Unveiling unconventional CH4-Xe compounds and their thermodynamic properties at extreme conditions

Inert gases (e.g., He and Xe) can exhibit chemical activity at high pressure, reacting with other substances to form compounds of unexpected chemical stoichiometry. This work combines first-principles calculations and crystal structure predictions to propose four unexpected stable compounds of CH4Xe3, (CH4)2Xe, (CH4)3Xe, and (CH4)3Xe2 at pressure ranges from 2 to 100 GPa. All structures are composed of isolated Xe atoms and CH4 molecules except for (CH4)3Xe2, which comprises a polymerization product, C3H8, and hydrogen molecules. Ab initio molecular dynamics simulations indicate that pressure plays a very important role in the different temperature driving state transitions of CH4-Xe compounds. At lower pressures, the compounds follow the state transition of solid-plastic-fluid phases with increasing temperature, while at higher pressures, the stronger Xe-C interaction induces the emergence of a superionic state for CH4Xe3 and (CH4)3Xe2 as temperature increases. These results not only expand the family of CH4-Xe compounds, they also contribute to models of the structures and evolution of planetary interiors.

Mixture of hydrogen and methane under planetary interior conditions

We employ first-principles molecular dynamics simulations to provide equation-of-state data, pair distribution functions (PDFs), diffusion coefficients, and band gaps of a mixture of hydrogen and methane under planetary interior conditions as relevant for Uranus, Neptune, and similar icy exoplanets. We test the linear mixing approximation, which is fulfilled within a few percent for the chosen P-T conditions. Evaluation of the PDFs reveals that methane molecules dissociate into carbon clusters and free hydrogen atoms at temperatures greater than 3000 K. At high temperatures, the clusters are found to be short-lived. Furthermore, we calculate the electrical conductivity from which we derive the non-metal-to-metal transition region of the mixture. We also calculate the electrical conductivity along the P-T profile of Uranus [N. Nettelmann et al., Planet. Space Sci., 2013, 77, 143-151] and observe the transition of the mixture from a molecular to an atomic fluid as a function of the radius of the planet. The density and temperature ranges chosen in our study can be achieved using dynamic shock compression experiments and seek to aid such future experiments. Our work also provides a relevant data set for a better understanding of the interior, evolution, luminosity, and magnetic field of the ice giants in our solar system and beyond.

Analysing the stability of He-filled hydrates: how many He atoms fit in the sII crystal?

Clathrate hydrates have the ability to encapsulate atoms and molecules within their cavities, and thus they could be potentially large storage capacity materials. The present work studies the multiple cage occupancy effects in the recently discovered He@sII crystal. On the basis of previous theoretical and experimental findings, the stability of He(1/1)@sII, He(1/4)@sII and He(2/4)@sII crystals was analysed in terms of structural, mechanical and energetic properties. For this purpose, first-principles DFT/DFT-D computations were performed by using both semi-local and non-local functionals, not only to elucidate which configuration is the most energetically favoured, but also to scrutinize the relevance of the long-range dispersion interactions in these kinds of compounds. We have encountered that dispersion interactions play a fundamental role in describing the underlying interactions, and different tendencies were observed depending on the choice of the functional. We found that PW86PBE-XDM shows the best performance, while the non-local functionals tested here were not able to correctly account for them. The present results reveal that the most stable configuration is the one presenting singly occupied D cages and tetrahedrally occupied H cages (He(1/4)@sII) in line with the experimental observation.

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

Thermodynamics of diamond formation from hydrocarbon mixtures in planets

Hydrocarbon mixtures are extremely abundant in the Universe, and diamond formation from them can play a crucial role in shaping the interior structure and evolution of planets. With first-principles accuracy, we first estimate the melting line of diamond, and then reveal the nature of chemical bonding in hydrocarbons at extreme conditions. We finally establish the pressure-temperature phase boundary where it is thermodynamically possible for diamond to form from hydrocarbon mixtures with different atomic fractions of carbon. Notably, here we show a depletion zone at pressures above 200 GPa and temperatures below 3000 K-3500 K where diamond formation is thermodynamically favorable regardless of the carbon atomic fraction, due to a phase separation mechanism. The cooler condition of the interior of Neptune compared to Uranus means that the former is much more likely to contain the depletion zone. Our findings can help explain the dichotomy of the two ice giants manifested by the low luminosity of Uranus, and lead to a better understanding of (exo-)planetary formation and evolution.

