Burkhard Militzer

Our new ab initio calculations show that the interior temperature of Uranus is 30% colder than previously predicted when the same assumptions are made as before (4300 K instead of 5800 K). If one assumes that latent heat is released at the phase transition from liquid to superionic water, the interior is still 15% colder than before (4900 K). This colder temperature makes it much more likely for the phase separation of planetary ices that we predicted or the diamond rain to occur in the interiors of Uranus and Neptune.

Whether new models of type B or C (see left graph) are more realistic depends on the question whether there is an exothermic or endothermic first-order phase transition in the mantles of Uranus and Neptune as we discuss in our recent paper.

It was a major surprise when the Voyager 2 spacecraft discovered in 1986 and 1989 that the two ice giant planets in our solar system, Uranus and Neptune, do not have the typical dipolar magnetic fields. Instead of having well-defined north and south poles that we know from Earth, Jupiter and Saturn, these magnetic fields are much more disordered. It has remained unexplained for 30+ years what Uranus and Neptune are missing for their magnetic fields to organize themselves into strong dipolar fields. Our research article now offers a really attractive solution to this puzzle:

Phase separation of planetary ices explains nondipolar magnetic fields of Uranus and Neptune.

Our computer simulations of planetary ices (water, methane and ammonia) predict that they phase separate into two fluids (a bit like oil and water) at high pressure. Uranus and Neptune are thus predicted to have two distinct, liquid layers in their interiors: a thin convecting upper layer, rich in water, where the disordered magnetic field is generated and a lower layer composed of carbon, nitrogen and hydrogen that is magnetically inactive.

• Here is a recording of a research presentation on this subject, which you also find on youtube. Forward to minute 30:39 for the new results. Here are slides in pptx and pdf formats.
• Robert Sanders from Media Relations at UCB wrote an article entitled “A clue to what lies beneath the bland surfaces of Uranus and Neptune”.
• Jonathan O'Callaghan reported in the NY Times “Vast Oceans of Water May Be Hiding Within Uranus and Neptune”.
• John Wenz wrote in Astronomy Magazin “Uranus and Neptune have weird magnetic fields - this might be why”.
• Rosemary Pennington and John Bailer recorded with me an episode entitled “Out of this world statistics” for their Stats+Stories podcast series.
• On National Public Radio's popular show Science Friday, you can find an interview entitled “Might Uranus And Neptune Have Deep, Multi-Layer Oceans?”
• Finally some data files for the interior structures of Uranus and Neptune can be found on Zenodo.

In our latest article, we describe how a doubly superionic state can be generated and detected with dynamic compression experiments. X-ray diffraction (XRD) serves as a primary tool to determine whether the nitrogen atoms are ordered or disordered, which marks the differences between a hydrogen superionic and a doubly superionic states. When the material transitions from one state to the other, the first three peaks in the XRD spectrum disappear (left graph). When the material melts completely, a very broad peak appears that is centered at the (1 2 2) Bragg deflection.

To reach a doubly superionic state at high pressure and temperature, we propose shock+ramp compression experiments or triple shock experiments.

At high pressure and temperature, water assumes superionic state, in which the smaller hydrogen atoms behave like a liquid while the larger oxygen nuclei remain confined to their lattice sites. In our latest work, Kyla de Villa, Felipe Gonzalez and I predict the existence of a novel state of matter: double superionicity. On the left, we show for the material H₃NO₄ that the hydrogen and the nitrogen nuclei are mobile while the oxygen atoms remain confined to their lattice sites. Here is a larger .mp4 animation.

• When ice compounds like H₃NO₄, CH₂N₂, or HCNO are gradually heated at high pressure, our computer simulations predict that the hydrogen nuclei are mobilized first and the material changes from a solid to a hydrogen superionic state.
• Upon further heating, we find that a second type of nuclei like N in H₃NO₄ is mobilized and the material assumed a double superionic state, in which two types of nuclei behave like a liquid while the oxygen nuclei remain confined to the their lattice sites. Upon further heating the lattice oxygen nuclei melts also and the material assume a liquid state.
• We predict superionicity to be a common feature among compounds in the interiors of Uranus and Neptune. It will contribute the electrical conductity and thus enhance the generation of the magnetic fields in their interiors.

