Thermal Conductivity of Silicate Liquid Determined by Machine Learning Potentials

Abstract

Silicate liquids play a critical role in the thermal evolution of Earth, at scales ranging from dikes and sills to magma oceans. In the present-day Earth, silicate melts exist transiently in the crust and upper mantle, and are thought to exist at depths as great as the core-mantle boundary (CMB). The rate of transport of heat through a magma is governed by the thermal conductivity. The value of the thermal conductivity, k is important for understanding processes ranging from double diffusive convection in magma chambers to the earliest thermal evolution of a putative molten Earth (Elkins-Tanton, 2012;Huppert & Sparks, 1984). Yet, the thermal conductivity of silicate liquids at pressures greater than 1 bar is unknown. The pressure dependence of k may be large: the thermal conductivity of crystals may vary by an order of magnitude over the pressure range of the Earth's mantle at elevated temperature (Stackhouse et al., 2010). Even at 1 bar, the thermal conductivity of silicate liquids is still highly uncertain, with different experimental techniques yielding values that may differ by as much as a factor of 10 (Hasegawa et al., 2012;Kang & Morita, 2006).Here, we predict the thermal conductivity of a silicate liquid, with an approach combining the Green-Kubo method with ab initio electronic structure calculations and the development of a machine learning potential. The Green-Kubo method is the most widely used means of determining the thermal conductivity in materials simulations based on classical potentials because it is an equilibrium method that is readily controlled (Sellan et al., 2010). Combining the Green-Kubo method with ab initio theory however has proved challenging because there is no simple way of decomposing the total energy into individual contributions from each atom. Because of this limitation, previous ab initio calculations of the thermal conductivity have used alternatives to the Green-Kubo method, including nonequilibrium methods (Stackhouse et al., 2010), which have also been combined with classical potentials in studies of silicate liquids (Tikunoff & Spera, 2014). It

Deep potentials for materials science

“…A DP was developed to simulate liquid and glassy silica which proved to have satisfactory accuracy based upon a relatively small training dataset [143]. Other DPs were developed to calculate transport properties of silicate in the mantle [144][145][146]. DPs were also employed in large-scale calculations of thermodynamic, transport, and structural properties in different molten salts [149][150][151][152][153][154][155][156][157].…”

Thermal Conductivity of Hydrous Wadsleyite Determined by Non‐Equilibrium Molecular Dynamics Based on Machine Learning

“…In‐situ measurements of the thermal conductivity of minerals remain challenging (Y. Zhou et al., 2022). Theoretical approaches (Carbogno et al., 2017; Deng & Stixrude, 2021; Müller‐Plathe, 1997; Stackhouse & Stixrude, 2010; D.‐B. Zhang et al., 2017) have been used to obtain the thermal conductivity of minerals at high temperatures and pressures.…”

“…Zhou et al, 2022). Theoretical approaches (Carbogno et al, 2017;Deng & Stixrude, 2021;Müller-Plathe, 1997;D.-B. Zhang et al, 2017) have been used to obtain the thermal conductivity of minerals at high temperatures and pressures.…”

Atomic transport properties of liquid iron at conditions of planetary cores

“…As such, the energy and stress were converged to 3.4 meV/atom and 1.4 GPa at 7.0 g/cm 3 and 6.0 meV/atom and 5.8 GPa at 25 g/cm 3 ; the mean errors in ionic forces were 0.01 eV/Å at 7.0 g/cm 3 and 0.1 eV/Å at 25 g/cm 3 , respectively. Errors of such magnitude are typical among AIMD simulations 32 and are adequate for the present study. The cubic simulation cell contained 108 iron atoms, with the ionic temperature controlled by using a Nosé thermostat.…”