Diamond formation kinetics in shock-compressed C─H─O samples recorded by small-angle x-ray scattering and x-ray diffraction

Extreme conditions inside ice giants such as Uranus and Neptune can result in peculiar chemistry and structural transitions, e.g., the precipitation of diamonds or superionic water, as so far experimentally observed only for pure C─H and H2O systems, respectively. Here, we investigate a stoichiometric mixture of C and H2O by shock-compressing polyethylene terephthalate (PET) plastics and performing in situ x-ray probing. We observe diamond formation at pressures between 72 ± 7 and 125 ± 13 GPa at temperatures ranging from ~3500 to ~6000 K. Combining x-ray diffraction and small-angle x-ray scattering, we access the kinetics of this exotic reaction. The observed demixing of C and H2O suggests that diamond precipitation inside the ice giants is enhanced by oxygen, which can lead to isolated water and thus the formation of superionic structures relevant to the planets' magnetic fields. Moreover, our measurements indicate a way of producing nanodiamonds by simple laser-driven shock compression of cheap PET plastics.

Evidence for superionic H2O and diffusive He-H2O at high temperature and high pressure

We present the evidence of superionic phase formed in H₂O and, for the first time, diffusive H₂O-He phase, based on time-resolved x-ray diffraction experiments performed on ramp-laser-heated samples in diamond anvil cells. The diffraction results signify a similar bcc-like structure of superionic H₂O and diffusive He-H₂O, while following different transition dynamics. Based on time and temperature evolution of the lattice parameter, the superionic H₂O phase forms gradually in pure H₂O over the temperature range of 1350-1400 K at 23 GPa, but the diffusive He-H₂O phase forms abruptly at 1300 K at 26 GPa. We suggest that the faster dynamics and lower transition temperature in He-H₂O are due to a larger diffusion coefficient of interstitial-filled He than that of more strongly bound H atoms. This conjecture is then consistent with He disordered diffusive phase predicted at lower temperatures, rather than H-disordered superionic phase in He-H₂O.

Superionic Silica-Water and Silica-Hydrogen Compounds in the Deep Interiors of Uranus and Neptune

Silica, water, and hydrogen are known to be the major components of celestial bodies, and have significant influence on the formation and evolution of giant planets, such as Uranus and Neptune. Thus, it is of fundamental importance to investigate their states and possible reactions under the planetary conditions. Here, using advanced crystal structure searches and first-principles calculations in the Si-O-H system, we find that a silica-water compound (SiO_{2})_{2}(H_{2}O) and a silica-hydrogen compound SiO_{2}H_{2} can exist under high pressures above 450 and 650 GPa, respectively. Further simulations reveal that, at high pressure and high temperature conditions corresponding to the interiors of Uranus and Neptune, these compounds exhibit superionic behavior, in which protons diffuse freely like liquid while the silicon and oxygen framework is fixed as solid. Therefore, these superionic silica-water and silica-hydrogen compounds could be regarded as important components of the deep mantle or core of giants, which also provides an alternative origin for their anomalous magnetic fields. These unexpected physical and chemical properties of the most common natural materials at high pressure offer key clues to understand some abstruse issues including demixing and erosion of the core in giant planets, and shed light on building reliable models for solar giants and exoplanets.

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$\end{document}(C10H8O4)n, also called mylar) shock-compressed to (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$155 \pm 20$$\end{document}155±20) GPa and (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$6000 \pm 1000$$\end{document}6000±1000) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