In our latest article, we study Jupiter's interior structure and introduce a new general-purpose Quadratic Monte Carlo (QMC) technique that is much more efficient in confining fitness landscapes than the popular affine invariant MCMC method that relies on linear stretch moves. We compare how long it takes the ensembles of walkers in both methods to travel to the most relevant parameter region. Once there, we compare the autocorrelation time and error bars of the two methods. For a ring potential and the 2d Rosenbrock function, we find that our quadratic Monte Carlo technique is significantly more efficient. This suggests a lot of computer time and thus electrical energy can be saved.
Here we provide our open QMC source code, installation instructions and three example applications and implementations.

In our latest article, F. Gonzalez-Cataldo, B.K. Godwal, K. Driver, R. Jeanloz, and I study with computer simulations a material becomes during ramp compression experients. The work was motivated by the ramp compression experiments on diamond by R. Smith et al. that reached stress conditions of several tera Pascals. We found that for a given density, the measured stresses were too high to be compatible with results from ab initio simulations. The measured density-stress point can be matched with simulation results of liquid carbon (yellow symbols). This assumes the diamond samples melted during compression, which is under debate. There was sufficient energy in the experiment for this occur but no evidence for it was collected during the measurements. Later experiments by A. Lazicki et al. demonstrated that carbon remained solid. So we derive a multi-step model for ramp compression of solid carbon (red circles). For a assumed step number and size, this models allow us to estimate how much plastic work occured during the ramp compression.

In our latest article, we study how the shape and gravity field of strongly irradiated, giant exoplanets is destorted by the external gravity field of their massive host stars. A planet's response to such external fields is expressed by the tidal Love number, k₂₂, which has been inferred from telescope observations for the exoplanets WASP 4b (green color), HAT-P 13b (red), WASP 18b (blue). In the digram on the left, we compared these observations (solid circles) with our calculated values that we represent with triangles of corresponding colors. The upper triangles represent models without rocky core while the lower triangles show predictios for the largest possible cores. The beige symbols show our predictions for the exoplanets WASP 12b, 103b, 121b, Kepler 57b, and Corot 3b. We find that the static Love number, k₂₂ cannot exceed the value 0.6 (yellow shaded region), which is in contradiction with some of the observations. We suggest additional observations to be made and existing data to be re-analyzed because this discrepancy may imply that the orbits of the observed exoplanets could be affected by other factors like not-yet-detected exoplanets. In our paper, we also derived the gravity harmonics, shape, of moment of inertia for our planet models.

With the goal of making warm dense matter computations more reliable and efficient, we make available our first-principles equation of state (FPEOS) database for materials at extreme conditions. We provide our EOS tables the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B₄C, BN, CH₄, CH₂, C₂H₃, CH, C₂H, MgO, and MgSiO₃ that are solely based on results from ~5000 path integral Monte Carlo and density functional molecular dynamics simulations. For all these materials, we provide the pressure and internal energy over a density-temperature range from ~0.5 to 50 g/cc and from ~10⁴ to 10⁹ K. In our recent article, we compute isobars, adiabats, and shock Hugoniot curves in the regime of L and K shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H₂O, H₂O₂, Al₂O₃, CO, and CO₂ to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures (left graph). We provide all FPEOS tables as well as C++ and Python computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

With density functional molecular dynamics simulations, we computed the phase diagram of MgO in the pressure range from 50 to 2000 GPa up to temperature of 20000 K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. The B1 structure is a NaCl-type crystal, in which Mg and O nuclei occupy alterating sites. Each atomic species by themselves forms a face-centered cubic lattice. In the B2 structure, is a CsCl-type crystal. Each atom species by themselves form a simple cubic structure. With our computer simulation, we show that anharmonic effects stabilize the B1 phase. We predict the B1-B2-liquid triple point to occur at approximately T = 10000 K and P = 370 GPa, which is higher in pressure than was inferred with quasi-harmonic methods. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small pressure-temperature interval. This may render it difficult to observe this phase with shock experiments because of kinetic effects. Here are a copy of our article and a few slides in PPTX and PDF formats available to download.

