Ab initio Lattice Thermal Conductivity of ${\mathrm{MgSiO}}_3$ Perovskite as Found in Earth’s Lower Mantle

The lattice thermal conductivity (${\kappa }_{\mathrm{lat}}$) of ${\mathrm{MgSiO}}_3$ perovskite (Mg-Pv) under high-pressure and high-temperature conditions was computed based on the ab initio anharmonic lattice dynamics method with the density functional perturbation theory. ${\kappa }_{\mathrm{lat}}$ of Mg-Pv is found to increase with increasing pressure from 9.8 (at 23.5 GPa) to $43.6{\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ (at 136 GPa) at 300 K, while decreasing with increasing temperature from 28.1 (at 300 K) to $2.3{\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ (at 4000 K) at 100 GPa. A multiphase composite average yielded a mantle Rayleigh number adequate to promote the vigorous thermal convection of the mantle that is expected geophysically.

Figure 1

Calculated anharmonic properties of Mg-Pv. (a) TDoS for the total (solid lines), the summation $D_{\mathbf{q}=\overrightarrow{\mathbf{0}}}^{\uparrow }$ Eq. (4) (dotted lines), and the difference process $D_{\mathbf{q}=\overrightarrow{\mathbf{0}}}^{\downarrow }(\omega )$ Eq. (5) (dashed lines). (b) Damping function ${\mathit{\Gamma }}_{\mathbf{q}=\overrightarrow{0}}$ Eq. (2) of the lowest (solid lines) and the highest optic phonon branches (dashed lines) at 300 K, which have harmonic frequencies of 186.9 and $852.4{\mathrm{cm}}^{-1}$ at 0 GPa and 235.1 and $1127.3{\mathrm{cm}}^{-1}$ at 100 GPa, respectively. Shaded areas represent ${\mathit{\Gamma }}_{\mathbf{q}=\overrightarrow{0}}$ below the highest phonon frequencies.

Figure 2

Calculated ${\kappa }_{\mathrm{lat}}$ of Mg-Pv. (a) Volume dependence of ${\kappa }_{\mathrm{lat}}$ at several temperatures from 300 K to 4000 K with regression curves to Eq. (6). (b) ${\kappa }_{\mathrm{lat}}$ converted to a function of pressure with experimental data (filled symbols) [1, 3, 4].

Figure 3

Pressure and temperature color contour plot of ${\kappa }_{\mathrm{LM}}$. White thick and gray thin solid lines represent a typical mantle geotherm [27] and the Pv-PPv phase boundary [19], respectively. Vertical dotted line represents the CMB pressure.