First principles study of dense and metallic nitric sulfur hydrides

Studies of molecular mixtures containing hydrogen sulfide (H₂S) could open up new routes towards hydrogen-rich high-temperature superconductors under pressure. H₂S and ammonia (NH₃) form hydrogen-bonded molecular mixtures at ambient conditions, but their phase behavior and propensity towards mixing under pressure is not well understood. Here, we show stable phases in the H₂S-NH₃ system under extreme pressure conditions to 4 Mbar from first-principles crystal structure prediction methods. We identify four stable compositions, two of which, (H₂S) (NH₃) and (H₂S) (NH₃)₄, are stable in a sequence of structures to the Mbar regime. A re-entrant stabilization of (H₂S) (NH₃)₄ above 300 GPa is driven by a marked reversal of sulfur-hydrogen chemistry. Several stable phases exhibit metallic character. Electron-phonon coupling calculations predict superconducting temperatures up to 50 K, in the Cmma phase of (H₂S) (NH₃) at 150 GPa. The present findings shed light on how sulfur hydride bonding and superconductivity are affected in molecular mixtures. They also suggest a reservoir for hydrogen sulfide in the upper mantle regions of icy planets in a potentially metallic mixture, which could have implications for their magnetic field formation.

Gibbs-ensemble Monte Carlo simulation of H2-H2O mixtures

The miscibility gap in hydrogen-water mixtures is investigated by conducting Gibbs-ensemble Monte Carlo simulations with analytical two-body interaction potentials between the molecular species. We calculate several demixing curves at pressures below 150 kbar and temperatures of 1000 K ≤T≤ 2000 K. Despite the approximations introduced by the two-body interaction potentials, our results predict a large miscibility gap in hydrogen-water mixtures at similar conditions as found in experiments. Our findings are in contrast to those from ab initio simulations and provide a renewed indication that hydrogen-water immiscibility regions may have a significant impact on the structure and evolution of ice giant planets like Uranus and Neptune.

Minimization of Gibbs Energy in High-Pressure Multiphase, Multicomponent Mixtures through Particle Swarm Optimization

We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.

Fluid-like elastic response of superionic NH3 in Uranus and Neptune

Nondipolar magnetic fields exhibited at Uranus and Neptune may be derived from a unique geometry of their icy mantle with a thin convective layer on top of a stratified nonconvective layer. The presence of superionic H₂O and NH₃ has been thought as an explanation to stabilize such nonconvective regions. However, a lack of experimental data on the physical properties of those superionic phases has prevented the clarification of this matter. Here, our Brillouin measurements for NH₃ show a two-stage reduction in longitudinal wave velocity (V _p) by ∼9% and ∼20% relative to the molecular solid in the temperature range of 1,500 K and 2,000 K above 47 GPa. While the first V _p reduction observed at the boundary to the superionic α phase was most likely due to the onset of the hydrogen diffusion, the further one was likely attributed to the transition to another superionic phase, denoted γ phase, exhibiting the higher diffusivity. The reduction rate of V _p in the superionic γ phase, comparable to that of the liquid, implies that this phase elastically behaves almost like a liquid. Our measurements show that superionic NH₃ becomes convective and cannot contribute to the internal stratification.

Metallization of Shock-Compressed Liquid Ammonia

Ammonia is predicted to be one of the major components in the depths of the ice giant planets Uranus and Neptune. Their dynamics, evolution, and interior structure are insufficiently understood and models rely imperatively on data for equation of state and transport properties. Despite its great significance, the experimentally accessed region of the ammonia phase diagram today is still very limited in pressure and temperature. Here we push the probed regime to unprecedented conditions, up to ∼350  GPa and ∼40 000  K. Along the Hugoniot, the temperature measured as a function of pressure shows a subtle change in slope at ∼7000  K and ∼90  GPa, in agreement with ab initio simulations we have performed. This feature coincides with the gradual transition from a molecular liquid to a plasma state. Additionally, we performed reflectivity measurements, providing the first experimental evidence of electronic conduction in high-pressure ammonia. Shock reflectance continuously rises with pressure above 50 GPa and reaches saturation values above 120 GPa. Corresponding electrical conductivity values are up to 1 order of magnitude higher than in water in the 100 GPa regime, with possible significant contributions of the predicted ammonia-rich layers to the generation of magnetic dynamos in ice giant interiors.

The interiors of Uranus and Neptune: current understanding and open questions

Uranus and Neptune form a distinct class of planets in our Solar System. Given this fact, and ubiquity of similar-mass planets in other planetary systems, it is essential to understand their interior structure and composition. However, there are more open questions regarding these planets than answers. In this review, we concentrate on the things we do not know about the interiors of Uranus and Neptune with a focus on why the planets may be different, rather than the same. We next summarize the knowledge about the planets' internal structure and evolution. Finally, we identify the topics that should be investigated further on the theoretical front as well as required observations from space missions. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.