This joint theoretical-experimental project was sparked by a drastic disagreement between laboratory data and results from computer simulations for the diffusion of helium atoms in quartz crystals. This is important because the diffusion of noble gases in minerals is often utilized to reconstruct the thermal histories of rocks. Computer simulations of helium in perfect quartz crystals predicted that already at room temperature, all helium atoms would diffuse out of the crystal because the helium atoms encounter very lower energy barriers along the crystal's z channel. Taken at face value, this would imply all helium would have diffused out of the crystal before the experiments even began. Conversely, however, the lab measurements showed that temperatures between 70 and 220 ^oC were required for most helium atoms diffuse out of quartz crystals. In our article, this discrepancy is resolved by introducing the novel hypothesis that helium atom reside inside nanopores in the quartz crystal. The calculations showed that activation energy for helium atoms to diffuse from the nanopore into the crystal matched experimental data. A consistent effective diffusion model was constructed and the nanopore concentration was estimated to be approximately 10^-5.

In our latest article about warm dense matter, we employ path integral Monte Carlo and density function molecular dynamics simulations to study the properties of hot, dense magensium at high temperature and density. On the left, we show our prediction for the principal shock Hugoniot curve, which will most likely be the first quantity to be measure when laboratory experiments reach these conditions in the future. We identify four main excitation mechanisms that control the density that is reached in these compression experiments. In the low-pressure regime, excitations of L-shell electrons increase the shock compression ratio above the canonical value of 4. At higher pressure, the excitations of K-shell electrons maintain a high compression ratio of about 4.9. The compression ratio starts to decrease again once all K-shell electrons have been ionized. However, this decrease in compensated by the onset of radiative effects. Photons that are spontaneously emitted start making substantial controbutions to the energy and pressure. In compression, relativistic effects, that increase the energy of the electrons, play only a minor role.

At the ambient conditions, fluorine is a highly reactive molecular gas. However, at high pressure, its properties change in a remarkable way. In our latest article, Mark Olson, Shefali Bhatia, Paul Larson and I use computer simulations to predict that fluorine forms a polyermic and metallic structure at 31 Mbar. Instead of the usual diatomic F₂ bonding, the three quarters of the F atoms (blue) in the structure on the left are arranged in a 3D set of chains. The remaining quarter of atoms (red) occupied voids in between these chains. While flourine typically does not conduct electricity, our new high-pressure structure is an excellent conductor.
We obtained these results with a novel computer algorithm that allows us to efficiently predict crystal structures under symmetry and geometric constraints. We compare fluorine, chlorine and iodine and make reference to X-ray diffration experiments.

The four Galilean satellites, Io, Europa, Ganemede, and Callisto as well as the sun all change the shape of Jupiter very slighly through their gravitational forces. In this paper, we calculate the strengh of this tidal response, which is represented as a series of Love numbers (k_nm). We determine which Love numbers can be detected with the Juno spacecraft in the course of the on-going mission. The graph on the left suggests that Io's k₂₂, k₃₃, k₄₂, and k₃₁ lead to strong signals and should thus all be detectable. We predict a remarkably small range for Io's equilibrium Love number k₂₂ = 0.58976 ± 0.0001. Any deviation from this prediction can then be attributed with dynamic tidal effects.

Late during solar system formation, rocky planets grow through massive impacts. The shock Hugoniot curve characterize how hot and dense the rocky mantle becomes during an impact. In two recent papers, we determined the shock Hugoniot curves of MgO and MgSiO₃ with path integral and density functional molecular dynamics simulations. In the graph on the left, we show how the ionizations of K and L shell electrons increases the density during an impact event. We also provided equation of state tables over a large range of density-temperature conditions for both materials.

