Lawrence Livermore National Laboratory



Jon Eggert

Overview

High-pressure thermal conductivity is one of the most difficult physical properties of materials to measure. Within the Earth's interior, the thermal conductivity of Fe and Fe-rich alloys at core pressure–temperature conditions is a key parameter for heat transport models and plays an important role in determining the temperature profile and energy balance of our planet. An accurate measurement of thermal conductivity is critical to our understanding of planetary accretion and differentiation processes (Stevenson 1990), mantle and core temperatures (Stacey and Loper 1984), the generation of Earth's magnetic field (Stevenson 2003), and the evolution of the Earth's interior (Labrosse et al. 1997, Gubbins et al. 2004). Thermal conductivity also plays an important role in resolidification morphology and kinetics, but the lack of experimental data makes these processes difficult to model. The thermal conductivity of the Earth's core is poorly constrained because of the extreme difficulty of obtaining thermal transport measurements under the extreme pressure and temperature conditions. Two experimental studies reported thermal conductivity values for Fe that vary by a factor of seven at a pressure of approximately 130 GPa. We proposed to measure the thermal conductivity of Fe at core conditions using a "plasma-piston" ramp compression and pressure-hold technique that we developed on the Omega laser. With this approach, Fe samples are quasi-isentropically compressed and held at pressures between 50 and 350 GPa. Simultaneously, the plasma-piston drive causes a time-varying thermal wave to propagate through the "cold" compressed material. Using the Omega streaked optical pyrometer (SOP) diagnostic, the transit time of the heat wave through multiple Fe thicknesses will place the first experimental constraint of thermal conductivity within the Earth's core

Background and Research Objectives

Fourier's Law defines thermal conductivity as the ratio of heat flow rate (or heat flux) across a unit cross-section over the temperature gradient. Heat may be transmitted in media by means of various excitations (e.g., lattice waves, electrical carriers, electromagnetic waves, or spin waves). While electrons are responsible for most of the heat conduction in metals, lattice vibrations (i.e., phonons) are the dominant heat-transfer mechanism in insulators. Conduction and convection are the principal mechanisms for transporting heat from the planet's core to the surface (Arevalo et al. 2009, Goncharov et al. 2015, Lay et al. 2008). A structural representation of the Earth's interior based predominantly on seismic data is shown in the figure, along with estimates of temperature and pressure as a function of depth (Duffy 2014) and the calculated percentage of heat flow across different boundary layers (Arevalo et al. 2009).



Figure 1.










Illustration of the Earth's interior showing the pressure–temperature estimates as a function of depth (from Duffy 2014). Heat transfer from the core to the Earth's surface is driven by thermal conduction and convection.


The planet's core (at an average pressure of approximately 135–360 GPa) is composed of a solid inner core (Fe) and a liquid outer core (Fe alloyed with lighter elements). The mantle layer consists primarily of magnesium silicates (e.g., MgO, MgSO3, and Mg2SiO4). Convection processes within the mantle are the driving force behind plate tectonics, whereas convection currents within the Earth's liquid outer core are believed to power the Earth's geodynamo, which is the mechanism responsible for the generation of the Earth's magnetic field caused by convection and conduction currents in the fluid core.

The standard model for describing the physical processes that drive the geodynamo are as follows. As the temperature in the core decreases over time due to heat conduction across the core–mantle boundary (CMB), levels of solidification increase at the inner-core/outer-core boundary. The kinetic energy released from a combination of the latent heat of crystallization and the partitioning of lighter buoyant impurities drives convection currents within the outer liquid core. This compositional convection mixes the outer core (as evidenced though seismic data) and powers the geodynamo where convective kinetic energy is converted to electrical and magnetic energy. The motion of the electrically conductive iron in the presence of the Earth's magnetic field induces electrical currents. Those currents generate their own magnetic field, and as a result of this internal feedback, the process is self-sustaining so long as there is an energy source sufficient to maintain convection. The standard model of how the geodynamo is powered is based on our understanding of the thermal conductivity of Fe and Fe-rich alloys at core pressure–temperature conditions and the conductive heat flow across the CMB (Pozzo et al. 2012). However, recent upward revision of the thermal conductivity of the outer liquid core based on density function theory calculations and extrapolations of low-pressure electrical resistance measurements have called into doubt this standard model of heat flow within the planet. A high thermal conductivity core means that there is less available energy to drive the geodynamo, which in turn calls into question long-standing assumptions about the solidification rate of the Earth's core and how the geodynamo evolved. If these new, higher estimates are correct, there is an energy deficit (under the standard model).

