Lattice thermal conductivity of lower mantle minerals and heat flux from Earth's core

Recent progress in the study on phonon heat transport property of Earth's lower mantle minerals

The lattice thermal conductivities (κlat) of Earth's lower mantle (LM) minerals is a crucial parameter in the study of deep Earth dynamics and its determination is also one of the grand challenges in condensed matter physics. Here, we review recent progress on theoretical and experimental studies for theκlatunder high pressure (P) and high temperature (T) condition up to 150 GPa and 4000 K. After the critical parameters necessary to obtain converged values of theκlatare summarized, the theoreticalκlatof the LM minerals, determined through various computational methodologies, is compiled along with experimental findings. Although significant scattering is found in the experimental results at LMP,T, the quantum anharmonic lattice dynamics theory combined with the phonon Boltzmann transport theory demonstrates a clear relationship in theκlatof the end-member LM phases, MgO, MgSiO3bridgmanite (Brg) and post-perovskite (PPv),κlatMgO>>κlatPPv>κlatBrg, and a discontinuous change in theκlatby ∼20%-50% expected across the Brg-PPv transition. Knowledge on the additional but geophysically important factors, such as the effects of iron solid solution, isotopic mass difference, and higher order crystal anharmonicity are also summarized in detail. Current problems and future perspectives are finally mentioned.

Unexpected thermal transport properties of MgSiO3monolayer at extreme conditions

The thermal transport properties of mantle minerals are of paramount importance to understand the thermal evolution processes of the Earth. Here, we perform extensively structural searches of two-dimensional MgSiO3monolayer by CALYPSO method and first-principles calculations. A stable MgSiO3monolayer withPmm2 symmetry is uncovered, which possesses a wide indirect band gap of 4.39 eV. The calculations indicate the lattice thermal conductivities of MgSiO3monolayer are 49.86 W (mK)-1and 9.09 W (mK)-1inxandydirections at room temperature. Our findings suggest that MgSiO3monolayer is an excellent low-dimensional thermoelectric material with highZTvalue of 4.58 from n-type doping in theydirection at 2000 K. The unexpected anisotropic thermal transport of MgSiO3monolayer is due to the puckered crystal structure and the asymmetric phonon dispersion as well as the distinct electron states around the Fermi level. These results offer a detailed description of structural and thermal transport properties of MgSiO3monolayer at extreme conditions.

Crustal melting in orogenic belts revealed by eclogite thermal properties

Partial melting in the continental crust may play a critical role on the behavior of continents during collision. However, the occurrence of partial melt in orogenic continental crust is not well understood. Since the temperature of the orogen is controlled by the thermal properties of constituent rocks, we measured the thermal conductivity and diffusivity of eclogite, the most important ultrahigh pressure metamorphic rocks, as a function of pressure, temperature, composition, and water content, and simulated the thermal structure of the Sulu and Himalaya-Tibet orogens in eastern and southwestern China, respectively. Our results show that the temperature at ~30-km depth beneath the orogens reaches the solidus of wet granite and phengite (~940 K), therefore, the partial melting in the orogenic continental crust is well explained. The melt may facilitate the exhumation of subducted crust, produce the low seismic-velocity zone, and cause the high-conductivity anomaly in the shallow depth of orogenic belts.

By measuring the thermal properties of eclogite at high pressures, the authors found that temperature of orogenic continental crust is sufficient to melt granite and phengite, leading to low-velocity and high-conductivity anomalies in orogenic belts.

High-pressure thermal conductivity and compressional velocity of NaCl in B1 and B2 phase

Sodium chloride (NaCl) is an important, commonly used pressure medium and pressure calibrant in diamond-anvil cell (DAC) experiments. Its thermal conductivity at high pressure–temperature (P–T) conditions is a critical parameter to model heat conduction and temperature distribution within an NaCl-loaded DAC. Here we couple ultrafast optical pump-probe methods with the DAC to study thermal conductivity and compressional velocity of NaCl in B1 and B2 phase to 66 GPa at room temperature. Using an externally-heated DAC, we further show that thermal conductivity of NaCl-B1 phase follows a typical T⁻¹ dependence. The high P–T thermal conductivity of NaCl enables us to confirm the validity of Leibfried-Schlömann equation, a commonly used model for the P–T dependence of thermal conductivity, over a large compression range (~ 35% volume compression in NaCl-B1 phase, followed by ~ 20% compression in the polymorphic B2 phase). The compressional velocities of NaCl-B1 and B2 phase both scale approximately linearly with density, indicating the applicability of Birch’s law to NaCl within the density range we study. Our findings offer critical insights into the dominant physical mechanism of phonon transport in NaCl, as well as important data that significantly enhance the accuracy of modeling the spatiotemporal evolution of temperature within an NaCl-loaded DAC.

