arXiv subjects

Burkhard Militzer

Publications and source records attributed to Burkhard Militzer.

At least 55 records · Page 3Linked to original sources

arXiv2017

Properties of hydrogen, helium, and silicon dioxide mixtures in giant planet interiors

Recent observations of Jupiter and Saturn provided by spacecraft missions, such as Juno and Cassini, compel us to revise and improve our models of giant planet interiors. Even though hydrogen and helium are by far the dominant species in these planets, heavy elements can play a significant role in the structure and evolution of the planet. For instance, giant-planet cores may be eroded by their surrounding fluid, which would result in a significantly increased concentration of heavy elements in the hydrogen-helium envelope. Furthermore, the heavy elements could inhibit convection by creating a stabilizing gradient of composition. In order to explore the effects of core erosion, we performed ab initio simulations to study structural, diffusion and viscosity properties of dense multi-component mixtures of hydrogen, helium, and silicon dioxide at relevant pressure-temperature conditions. We computed radial distribution functions to identify changes in the chemical behavior of the mixture and to reveal dissociation trends with pressure and temperature. The computed diffusion coefficients of the different species as well as the viscosity provide constraints for the time scale of the dynamics of the core erosion and the mixing of its constituents into the envelope, which will help improve planetary models.

astro-ph.EP↗

arXiv2017

Equation of state and shock compression of warm dense sodium - a first-principles study

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially-ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of $1.93-11.60$ g/cm$^{3}$ and $10^3-1.29\times10^8$ K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of $2\times10^6$ K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to $K$-shell and $L$-shell ionization. Our Hugoniot curves provide a benchmark for widely-used EOS models, SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10$^7$ K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.

astro-ph.SR↗

arXiv2016

Understanding Jupiter's Interior

This article provides an overview of how models of giant planet interiors are constructed. We review measurements from past space missions that provide constraints for the interior structure of Jupiter. We discuss typical three-layer interior models that consist of a dense central core and an inner metallic and an outer molecular hydrogen-helium layer. These models rely heavily on experiments, analytical theory, and first-principle computer simulations of hydrogen and helium to understand their behavior up to the extreme pressures ~10 Mbar and temperatures ~10,000 K. We review the various equations of state used in Jupiter models and compare them with shock wave experiments. We discuss the possibility of helium rain, core erosion and double diffusive convection may have important consequences for the structure and evolution of giant planets. In July 2016 the Juno spacecraft entered orbit around Jupiter, promising high-precision measurements of the gravitational field that will allow us to test our understanding of gas giant interiors better than ever before.

astro-ph.EP↗

arXiv2016

High-temperature miscibility of iron and rock during terrestrial planet formation

The accretion of a terrestrial body and differentiation of its silicate/oxide mantle from iron core provide abundant energy for heating its interior to temperatures much higher than the present day Earth. The consequences of differentiation on the structure and composition of planets are typically addressed considering only the interaction of molten iron with an immiscible `rocky' phase. We demonstrate that mixing in a representative system of liquid or solid MgO and liquid iron to a single homogeneous liquid occurs at sufficiently low temperature to be present in the aftermath of a giant impact. Applying the thermodynamic integration technique to density functional theory molecular dynamics simulations, we determine the solvus closure temperature for the Fe-MgO system for pressures up to 400 GPa. Solvus closure occurs at $\sim$4000 K at low pressure, and has a weak positive pressure dependence, such that its gradient with respect to depth is less steep than an adiabatic temperature profile. This predicts a new mode of core-mantle differentiation following the most energetic giant impacts, with exsolution of iron from the mixture beginning in the outer layers of the planet. We demonstrate that high-temperature equilibration results in delivery of nominally insoluble Mg-rich material to the early core. Since MgO is the least soluble major mantle component in iron at low temperatures, these results may represent an upper bound on temperature for mixing in terrestrial planets.

