Burkhard Militzer

A Massive Core in Jupiter Predicted From First-Principles Simulations

Hydrogen-helium mixtures at conditions of Jupiter’s interior are studied with first-principles computer simulations. The resulting equation of state (EOS) implies that Jupiter possesses a central core of 14 – 18 Earth masses of heavier elements, a result that supports core accretion as standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 2 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within modeling errors, consistent with abundances measured by the 1995 Galileo Entry Probe mission (equivalent to about 5 Earth masses of planetary ices when extrapolated to the mantle), suggesting that the composition found by the probe may be representative of the entire planet. Interior models derived from this first-principles EOS do not give a match to Jupiter’s gravity moment J4 unless one invokes interior differential rotation, implying that jovian interior dynamics has an observable effect on the measured gravity field.

Path integral monte carlo calculation of the deuterium hugoniot

Restricted path integral Monte Carlo simulations have been used to calculate the equilibrium properties of deuterium for two densities: 0.674 and 0.838 g cm(-3) ( r(s) = 2.00 and 1.86) in the temperature range of 10(5)</=T</=10(6) K. We carefully assess size effects and dependence on the time step of the path integral. Further, we compare the results obtained with a free particle nodal restriction with those from a self-consistent variational principle, which includes interactions and bound states. By using the calculated internal energies and pressures, we determine the shock Hugoniot and compare with recent laser shock wave experiments as well as other theories.

Hydrogen-Helium Mixtures in the Interiors of Giant Planets

Equilibrium properties of hydrogen-helium mixtures under conditions similar to the interior of giant gas planets are studied by means of first principle density functional molecular dynamics simulations. We investigate the molecular and atomic fluid phase of hydrogen with and without the presence of helium for densities between ρ = 0.19 gcm 3 and ρ = 0.66 gcm 3 and temperatures from T = 500K to T = 8000 K. Helium has a crucial influence on the ionic and electronic structure of the liquid. Hydrogen molecule bonds are shortened as well as strengthened which leads to more stable hydrogen molecules compared to pure hydrogen for the same thermodynamic conditions. The ab initio treatment of the mixture enables us to investigate the validity of the widely used linear mixing approximation. We find deviations of up to 8% in energy and volume from linear mixing at constant pressure in the region of molecular dissociation.

High pressure-temperature Raman measurements of H2O melting to 22 GPa and 900 K

The melting curve of H(2)O has been measured by in situ Raman spectroscopy in an externally heated diamond anvil cell up to 22 GPa and 900 K. The Raman-active OH-stretching bands and the translational modes of H(2)O as well as optical observations are used to directly and reliably detect melting in ice VII. The observed melting temperatures are higher than previously reported x-ray measurements and significantly lower than recent laser-heating determinations. However, our results are in accord with earlier optical determinations. The frequencies and intensities of the OH-stretching peaks change significantly across the melting line while the translational mode disappears altogether in the liquid phase. The observed OH-stretching bands of liquid water at high pressure are very similar to those obtained in shock-wave Raman measurements.

Solubility of Water Ice in Metallic Hydrogen: Consequences for Core Erosion in Gas Giant Planets

Using ab initio simulations we investigate whether water ice is stable in the cores of giant planets, or whether it dissolves into the layer of metallic hydrogen above. By Gibbs free energy calculations we find that for pressures between 10 and 40 Mbar the ice-hydrogen interface is thermodynamically unstable at temperatures above approximately 3000 K, far below the temperature of the core-mantle boundaries in Jupiter and Saturn. This implies that the dissolution of core material into the fluid layers of giant planets is thermodynamically favored, and that further modeling of the extent of core erosion is warranted.

Rocky core solubility in Jupiter and giant exoplanets.

Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10,000 K, implying the potential for significant redistribution of rocky core material in Jupiter and larger exoplanets.

Evolutionary search for low autocorrelated binary sequences

The search for low autocorrelated binary sequences is a classical example of a discrete frustrated optimization problem. We demonstrate the efficiency of a class of evolutionary algorithms to tackle the problem. A suitable mutation operator using a preselection scheme is constructed, and the optimal parameters of the strategy are determined.

First-principles calculation of the elastic moduli of sheet silicates and their application to shale anisotropy

Abstract The full elastic tensors of the sheet silicates muscovite, illite-smectite, kaolinite, dickite, and nacrite have been derived with first-principles calculations based on density functional theory. For muscovite, there is excellent agreement between calculated properties and experimental results. The influence of cation disorder was investigated and found to be minimal. On the other hand, stacking disorder is found to be of some relevance for kaolin minerals. The corresponding single-crystal seismic wave velocities were also derived for each phase. These revealed that kaolin minerals exhibit a distinct type of seismic anisotropy, which we relate to hydrogen bonding. The elastic properties of a shale aggregate was predicted by averaging the calculated properties of the contributing mineral phases over their orientation distributions. Calculated elastic properties display higher stiffness and lower p-wave anisotropy. The difference is likely due to the presence of oriented flattened pores in natural samples that are not taken into account in the averaging.

Path integral Monte Carlo simulation of the low-density hydrogen plasma

Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of 9.83 x 10(-4)</=rho</=0.153 g cm(-3) and 5000</=T</=250 000 K. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral, and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.

Measurement of thermal diffusivity at high pressure using a transient heating technique

We describe a flash-heating procedure designed to measure thermal diffusivity of materials at high pressure and temperature in diamond anvil cells. This technique involves time-resolved radiometry combined with a pulsed IR laser source. Results for MgO, NaCl, and KCl are presented (to P=32GPa and T=2600K). These measurements agree with previous studies at low pressure and high temperature and enable to test models for the combined P-T dependence of thermal conductivity. This technique can be extended to a broader range of pressures and can be used to address a variety of problems in geoscience, planetary sciences, and materials science.