Thermal conductivity of CaO under the conditions of the Earth's interior

The thermal conductivity of mantle materials, viz., oxides, perovskites, and silicates, controls the heat balance and thermal evolution of the Earth. We report the pressure $(P)$ and temperature $(T)$ dependence of lattice thermal conductivity of quicklime, an important insulating oxide in the deepest mantle, by employing the phonon anharmonicity added and density functional theory assisted Debye-Callaway (DC) model. The previous [Vyas et al., Phys. Rev. B 107, 014107 (2023) and Physica B 645, 414250 (2022)] first-principles calculations that included the anharmonic contribution to the vibrational response were utilized to deduce the input parameters of the DC model, such as the characteristic temperature, the average phonon velocity, and the thermal Gr\"uneisen parameter. In this paper, instead of the conventional Debye temperature, we used a different characteristic temperature $(\ensuremath{\theta})$ to derive the resistive umklapp phonon scattering rate. The equilibrium value of $\ensuremath{\theta}$ is derived from the second-order volume $(V)$ derivative of the self-consistent plane-wave total energy, whereas the $V$ and $T$ variation of $\ensuremath{\theta}$ is governed by the explicit $V,T$-dependent Gr\"uneisen parameter. We employed the lowest-order thermodynamic perturbation theory to find an explicit $T$-dependent thermal gamma and thereby $\ensuremath{\theta}(V,T)$. The high-$P,\phantom{\rule{4pt}{0ex}}T$ lattice thermal conductivity (${K}_{\mathrm{lat}}$) results for the B2 phase (CsCl structure) of CaO were also computed and compared with those derived using the Boltzmann transport equation (BTE) approach. While the DC model relies on the equation of states and average phonon group velocity, the discrepancy in high-$P$ data suggests that the effect of inflection of the phonon-phonon scattering mechanism with volume is critical. However, the DC model remains successful for the high-$T$ and low-$P$ evaluation of ${K}_{\mathrm{lat}}$, and the calculated results for high-$T$ but zero-pressure $({K}_{\mathrm{lat}})$ coincides with results based on the BTE approach. Further, we also obtained the radiative part of the thermal conductivity (${K}_{\mathrm{rad}}$) from the absorption coefficient that was derived within the independent particle approximation and using the Planck function for the blackbody radiation. The computed results at $P$ and $T$ relevant to the Earth's lower mantle and outer core regions suggest that (i) the radiative component ${K}_{\mathrm{rad}}$ remains two to three orders of magnitude smaller compared to the lattice part, and it is negligible; (ii) the B2 phase of CaO is important at the examined $P,T$ plane, and decisively contributes to the heat transport; and (iii) the estimated value $(\ensuremath{\sim}4.9\text{--}8\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1\phantom{\rule{4pt}{0ex}}}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1})$ of ${K}_{\mathrm{lat}}$ at the core-mantle boundary is of the same order of magnitude as that of cubic $\mathrm{CaSi}{\mathrm{O}}_{3}$ perovskite, and $\mathrm{MgSi}{\mathrm{O}}_{3}$ perovskite and bridgmanite along the geotherm.