Saturn's rotation period cannot be measured directly and has thus been very uncertain. Estimates vary between 10:32:45 h and 10:47:06 h, which is an uncomfortably large range that introduces uncertainties into the analysis of various spacecraft measurements and remote observations. The rotation period cannot be derived from Saturn's magnetic field because it is perfectly aligned with the planet's axis of rotation. This is not case for Jupiter and its rotation period has been determined precisely to be 9:55:27 h. In our latest article, we combined gravity data from the Cassini mission and Voyager's measurements of the planet's shape to determine a rotation period of 10:33:34 h ± 55 s. The faster a planet rotates to more oblate it becomes, which enabled us to infer its rotation period.
For this analysis, we developed an accelerated version of the Concentric MacLaurin Spheroid (CMS) method that enabled to constructed Monte Carlo ensembles of plausible interior models. We currently apply this approach to construct models for Jupiter's interior to match gravity measurements by the Juno spacecraft.

Modeling the behavior of interacting quantum systems on a classical computer is challenging. Here we the Feynman's path integral method to map a system of quantum particles onto a system of classical paths. While most thermodynamic properties can be derived from simulations of closed paths, the computation of the momentum distribution requires open paths. In this article, we compute the momentum distribution of the homogeneous electron gas with path integral Monte Carlo (PIMC) simulations.
Since thsi is a fermionic system, we employed the restricted path approach to deal with the fermion sign problem. In the restricted PIMC method, only node-avoiding (NA) paths contribute. For two particles, the nodal restriction prohibits all permutations. However, if simulations with the direct fermion method are performed no restrictions are applied. Nonpermuting paths that cross the nodes (NX) and those that avoid it (NA) both enter with a positive sign. Permuting paths (PNX) are now permitted and enter with a negative weight given by the (-1)^P factor.

We developed a new symmetry-driven structure search (SYDSS) algorithm to predict novel materials with ab initio simulations. In our recent article, we predict water and salt form a novel compound at high pressure. While at ambient conditions, water can only incorporate a modest amount of salt, we predict that both materials form a novel 1:1 stoichiometric H₂O-NaCl compound at high pressure. It is well-known that high pressure changes the crystal structure of materials, novel materials may form, and immiscible compounds can become miscible. In the same article, we also predict two unusual carbon oxides, C₂O and C₄O, to form while at ambient pressures, only CO₂ and CO are known to exist.

Most models for Jupiter's formation assume it started with a dense core of rock and ice. Once that reached a critical mass of ~10 Earth masses, the run-away accretion of hydrogen-helium gas set in, which lasted until Jupiter had consumed all the gas in its vicinity, leading to a giant planet of 318 Earth masses.
While the temperature and pressure conditions in the planet's center reached ~16000 K and ~40 Mbar, the fate of the core remains ill-understood. Typical core materials like water ice, MgO, SiO₂, and iron are all soluable in hydrogen, which assumes a metallic state under these extreme conditions. It is not unclear, however, if there was sufficent convective energy in Jupiter's early history to spread out the heavy core materials against the forces of gravity.
Here we construct a series of models for Jupiter's interior in order to match the recent gravity measurments of the Juno spacecraft. We demonstrate models with a dilute core match the observations better lending support to the hypothesis that heavy material in Jupiter's core have been redistributed over a substantial fraction of the planet's radius. Different terms ranging from diffuse, dilute, expanded and even fuzzy have been invoked to describe such a core. A Jupiter model with a dilute core is shown on the left.

Giant planets are primarily composed of hydrogen and helium but they also contain a small amount of heavier elements. In the atmosphere they make up less than 3% by mass but they dominate the planets opacity. Without their presence we would be able to see through Jupiter's molecular layer and directly observe the planet's metallic interior where its magnetic field is generated. Most scientists assume Jupiter has a core composed of heavy elements. Its size and composition is uncertain but we estimated its mass to be worth 12 Earth masses. The total heavy element fraction in the planet could be as high as 7%.
In this article, Francois Soubiran investigates the properties of various heavy elements in giant planet interiors. The equation of state is computed for C, N, O, Si, Fe, MgO and SiO₂ mixed with hydrogen and helium. Effective mixing rules are derived to make models of giant planet interiors more accurate.

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.

