

This work presents the first-principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an iterative solution of the Peierls-Boltzmann transport equation. We have used the nonperturbative Green's function methodology to compute the phonon-point defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants, and structural relaxation near the point defects. The point defects considered in this work include the vacancy of thorium ($V_{\mathrm{Th}}$) and oxygen ($V_O$), substitutions of helium (${\mathrm{He}}_{\mathrm{Th}}$), krypton (${\mathrm{Kr}}_{\mathrm{Th}}$), zirconium (${\mathrm{Zr}}_{\mathrm{Th}}$), iodine ($I_{\mathrm{Th}}$), and xenon (${\mathrm{Xe}}_{\mathrm{Th}}$) in the thorium site, and the three different configurations of the Schottky defects. The results of the phonon-defect scattering rate reveal that among all the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to the substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows ${\mathrm{He}}_{\mathrm{Th}}>{\mathrm{Kr}}_{\mathrm{Th}}>{\mathrm{Zr}}_{\mathrm{Th}}>I_{\mathrm{Th}}>{\mathrm{Xe}}_{\mathrm{Th}}$ based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element, and the noble gases helium, xenon, and krypton. These results can serve as a benchmark for analytical models and help the engineering-scale modeling effort for nuclear design.