Exposing the hidden influence of selection rules on phonon-phonon scattering by pressure and temperature tuning

Selection rules act to restrict the intrinsic anharmonic interactions between phonons in all crystals. Yet their influence on phonon propagation is hidden in most materials and so, hard to interrogate experimentally. Using ab initio calculations, we show that the otherwise invisible impact of selection rules on three-phonon scattering can be exposed through anomalous signatures in the pressure (P) and temperature (T) dependence of the thermal conductivities, κ, of certain compounds. Boron phosphide reveals such underlying behavior through an exceptionally sharp initial rise in κ with increasing P, which may be the steepest of any material, and also a peak and decrease in κ at high P. These features are in stark contrast to the measured behavior for many solids, and they occur at experimentally accessible conditions. These findings give a deep understanding of phonon lifetimes and heat conduction in solids, and motivate experimental efforts to observe the predicted behavior.

Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo

We measure the electrical resistivity of hcp iron up to ∼170  GPa and ∼3000  K using a four-probe van der Pauw method coupled with homogeneous flattop laser heating in a DAC, and compute its electrical and thermal conductivity by first-principles molecular dynamics including electron-phonon and electron-electron scattering. We find that the measured resistivity of hcp iron increases almost linearly with temperature, and is consistent with our computations. The results constrain the resistivity and thermal conductivity of hcp iron to ∼80±5  μΩ cm and ∼100±10  W m^{-1} K^{-1}, respectively, at conditions near the core-mantle boundary. Our results indicate an adiabatic heat flow of ∼10±1  TW out of the core, supporting a present-day geodynamo driven by thermal and compositional convection.

Combination of pulsed light heating thermoreflectance and laser-heated diamond anvil cell for in-situ high pressure-temperature thermal diffusivity measurements

By combining thermoreflectance measurements and laser heated diamond anvil cell (LHDAC) techniques, an instrument for the measurement of in situ high pressure-temperature thermal diffusivity of materials was developed. In an LHDAC system, high-power continuous-wave laser beams irradiate both faces of a disk-shaped metal sample loaded into diamond anvil cells (DACs), to maintain a stable high-temperature condition. During the operation of the LHDAC system, temperature of the sample is determined from the thermal radiation spectrum between 640 and 740 nm to fit Planck's law. Subsequently, a pulsed laser beam irradiates the metal disk to induce a temperature gradient inside the sample, and the transient temperature, caused by heat diffusion, is measured by a continuous wave probe laser based on the thermoreflectance phenomenon. We determined the thermal conductivities of Pt and Fe up to approximately 60 GPa and 2000 K using the measured thermal diffusivities and obtained values consistent with previous works. The uncertainties in the pressure and the temperature are estimated to be approximately 10%, and that in the thermal conductivity is estimated to approximately 15%. The system developed in this study enables us to determine thermal transport properties of materials under pressure-temperature conditions of the deep Earth.

Effects of iron spin transition on the electronic structure, thermal expansivity and lattice thermal conductivity of ferropericlase: a first principles study

The effects of the spin transition on the electronic structure, thermal expansivity and lattice thermal conductivity of ferropericlase are studied by first principles calculations at high pressures. The electronic structures indicate that ferropericlase is an insulator for high-spin and low-spin states. Combined with the quasiharmonic approximation, our calculations show that the thermal expansivity is larger in the high-spin state than in the low-spin state at ambient pressure, while the magnitude exhibits a crossover between high-spin and low-spin with increasing pressure. The calculated lattice thermal conductivity exhibits a drastic reduction upon the inclusion of ferrous iron, which is consistent with previous experimental studies. However, a subsequent enhancement in the thermal conductivity is obtained, which is associated with the spin transition. Mechanisms are discussed for the variation in thermal conductivity by the inclusion of ferrous iron and the spin transition.

Non-monotonic pressure dependence of the thermal conductivity of boron arsenide

Recent experiments demonstrate that boron arsenide (BAs) is a showcase material to study the role of higher-order four-phonon interactions in affecting heat conduction in semiconductors. Here we use first-principles calculations to identify a phenomenon in BAs and a related material - boron antimonide, that has never been predicted or experimentally observed for any other material: competing responses of three-phonon and four-phonon interactions to pressure rise cause a non-monotonic pressure dependence of thermal conductivity, κ, which first increases similar to most materials and then decreases. The resulting peak in κ shows a strong temperature dependence from rapid strengthening of four-phonon interactions relative to three-phonon processes with temperature. Our results reveal pressure as a knob to tune the interplay between the competing phonon scattering mechanisms in BAs and similar compounds, and provide clear experimental guidelines for observation in a readily accessible measurement regime.

Thermal properties of materials are driven by complex many-body interactions among thermal atomic vibrations called phonons. Here the authors show, from first-principles, that a full description of the unusual thermal behaviour in boron arsenide requires considering often-neglected four-phonon interactions.

