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From Electrons to Planets

Principal Investigator: Ronald E. Cohen, Department of Earth and Environmental Sciences, Ludwig-Maximilians-Universität München (Germany)
HPC Platform: SuperMUC of LRZ
Date published: September 2018
LRZ Project ID: pr92ma

Scientists at the Ludwig-Maximilians-Universität in Munich are using SuperMUC as their prime computational HPC resource for the ERC Advanced Grant “Theory of Mantle, Core, and Technological Materials.” Their focus has been put on several different widely ranging areas, that all use the same underlying fundamental physics and computational methods. They have performed many large scale simulations of crystalline and liquid iron alloys at conditions of Earth’s core, up to 6000K and over 300 million atmospheres of pressure, and have computed the electrical and thermal conductivity, crucial for understanding the generation of Earth’s magnetic field and heat flow in the Earth. Without its magnetic field, life on Earth’s surface is impossible, since the magnetic field screens us from deadly solar radiation. Understanding how it is generated and how it initially arose is thus crucial for understanding Earth's history. All geological processes ranging from volcanoes, earthquakes, and plate tectonics also depend on the core heat flow, which the researchers have constrained. They are also studying the Fe-H system at much higher pressures and temperatures to understand the cores of giant planets like Jupiter and exoplanets in other star systems. Closer to home, the scientists are studying carbonated aqueous fluids in the upper mantle and transition zone of the Earth to understand fluid chemistry that drives many Earth processes. Finally the scientists are studying technological materials, like electrocalorics, which can reclaim waste heat as energy, and new types of active organic materials for new applications.

Introduction

Fluids are important in Earth’s interior, where they transport materials, lead to melting, and govern much of the behavior of the Earth ranging from earthquakes to volcanism and plate tectonics, yet fluid properties are extremely difficult to measure at high pressures. In the Earth, carbonated aqueous fluids separate from rocks in the slabs that are subducted into Earth’s transition zone and rise, reacting with mantle rocks, changing their chem-istry and mechanical properties, generating earthquakes, and leading to melting that causes volcanoes and large-scale motion in the Earth. Studying the chemistry of these fluids is made difficult by the fact that they react with whatever you encapsulate them in, such as a diamond anvil cell or metallic reaction vessels, and they do not diffract X-rays like crystals, so are difficult to obtain even basic quantities such as density. In giant planets like Jupiter, with enormous pressure and temperatures, this is even more of an issue, where we have very little experi-mental information. We are using first-principles methods to simulate such fluids, starting with electrons and nuclei, using highly accurate quantum mechanical methods to simulate fluids in the pressures and temperatures that range from Earth’s surface to its core, and to the center of Jupiter and beyond. The same methods can be used across all fields of materials, and we are also studying technological materials, particularly active materials that can be used to produce or harness energy, such as ferro-electrics. This is an European Research Council Advanced Grant project called Theory of Mantle, Core, and Technological Materials (ToMCaT).

Theory of Mantle, Core, and Technological MaterialsFigure 1. (1) We find spontaneous formation of molecules such as formate under transition zone conditions. (2) Snapshot of the simulation box showing water and CO2 molecules. (3) Hydrogen-Oxygen corresponding to the middle of the Earth’s upper mantle at two temperatures. 4) Self diffusion profile of H2O molecules in pure water spanning a pressure range covering Earth’s crust through the Upper Lower Mantle (dotted line). © LMU München

Results and Methods

C-H-O Fluids

Theory of Mantle, Core, and Technological MaterialsFigure 2. Speciation changes in pure water and a CO2 –poor mixture. As the pressure increases H2O mole-cules are dissociated more at lower pressures in the mixture. In a water-rich mixture and at 20 GPa, CO2 is no longer the stable molecular specie of C. © LMU München

We performed first-principles molecular dynamics (FPMD) obtained the equation of state as a function of pressure, temperature and composition. Unexpectedly, we find spontaneous molecular reactions, and we have identified from the computed vibrational spectra and analyzing atomic distances and animation frames.

