Lattice thermal conductivity of MgO at conditions of Earth’s interior

Abstract

Thermal conductivity of the Earth's lower mantle greatly impacts the mantle convection style and affects the heat conduction from the core to the mantle. Direct laboratory measurement of thermal conductivity of mantle minerals remains a technical challenge at the pressure-temperature (P-T) conditions relevant to the lower mantle, and previously estimated values are extrapolated from low P-T data based on simple empirical thermal transport models. By using a numerical technique that combines first-principles electronic structure theory and Peierls-Boltzmann transport theory, we predict the lattice thermal conductivity of MgO, previously used to estimate the thermal conductivity in the Earth, at conditions from ambient to the core-mantle boundary (CMB). We show that our first-principles technique provides a realistic model for the P-T dependence of lattice thermal conductivity of MgO at conditions from ambient to the CMB, and we propose thermal conductivity profiles of MgO in the lower mantle based on geotherm models. The calculated conductivity increases from 15 -20 W∕K-m at the 670 km seismic discontinuity to 40 -50 W∕K-m at the CMB. This large depth variation in calculated thermal conductivity should be included in models of mantle convection, which has been traditionally studied based on the assumption of constant conductivity.first-principles | phonon transport theory | phonon lifetime | high pressure | Lower Mantle T hermal conductivity (κ) is one of the most important mineral properties in determining the heat budget of the Earth. Heat in the Earth's interior is transferred by convection in the mantle and core and regulated by conduction at thermal boundary layers. As defined by Fourier's law of heat conduction J Q ¼ −κ · ∇T, determines the conducting heat flow density (J Q ) in the presence of a temperature gradient ∇T. κ also appears in the Rayleigh number, which measures the convective vigor of a system. Thus, the thermal conductivity of the lower mantle affects the structure, thickness, and dynamics of the CMB (1, 2), the style and structure of mantle convection (3-5), and the amount of heat conducted from the core to the mantle (6) that in turn influences the generation of the Earth's magnetic field (7).Despite its importance, thermal conductivity remains as one of the least constrained physical properties of minerals, especially at lower-mantle pressures (P) and temperatures (T) and approximately 1,900-4,000 K (9-12). Experimental data at deep mantle conditions are scarce due to the technical difficulty of measuring thermal conductivity at these extremes. Thermal conductivity of lower-mantle minerals is often estimated either by extrapolating data from lower P-T conditions and/or employing theoretical models with parameters fitted with lower P-T data (1, 13). However, direct extrapolation to deep mantle conditions can be unreliable beyond the P-Trange of the measurements, and empirical models are often based on untested assumptions. For example, the sound velocities are used to approximate phonon vel...

Thermal conductivity of diamond under extreme pressure: A first-principles study

“…To connect to previous theories, we will also discuss in this section the application to diamond of the Leibfried and Schlömann model [23] as well as previous first principles approaches [27,30,31]. We will show that these theories are not appropriate for diamond because of its stiff lattice and resulting high phonon frequency scale.…”

“…As a result of the complexity of accurately representing this interaction theoretical descriptions of k(P) have frequently relied on the simple Leibfried and Schlömann model [23,24], which makes many approximations and also assumes that the temperature range considered is well above the Debye temperature, θ D . Over the past few years, quantitative first principles approaches have been developed to calculate the thermal conductivity of semiconductors and insulators [25][26][27][28][29][30][31][32][33][34][35][36][37][38], and some of these were directly applied to examine the k(P) for MgO [27,30,31].…”

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