Effects of iron on the lattice thermal conductivity of Earth's deep mantle and implications for mantle dynamics

Iron may critically influence the physical properties and thermochemical structures of Earth's lower mantle. Its effects on thermal conductivity, with possible consequences on heat transfer and mantle dynamics, however, remain largely unknown. We measured the lattice thermal conductivity of lower-mantle ferropericlase to 120 GPa using the ultrafast optical pump-probe technique in a diamond anvil cell. The thermal conductivity of ferropericlase with 56% iron significantly drops by a factor of 1.8 across the spin transition around 53 GPa, while that with 8-10% iron increases monotonically with pressure, causing an enhanced iron substitution effect in the low-spin state. Combined with bridgmanite data, modeling of our results provides a self-consistent radial profile of lower-mantle thermal conductivity, which is dominated by pressure, temperature, and iron effects, and shows a twofold increase from top to bottom of the lower mantle. Such increase in thermal conductivity may delay the cooling of the core, while its decrease with iron content may enhance the dynamics of large low shear-wave velocity provinces. Our findings further show that, if hot and strongly enriched in iron, the seismic ultralow velocity zones have exceptionally low conductivity, thus delaying their cooling.

Lattice Thermal Conductivity of MgSiO3 Perovskite from First Principles

We investigate lattice thermal conductivity κ of MgSiO₃ perovskite (pv) by ab initio lattice dynamics calculations combined with exact solution of linearized phonon Boltzmann equation. At room temperature, κ of pristine MgSiO₃ pv is found to be 10.7 W/(m · K) at 0 GPa. It increases linearly with pressure and reaches 59.2 W/(m · K) at 100 GPa. These values are close to multi-anvil press measurements whereas about twice as large as those from diamond anvil cell experiments. The increase of k with pressure is attributed to the squeeze of weighted phase-spaces phonons get emitted or absorbed. Moreover, we find κ exhibits noticeable anisotropy, with κ _zz being the largest component and [Formula: see text] being about 25%. Such extent of anisotropy is comparable to those of upper mantle minerals such as olivine and enstatite. By analyzing phonon mean free paths and lifetimes, we further show that the weak temperature dependence of κ observed in experiments should not be caused by phonons reaching 'minimum' mean free paths. These results clarify the microscopic mechanism of thermal transport in MgSiO₃ pv, and provide reference data for understanding heat conduction in the Earth's deep interior.

Low core-mantle boundary temperature inferred from the solidus of pyrolite

The melting temperature of Earth's mantle provides key constraints on the thermal structures of both the mantle and the core. Through high-pressure experiments and three-dimensional x-ray microtomographic imaging, we showed that the solidus temperature of a primitive (pyrolitic) mantle is as low as 3570 ± 200 kelvin at pressures expected near the boundary between the mantle and the outer core. Because the lowermost mantle is not globally molten, this provides an upper bound of the temperature at the core-mantle boundary (T(CMB)). Such remarkably low T(CMB) implies that the post-perovskite phase is present in wide areas of the lowermost mantle. The low T(CMB) also requires that the melting temperature of the outer core is depressed largely by impurities such as hydrogen.

Strategies for in situ laser heating in the diamond anvil cell at an X-ray diffraction beamline

An overview of several innovations regarding in situ laser-heating techniques in the diamond anvil cell at the high-pressure beamline ID27 of the European Synchrotron Radiation Facility is presented. Pyrometry measurements have been adapted to allow simultaneous double-sided temperature measurements with the installation of two additional online laser systems: a CO2 and a pulsed Nd:YAG laser system. This reiteration of laser-heating advancements at ID27 is designed to pave the way for a new generation of state-of-the-art experiments that demand the need for synchrotron diffraction techniques. Experimental examples are provided for each major development. The capabilities of the double pyrometer have been tested with the Nd:YAG continuous-wave lasers but also in a time-resolved configuration using the nanosecond-pulsed Nd:YAG laser on a Fe sample up to 180 GPa and 2900 K. The combination of time-resolved X-ray diffraction with in situ CO2 laser heating is shown with the crystallization of a high-pressure phase of the naturally found pyrite mineral MnS2 (11 GPa, 1100-1650 K).

Ab initio lattice thermal conductivity of MgSiO3 perovskite as found in Earth's lower mantle

The lattice thermal conductivity (κ(lat)) of MgSiO3 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. κ(lat) of Mg-Pv is found to increase with increasing pressure from 9.8 (at 23.5 GPa) to 43.6  W m(-1)  K(-1) (at 136 GPa) at 300 K, while decreasing with increasing temperature from 28.1 (at 300 K) to 2.3  W m(-1)   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.

Effect of mass disorder on the lattice thermal conductivity of MgO periclase under pressure

Thermal conductivity of mantle materials controlling the heat balance and thermal evolution of the Earth remains poorly constrained as the available experimental and theoretical techniques are limited in probing minerals under the relevant conditions. We report measurements of thermal conductivity of MgO at high pressure up to 60 GPa and 300 K via diamond anvil cells using the time-domain thermoreflectance technique. These measurements are complemented by model calculations which take into account the effect of temperature and mass disorder of materials within the Earth. Our model calculations agree with the experimental pressure dependencies at 300 and 2000 K for MgO. Furthermore, they predict substantially smaller pressure dependence for mass disordered materials as the mechanism of scattering changes. The calculated thermal conductivity at the core-mantle boundary is smaller than the majority of previous predictions resulting in an estimated total heat flux of 10.4 TW, which is consistent with modern geomodeling estimates.