astro-ph.EP↗

arXiv2016

Tidal Response of Preliminary Jupiter Model

In anticipation of improved observational data for Jupiter's gravitational field from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen-helium mixtures. We calculate hydrostatic-equilibrium gravity terms using the non-perturbative concentric Maclaurin Spheroid (CMS) method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly-rotating planet like Jupiter. Our predicted static tidal Love number $k_2 = 0.5900$ is $\sim$10\% larger than previous estimates. The value is, as expected, highly correlated with the zonal harmonic coefficient $J_2$, and is thus nearly constant when plausible changes are made to interior structure while holding $J_2$ fixed at the observed value. We note that the predicted static $k_2$ might change due to Jupiter's dynamical response to the Galilean moons, and find reasons to argue that the change may be detectable, although we do not present here a theory of dynamical tides for highly oblate Jovian planets. An accurate model of Jupiter's tidal response will be essential for interpreting Juno observations and identifying tidal signals from effects of other interior dynamics in Jupiter's gravitational field.

astro-ph.EP↗

arXiv2016

The properties of heavy elements in giant planet envelopes

The core accretion model for giant planet formation suggests a two layer picture for the initial structure of Jovian planets, with heavy elements in a dense core and a thick H-He envelope. Late planetesimal accretion and core erosion could potentially enrich the H-He envelope in heavy elements, which is supported by the three-fold solar metallicity that was measured in Jupiter's atmosphere by the Galileo entry probe. In order to reproduce the observed gravitational moments of Jupiter and Saturn, models for their interiors include heavy elements, $Z$, in various proportions. However, their effect on the equation of state of the hydrogen-helium mixtures has not been investigated beyond the ideal mixing approximation. In this article, we report results from \textit{ab initio} simulations of fully interacting H-He-$Z$ mixtures in order to characterize their equation of state and to analyze possible consequences for the interior structure and evolution of giant planets. Considering C, N, O, Si, Fe, MgO and SiO$_2$, we show that the behavior of heavy elements in H-He mixtures may still be represented by an ideal mixture if the effective volumes and internal energies are chosen appropriately. In the case of oxygen, we also compute the effect on the entropy. We find the resulting changes in the temperature-pressure profile to be small. A homogeneous distribution of 2\% oxygen by mass changes the temperature in Jupiter's interior by only 80 K.

astro-ph.EP↗

arXiv2016

The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn's tidal response

We extend to three dimensions the Concentric Maclaurin Spheroid method for obtaining the self-consistent shape and gravitational field of a rotating liquid planet, to include a tidal potential from a satellite. We exhibit, for the first time, the important effect of the planetary rotation rate on tidal response of gas giants. Simulations of planets with fast rotation rates like those of Jupiter and Saturn, exhibit significant changes in calculated tidal love numbers $k_{nm}$ when compared with non-rotating bodies. A test model of Saturn fitted to observed zonal gravitational multipole harmonics yields $k_2=0.413$, consistent with a recent observational determination from Cassini astrometry data (Lainey et al., 2016). The calculated love number is robust under reasonable assumptions of interior rotation rate, satellite parameters, and details of Saturn's interior structure. The method is benchmarked against several published test cases.

astro-ph.EP↗

arXiv2015

Hydrogen-Water Mixtures in Giant Planet Interiors Studied with Ab Initio Simulations

We study water-hydrogen mixtures under planetary interior conditions using ab initio molecular dynamics simulations. We determine the thermodynamic properties of various water-hydrogen mixing ratios at temperatures of 2000 and 6000 K for pressures of a few tens of GPa. These conditions are relevant for ice giant planets and for the outer envelope of the gas giants. We find that at 2000 K the mixture is in a molecular regime, while at 6000 K the dissociation of hydrogen and water is important and affects the thermodynamic properties. We study the structure of the liquid and analyze the radial distribution function. We provide estimates for the transport properties, diffusion and viscosity, based on autocorrelation functions. We obtained viscosity estimates of the order of a few tenths of mPa.s for the conditions under consideration. These results are relevant for dynamo simulations of ice giant planets.

astro-ph.EP↗

arXiv2015

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy that we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6 g/cm, 5.0*10^5 - 1.3*10^8 K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

cond-mat.mtrl-sci↗

arXiv2015

High-pressure, temperature elasticity of Fe- and Al-bearing MgSiO3: implications for the Earth's lower mantle