When the Juno spacecraft arrives at Jupiter in July of this year, it will map out the planet's gravity field with unprecedented precision. What can we expect to learn about Jupiter's interior? Based on earlier measurements and on results from ab initio computer simulations of mixtures of hydrogen, helium, and some heavier elements, Bill Hubbard and I put together a number of different interior models (ApJ, 2016) . We predict a massive core of 12 Earth masses consistent with earlier models. Furthermore, we predict that helium rain has occurred on this planet for some time, which is a direct consequence of combining the measurements of the Galileo entry probe with results from ab initio calculations for the hydrogen-helium immiscibility and adiabats.

Despite a wealth of seismic observations, many questions about the compositions of the Earth's mantle have remained unanswered. In a recent study (EPSL, 2016) lead by Shuai Zhang, we show that the assumption of a pyrolitic composition for the deep Earth is in good agreement with the preliminary reference Earth model (PREM), which is a 1D seismological representation of the Earth's interior. In collaboration with Tao Liu and Stephen Stackhouse (Leeds U.) and Sanne Cottaar (Cambridge U.), we performed ab initio molecular dynamics to calculate the elastic and seismic properties of pure, Fe³⁺ and Fe²⁺, and Al³⁺ bearing MgSiO₃ perovskite and post-perovskite over a wide range of pressures, temperatures, and Fe/Al compositions.

In our recent publication in Physical Review Letters, Kevin Driver and I extended 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/cc, 5x10⁵ - 1.3x10⁸K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with pair correlation functions. On the left, we estimate the degree of ionization by comparing the integrated nucleus-electron pair correlation functions from PIMC (symbols) with results for isolated atoms (black dashed lines).

In two articles, Kevin Driver, Francois Soubiran, Shuai Zhang, and I combine path integral Monte Carlo simulations and density functional molecular dynamics to study oxygen and nitrogen in the regime of warm dense matter. We characterize both material at extreme pressure and temperature conditions that exist in stellar interiors and can be probed with shock wave experiments. We use pair correlation functions and the electronic density of states to describe changes in the structure of the plasma. We compute the shock Hugoniot curves to compare with laboratory experiments. For nitrogen, we characterize the regime of molecular dissociation that leads to a region of dP/dT<0 at high pressure, which is shown in green in the phase diagram on the left.

Ice giant planets are typically assumed to have a hydrogen-rich atmosphere, an intermediate ice layer, and a rocky core. Such three-layer models satisfy the observational constraints for Uranus and Neptune. However, it remains unclear whether these planets have oceans, which would imply the existence of a sharp boundary between the hydrogen and water layers. Alternatively, the density and the water contents of the atmosphere could increase gradually. Recent laboratory experiments by Bali at el. (2013) favored the ocean hypothesis. In our ApJ article, Francois Soubiran and I used ab initio computer simulations to determine whether H₂ and H₂O are missible at high pressure. Contrary to the experimental predictions, we find that both materials are fully miscible under ice giant interior conditions. We predict that these planets can only have oceans if icy building blocks were delivered before the gas was accreted during planet formation.

All known terrestrial planets have a separate iron core and a rocky mantle because metallic iron has a low solubility in rocky materials under typical pressure-temperature conditions in the planetary interiors. However, at sufficiently high temperatures, all materials eventually become miscible, even oil and water.
In our recent article, Sean Wahl and I use ab initio computer simulations to determine what temperature would be required for iron and MgO to become miscible in all proportions. We find that the required temperature rises from 4000 to 10,000 K as the pressure is increased from 0 to 500 GPa. Such extreme conditions can be reached during a giant impact on a terrestral planet, implying that not all iron would settle into core during such an event.

Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors. In our manuscript, a comprehensive equation of state table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation.
We present a revision to the mass-radius relationship which makes the hottest exoplanets increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses greater than ~0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant "inflated giant exoplanets".
Our full EOS table as well as our free energy interpolation code has just been made available here.

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. Here, 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 of water ice with P21/m and I4/mmm symmetry to form at 135 and 330 Mbar, respectively. Here is a slide that summarizes the seven new high pressure ice phases that were recently predicted with ab initio calculations.