Theory of Mantle, Core, and Technological MaterialsFigure 3. Density versus pressure for 3 compositions in the Fe-H liquid system. Different types of symbols mark different temperatures, while colors mark compositions. Earth’s inner core density is shown for reference. The existence of a Jovian core is still a debated subject, the vertical grey line shows the possible density range at an inner core pressure of 7 TPa. © LMU München

The Equation of State and Phase Diagram of Fluids at Giant Planet Core Conditions

We have performed FPMD on iron fluids, Fe-H fluids, and pure iron metal (Fig. 3). After the structural analysis of these fluids we have found that regardless of composition no Fe-H molecules form. These results are now being used to model Jupiter and other giant planets.

Iron at Earth Core Conditions

We have computed the thermal conductivity of pure solid iron throughout Earth's conditions using Density Func-tional Theory (DFT) and Dynamical Mean Field Theory (DMFT). Our predicted thermal conductivity at Core-Mantle boundary conditions (T≈4000 K and P≈125 GPa) is about 93 W/m/K, 30% lower than previous theoretical results, [1] which neglected the contribution due to elec-tron-electron scattering. Considering that melting and the existence of light elements at Earth’s core will further decrease thermal conductivity, the heat conduction down the core adiabat will be about 9-12 TW. Comparing this with the estimated total heat from the core, 8-16 TW, suggests that the geodynamo might be sustained mainly by thermal convection.

Theory of Mantle, Core, and Technological MaterialsFigure 4. Computed thermal conductivity for iron at 100-140 GPa, for comparison with experiments. © LMU München

Tuning Electrocalorics

The electrocaloric effect is the change in temperature with applied electric field in pyroelectrics, or the change in electric field with temperature. It can be used for solid state refrigeration or energy scavenging, and will play an important role in our energy future. However, how to op-timize it is not well known. We have performed extensive molecular dynamics simulations using the shell model fit to first-principles calculations for PMN-PT [3] and BaTiO3 [4] as functions of temperature, composition, and applied electric field, magnitude and direction.

Ferroelectric perovskite oxides possess a large electro-caloric (EC) effect, but usually at high temperatures near the ferroelectric/paraelectric phase transition temperature, which limits their potential application as next generation solid-state cooling devices. In PMN-PT (PbMg1/3Nb2/3O3-PbTiO3). We find that the maximum EC strength of PMN-PT occurs within the morphotropic phase boundary (MPB) region at 300 K (Fig. 5). The large adiabatic temperature change is caused by easy rotation of polarization within the MPB region.

Theory of Mantle, Core, and Technological Materials

Figure 5. Adiabatic temperature change in PMN0.4PT0.6 in applied electric field. This electrocaloric effect can be used for solid state refrigeration and energy scavenging from excess heat. © LMU München

On-going Research/Outlook

First-principles molecular dynamics for fluids is enor-mously computationally intensive. The computations have taken about 60 million CPU hours so far, and there is more to do. The problem is that to get chemical accuracy for fluid properties and constitution requires on the order of 10 picoseconds of simulation time for each volume, composition, and temperature point, which is 20,000 self-consistent calculations for systems of 108-192 atoms for Fe-H and H2O-CO2, respectively. On the SuperMUC we can run efficiently on hundreds of processors, even a whole island, to make this work possible. We are now working on getting our final well-converged results, which we can then apply to planetary interiors. The work on transport properties is also moving from perfect crystals to complex fluids such as Earth’s outer core, Jupiter, and exoplanets.

Project Team

Ronald E. Cohen (PI), Alexandra Seclaman, Honghui Wu, Junqing Xu, Bogdan Yavorksyy, Haiwu Zhang

References and Links

[1] http://www.tomcat.mineralogie.geowissenschaften.uni-muenchen.de/
[2] M. Pozzo et al., Nature 485, 355 (2012).
[3] H. H. Wu and R. E. Cohen, Phys. Rev. B 054116 (2017).
[4] [1] H. H. Wu and R. E. Cohen, J. Phys. Condens. Matter. 29, 485704 (2017).

Scientific Contact

Professor Dr. Ronald Cohen
Ludwig Maximilians Universität München
Department für Geo- und Umweltwissenschaften
Theresienstrasse 41, Room 207, D-80333 München (Germany)
e-mail: ronald.cohen [@] min.uni-muenchen.de

NOTE: This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2018":

LRZ project iD: pr92ma

September 2018