To experimentally investigate the thermal conductivity of Fe at pressure and temperature conditions relevant to the Earth's core, we conducted experiments at the Omega laser, where a gold "halfraum" (i.e., half of a hohlraum) was irradiated by 15 laser beams to simultaneously launch a ramp and temperature wave into a Fe sample. The velocity of the pressure and thermal waves was measured with a velocity interferometer and a streaked optical pyrometer. Analysis of this data and comparison with hydrodynamic simulations is ongoing to constrain the thermal conductivity.

Impact on Mission

This project supports the NNSA goal to strengthen the science, technology, and engineering base by advancing those competencies that are the foundation of the NNSA mission. Our research also supports Lawrence Livermore National Laboratory's core competencies in earth and atmospheric science, and high-energy-density science.

High-pressure thermal conductivity is one of the most important and yet most difficult to measure physical properties of materials. It is a critical parameter in the design calculations for many high-energy-density physics experiments, including inertial confinement fusion experiments on the National Ignition Facility. The experimental approach developed through this project will open up new capabilities in constraining thermal conductivity at high pressure and low temperature. The analysis of the data is ongoing in collaboration with the group of Prof. June Wicks at Johns Hopkins University.

Conclusion

We have established a close collaboration with the group of Prof. June Wicks at Johns Hopkins University. Members of Prof. Wicks's group are processing the data obtained from the Omega laser facility. The initial approach is to match the Omega VISAR (velocity interferometer system for any reflector) and SOP data using the HYADES 1D hydrocode. Those simulations which match the Fe particle velocity and heat wave propagation data will provide a solution to the thermal conductivity. The research is ongoing, and more experiments were planned.

References

Arevalo, R., et al. 2009. "The K/U Ratio of the Silicate Earth: Insights into Mantle Composition, Structure and Thermal Evolution." Earth and Planetary Science Letters 278: 361–69.

Duffy, T. S. 2014. "Crystallography's Journey to the Deep Earth." Nature 506(7489): 427–29. doi: 10.1038/506427a.

Goncharov, A. F., et al. 2015. "Experimental Study of Thermal Conductivity at High Pressures: Implications for the Deep Earth's interior." Physics of the Earth and Planetary Interiors 247: 11–16. doi: 10.1016/j.pepi.2015.02.004.

Gubbins, D., et al. 2004. "Gross Thermodynamics of 2-Component Core Convection." Geophysical Journal International 157(3): 1407–14. doi: 10.1111/j.1365-246X.2004.02219.x.

Labrosse, S., et al. 1997. "On Cooling of the Earth's Core." Physics of the Earth and Planetary Interiors 99(7605): 99–101. doi: 10.1038/nature18009.

Lay, T., et al. 2008. "Core-Mantle Boundary Heat Flow." Nature Geoscience 1(1): 25–32. doi: 10.1038/ngeo.2007.44.

Pozzo, M., et al. 2012. "Thermal and Electrical Conductivity of Iron at Earth's Core Conditions." Nature 485: 355–58.

Stacey, F. D., and D. E. Loper. 1984. "Thermal Histories of the Core and Mantle." Physics of the Earth and Planetary Interiors 36(2): 99–115. doi: 10.1016/0031-9201(84)90011-6.

Stevenson, D .J. 1990. "Fluid Dynamics of Core Formation." in Origin of the Earth. Oxford University Press, New York.

——— . 2003. "Planetary Magnetic Fields." Earth and Planetary Science Letters 208: 1–11.