Lattice thermal conductivities of two SiO2 polymorphs by first-principles calculations and the phonon Boltzmann transport equation

Lattice thermal conductivities of two ${\mathrm{SiO}}_{2}$ polymorphs, i.e., $\ensuremath{\alpha}$ quartz (low) and $\ensuremath{\alpha}$ cristobalite (low), were studied using first-principles anharmonic phonon calculation and linearized phonon Boltzmann transport equation. Although $\ensuremath{\alpha}$ quartz and $\ensuremath{\alpha}$ cristobalite have similar phonon densities of states, phonon frequency dependencies of phonon group velocities and lifetimes are dissimilar, which results in largely different anisotropies of the lattice thermal conductivities. For $\ensuremath{\alpha}$ quartz and $\ensuremath{\alpha}$ cristobalite, distributions of the phonon lifetimes effective to determine the lattice thermal conductivities are well described by energy and momentum conservations of three phonon scatterings weighted by phonon occupation numbers and one parameter that represents the phonon-phonon interaction strengths.