Thermal conductivity of MgO, MgSiO3 perovskite and post-perovskite in
  the Earth's deep mantle

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Abstract

We report lattice thermal conductivities of MgO and MgSiO3 in the perovskite and post-perovskite structures at conditions of the Earth's lower mantle, obtained from equilibrium molecular dynamics simulations. Using an advanced ionic interaction potential, the full conductivity tensor was calculated by means of the Green-Kubo method, and the conductivity of MgSiO3 post-perovskite was found to be significantly anisotropic. The thermal conductivities of all three phases were parameterized as a function of density and temperature. Assuming a Fe-free lower-mantle composition with mole fractions xMgSiO3 = 0.66 and xMgO = 0.34, the conductivity of the two-phase aggregate was calculated along a model geotherm. It was found to vary considerably with depth, rising from 9.5 W/(mK) at the top of the lower mantle to 20.5 W/(mK) at the top of the thermal boundary layer above the core-mantle boundary. Extrapolation of experimental data suggests that at deep-mantle conditions, the presence of a realistic amount of iron impurities lowers the thermal conductivity of the aggregate by about 50% (Manthilake et al., 2011). From this result and our thermal conductivity model, we estimate the heat flux across the core-mantle boundary to be 10.8 TW for a Fe-bearing MgO/MgSiO3 perovskite aggregate and 10.6 TW for a Fe-bearing MgO/MgSiO3 post-perovskite aggregate.

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Post-perovskite phase transition in MgSiO3.

Motohiko Murakami, Kei Hirose, Katsuyuki Kawamura … (2004)

In situ x-ray diffraction measurements of MgSiO3 were performed at high pressure and temperature similar to the conditions at Earth's core-mantle boundary. Results demonstrate that MgSiO3 perovskite transforms to a new high-pressure form with stacked SiO6-octahedral sheet structure above 125 gigapascals and 2500 kelvin (2700-kilometer depth near the base of the mantle) with an increase in density of 1.0 to 1.2%. The origin of the D" seismic discontinuity may be attributed to this post-perovskite phase transition. The new phase may have large elastic anisotropy and develop preferred orientation with platy crystal shape in the shear flow that can cause strong seismic anisotropy below the D" discontinuity.

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Heat transport in silicon from first principles calculations

Gang Chen, Keivan Esfarjani, Harold T. Stokes (2011)

Using harmonic and anharmonic force constants extracted from density-functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First, from the harmonic, cubic, and quartic force constants we construct a force field for molecular dynamics (MD). It is exact in the limit of small atomic displacements and thus does not suffer from inaccuracies inherent in semi-empirical potentials such as Stillinger-Weber's. By using the Green-Kubo (GK) formula and molecular dynamics simulations, we extract the bulk thermal conductivity. This method is accurate at high temperatures where three-phonon processes need to be included to higher orders, but may suffer from size scaling issues. Next, we use perturbation theory (Fermi Golden rule) to extract the phonon lifetimes and compute the thermal conductivity \(\kappa\) from the relaxation time approximation. This method is valid at most temperatures, but will overestimate \(\kappa\) at very high temperatures, where higher order processes neglected in our calculations, also contribute. As a test, these methods are applied to bulk crystalline silicon, and the results are compared and differences discussed in more detail. The presented methodology paves the way for a systematic approach to model heat transport in solids using multiscale modeling, in which the relaxation time due to anharmonic 3-phonon processes is calculated quantitatively, in addition to the usual harmonic properties such as phonon frequencies and group velocities. It also allows the construction of accurate bulk interatomic potentials database.