Path integral Monte Carlo simulations are a powerful tool to study quantum systems at high temperature but applications to elements beyond hydrogen and helium with core electrons have so far not been possible. In our recent PRL article, Kevin Driver and I develop a new all-electron path integral Monte Carlo technique with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. Our results for pressures, internal energies, and pair correlation functions compare well with density functional molecular dynamics at temperatures of (2.5-7.5)·10⁵K. Both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cc and 10⁴-10⁹ K.

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 layer of metallic fluid hydrogen following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing magnesium oxide as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10000 K, implying significant redistribution of rocky core material in Jupiter and larger exoplanets.

Using path integral Monte Carlo simulations we have derived an equation of state (EOS) table for deuterium that covers typical intertial confinement fusion conditions at densities ranging from 0.002 to 1596 g/cm³ and temperatures of 1.35 eV ~ 5.5 keV. The small grey circles in the diagram on the left indicate the temperature-density conditions of our simulations. The EOS and related results are summarized in an article that has been published in Physical Review B.

The bonding properties of water ice at high pressure are studied in this article. By comparing the Wannier orbitals in the Pnma structure (shown in the image on the left), one can tell that they differ substantially from the sp³ hybridization in the ice X phase at lower pressures. Most strikingly, the white orbitals are not aligned with any hydrogen bond.

The four giant planets in our solar system grow so large because icy comets made their cores grow much faster than those of terrestrial planets, which enabled them to accrete large amounts of gas. With ab initio simulations, Hugh Wilson and I demonstrate in our recent manuscript that water ice is not thermodynamically stable at the temperature and pressure conditions where core is exposed to the layer of metallic hydrogen above. This implies that the cores in Jupiter and Saturn have been eroded over time, with the icy material being redistributed convectively throughout the planet.
Our work has implications for constraining the interior structure and evolution of giant planets and will be relevant for the interpretation of data from NASA's Juno mission to Jupiter (to be launched in August 2011). Core erosion could also provide a significant flux of heavy elements to the atmosphere of exoplanets and may explain why some of them have significantly inflated radii.

Water ice is one of the most prevalent substances in the solar system, with the majority of it existing at high pressures in the interiors of giant planets. The known phase diagram of water is extremely rich, with at least fifteen crystal phases observed experimentally. In our article in Physical Review Letters (see also cond-mat), Hugh Wilson and I explore the phase diagram of water ice by means of ab initio computer simulations and predict two new phases to occur at megabar pressures. In the figure from top to bottom, you see

1) ice X the highest pressure phase seen in experiments,
2) the Pbcm phase that was predicted with computer simulations in 1996,
3) our new Pbca phase that transforms out of the Pbcm phase via a phonon instability at 7.6 Mbar, and finally
4) our new Cmcm structure that is metallic and predicted to occur at 15.5 Mbar.

The known high pressure ice phases VII, VIII, X and Pbcm as well as our Pbca phase are all insulating and composed of two interpenetrating hydrogen bonded networks, but the Cmcm structure is metallic and consists of corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral positions between next-nearest O atoms while they occupy tetrahedral positions between nearest O atoms in the ice X, Pbcm, and Pbca phases.

When the Galileo entry probe entered Jupiter's atmosphere in 1995, it measured that the inert gas neon was depleted by a factor of 10 compared to the composition of sun, which represents the concentrations in nebula that formed our solar system with all its eight planets. So where is all the neon gone that was present in Jupiter initially? Using ab initio computer simulations Hugh Wilson and I link the missing neon to another process that was proposed to occur inside Jupiter: helium rain.
There is indirect evidence from luminosity measurements that helium rain occurs on Saturn but it was unclear whether it occurs inside Jupiter also. Our calculations now show that neon preferentially dissolves into helium droplets and it is therefore gradually sequestered into the deeper interior as the helium rain falls. The remaining hydrogen-rich envelope is slowly depleted of both neon and helium. The measured concentrations of both elements agree quantitatively with our calculations.
Read commentary by J. Fortney "Peering into Jupiter", UC Berkeley's press release, Discovery Channel and LA Times articles.