Fe and Al are two of the most important rock-forming elements other than Mg, Si, and O. Their presence in the lower mantle's most abundant minerals, MgSiO_3 bridgmanite, MgSiO_3 post-perovskite and MgO periclase, alters their elastic properties. However, knowledge on the thermoelasticity of Fe- and Al-bearing MgSiO_3 bridgmanite, and post-perovskite is scarce. In this study, we perform ab initio molecular dynamics to calculate the elastic and seismic properties of pure, Fe^{3+}- and Fe^{2+}-, and Al^{3+}-bearing MgSiO_3 perovskite and post-perovskite, over a wide range of pressures, temperatures, and Fe/Al compositions. Our results show that a mineral assemblage resembling pyrolite fits a 1D seismological model well, down to, at least, a few hundred kilometers above the core-mantle boundary, i.e. the top of the D'' region. In D'', a similar composition is still an excellent fit to the average velocities and fairly approximate to the density. We also implement polycrystal plasticity with a geodynamic model to predict resulting seismic anisotropy, and find post-perovskite with predominant (001) slip across all compositions agrees best with seismic observations in the D''.

physics.geo-ph↗

arXiv2015

Miscibility calculations for water and hydrogen in giant planets

We present results from ab initio simulations of liquid water-hydrogen mixtures in the range from 2 to 70 GPa and from 1000 to 6000 K, covering conditions in the interiors of ice giant planets and parts of the outer envelope of gas giant planets. In addition to computing the pressure and the internal energy, we derive the Gibbs free energy by performing a thermodynamic integration. For all conditions under consideration, our simulations predict hydrogen and water to mix in all proportions. The thermodynamic behavior of the mixture can be well described with an ideal mixing approximation. We suggest a substantial fraction of water and hydrogen in giant planets may occur in homogeneously mixed form rather than in separate layers. The extend of mixing depends on the planet's interior dynamics and its conditions of formation, in particular on how much hydrogen was present when icy planetesimals were delivered. Based on our results, we do not predict water-hydrogen mixtures to phase separate during any stage of the evolution of giant planets. We also show that the hydrogen content of an exoplanet is much higher if the mixed interior is assumed.

astro-ph.EP↗

arXiv2014

Equations of state and stability of MgSiO$_3$ perovskite and post-perovskite phases from quantum Monte Carlo simulations

We have performed quantum Monte Carlo (QMC) simulations and density functional theory (DFT) calculations to study the equations of state of MgSiO$_3$ perovskite (Pv) and post-perovskite (PPv), up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground state energies were derived using QMC and the temperature dependent Helmholtz free energies were calculated within the quasi-harmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO$_3$ agree well with experiments, and better than those from generalized gradient approximation (GGA) calculations. The Pv-PPv phase boundary calculated from our QMC equations of states is also consistent with experiments, and better than previous LDA calculations. We discuss the implications for double crossing of the Pv-PPv boundary in the Earth.

cond-mat.mtrl-sci↗

arXiv2013

A multiphase equation of state for carbon addressing high pressures and temperatures

We present a 5-phase equation of state (EOS) for elemental carbon. The phases considered are: diamond, BC8, simple-cubic, simple-hexagonal, and the liquid/plasma state. The solid phase free energies are constrained by density functional theory (DFT) calculations. Vibrational contributions to the free energy of each solid phase are treated within the quasiharmonic framework. The liquid free energy model is constrained by fitting to a combination of DFT molecular dynamics performed over the range 10,000 K < T < 100,000 K, and path integral quantum Monte Carlo calculations for T > 100,000 K (both for ρ between 3 and 12 g/cc, with select higher-ρ DFT calculations as well). The liquid free energy model includes an atom-in-jellium approach to account for the effects of ionization due to temperature and pressure in the plasma state, and an ion-thermal model which includes the approach to the ideal gas limit. The precise manner in which the ideal gas limit is reached is greatly constrained by both the highest temperature DFT data and the path integral data, forcing us to discard an ion-thermal model we had used previously in favor of a new one. Predictions are made for the principal Hugoniot and the room-temperature isotherm, and comparisons are made to recent experimental results.

cond-mat.mtrl-sci↗

arXiv2013

Solubility of Iron in Metallic Hydrogen and Stability of Dense Cores in Giant Planets

The formation of the giant planets in our solar system, and likely a majority of giant exoplanets, is commonly explained by the accretion of nebular hydrogen and helium onto a large core of terrestrial-like composition. The fate of this core has important consequences for the evolution of the interior structure of the planet. It has recently been shown that H2O, MgO and SiO2 dissolve in liquid metallic hydrogen at high temperature and pressure. In this study, we perform ab initio calculations to study the solubility of an innermost metallic core. We find dissolution of iron to be strongly favored above 2000 K over the entire pressure range (0.4-4 TPa) considered. We compare with and summarize the results for solubilities on other probable core constituents. The calculations imply that giant planet cores are in thermodynamic disequilibrium with surrounding layers, promoting erosion and redistribution of heavy elements. Differences in solubility behavior between iron and rock may influence evolution of interiors, particularly for Saturn-mass planets. Understanding the distribution of iron and other heavy elements in gas giants may be relevant in understanding mass-radius relationships, as well as deviations in transport properties from pure hydrogen-helium mixtures.

astro-ph.EP↗

arXiv2013

Superionic to superionic phase change in water: consequences for the interiors of Uranus and Neptune

Using density functional molecular dynamics free energy calculations, we show that the body-centered-cubic phase of superionic ice previously believed to be the only phase is in fact thermodynamically unstable compared to a novel phase with oxygen positions in fcc lattice sites. The novel phase has a lower proton mobility than the bc phase and may exhibit a higher melting temperature. We predict a transition between the two phases at a pressure of 1 +/- 0.5 Mbar, with potential consequences for the interiors of ice giants such as Uranus and Neptune.

astro-ph.EP↗

arXiv2012

Ab Initio Investigation of a Possible Liquid-Liquid Phase Transition in MgSiO3 at Megabar Pressures

We perform density functional molecular dynamics simulations of liquid and solid MgSiO3 in the pressure range of 120-1600 GPa and for temperatures up to 20000 K in order to provide new insight into the nature of the liquid-liquid phase transition that was recently predicted on the basis of decaying laser shock wave experiments [Phys. Rev. Lett. 108 (2012) 065701]. However, our simulations did not show any signature of a phase transition in the liquid phase. We derive the equation of state for the liquid and solid phases and compute the shock Hugoniot curves. We discuss different thermodynamic functions and by explore alternative interpretations of the experimental findings.

cond-mat.mtrl-sci↗

arXiv2012

H4O and other hydrogen-oxygen compounds at giant-planet core pressures

Water and hydrogen at high pressure make up a substantial fraction of the interiors of giant planets. Using ab initio random structure search methods we investigate the ground-state crystal structures of water, hydrogen, and hydrogen-oxygen compounds. We find that, at pressures beyond 14 Mbar, excess hydrogen is incorporated into the ice phase to form a novel structure with H4O stoichiometry. We also predict two new ground state structures, P2_1/m and I4/mmm, for post-C2/m water ice.

cond-mat.mtrl-sci↗

arXiv2012

Ab Initio Simulations of Hot, Dense Methane During Shock Experiments

Using density functional theory molecular dynamics simulations, we predict shock Hugoniot curves of precompressed methane up to 75000 K for initial densities ranging from 0.35 to 0.70 g/cc. At 4000 K, we observe the transformation into a metallic, polymeric state consisting of long hydrocarbon chains. These chains persist when the sample is quenched to 300 K, leading to an increase in shock compression. At 6000 K, the sample transforms into a plasma composed of many, short-lived chemical species. We conclude by discussing implications for the interiors of Uranus and Neptune and analyzing the possibility of creating a superionic state of methane in high pressure experiments.

cond-mat.mtrl-sci↗