The underexplored frontier of ice giant dynamos

The Voyager 2 flybys of Uranus and Neptune revealed the first multipolar planetary magnetic fields and highlighted how much we have yet to learn about ice giant planets. In this review, we summarize observations of Uranus' and Neptune's magnetic fields and place them in the context of other planetary dynamos. The ingredients for dynamo action in general, and for the ice giants in particular, are discussed, as are the factors thought to control magnetic field strength and morphology. These ideas are then applied to Uranus and Neptune, where we show that no models are yet able to fully explain their observed magnetic fields. We then propose future directions for missions, modelling, experiments and theory necessary to answer outstanding questions about the dynamos of ice giant planets, both within our solar system and beyond. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.

Coexistence of plastic and partially diffusive phases in a helium-methane compound

Helium and methane are major components of giant icy planets and are abundant in the universe. However, helium is the most inert element in the periodic table and methane is one of the most hydrophobic molecules, thus whether they can react with each other is of fundamental importance. Here, our crystal structure searches and first-principles calculations predict that a He3CH4 compound is stable over a wide range of pressures from 55 to 155 GPa and a HeCH4 compound becomes stable around 105 GPa. As nice examples of pure van der Waals crystals, the insertion of helium atoms changes the original packing of pure methane molecules and also largely hinders the polymerization of methane at higher pressures. After analyzing the diffusive properties during the melting of He3CH4 at high pressure and high temperature, in addition to a plastic methane phase, we have discovered an unusual phase which exhibits coexistence of diffusive helium and plastic methane. In addition, the range of the diffusive behavior within the helium-methane phase diagram is found to be much narrower compared to that of previously predicted helium-water compounds. This may be due to the weaker van der Waals interactions between methane molecules compared to those in helium-water compounds, and that the helium-methane compound melts more easily.

Formation of ammonia-helium compounds at high pressure

Uranus and Neptune are generally assumed to have helium only in their gaseous atmospheres. Here, we report the possibility of helium being fixed in the upper mantles of these planets in the form of NH₃-He compounds. Structure predictions reveal two energetically stable NH₃-He compounds with stoichiometries (NH₃)₂He and NH₃He at high pressures. At low temperatures, (NH₃)₂He is ionic with NH₃ molecules partially dissociating into (NH₂)^- and (NH₄)⁺ ions. Simulations show that (NH₃)₂He transforms into intermediate phase at 100 GPa and 1000 K with H atoms slightly vibrate around N atoms, and then to a superionic phase at  ~2000 K with H and He exhibiting liquid behavior within the fixed N sublattice. Finally, (NH₃)₂He becomes a fluid phase at temperatures of 3000 K. The stability of (NH₃)₂He at high pressure and temperature could contribute to update models of the interiors of Uranus and Neptune.

Demonstration of X-ray Thomson scattering as diagnostics for miscibility in warm dense matter

The gas and ice giants in our solar system can be seen as a natural laboratory for the physics of highly compressed matter at temperatures up to thousands of kelvins. In turn, our understanding of their structure and evolution depends critically on our ability to model such matter. One key aspect is the miscibility of the elements in their interiors. Here, we demonstrate the feasibility of X-ray Thomson scattering to quantify the degree of species separation in a 1:1 carbon-hydrogen mixture at a pressure of ~150 GPa and a temperature of ~5000 K. Our measurements provide absolute values of the structure factor that encodes the microscopic arrangement of the particles. From these data, we find a lower limit of [Formula: see text]% of the carbon atoms forming isolated carbon clusters. In principle, this procedure can be employed for investigating the miscibility behaviour of any binary mixture at the high-pressure environment of planetary interiors, in particular, for non-crystalline samples where it is difficult to obtain conclusive results from X-ray diffraction. Moreover, this method will enable unprecedented measurements of mixing/demixing kinetics in dense plasma environments, e.g., induced by chemistry or hydrodynamic instabilities.

Plastic and superionic phases in ammonia-water mixtures at high pressures and temperatures

The interiors of giant icy planets depend on the properties of hot, dense mixtures of the molecular ices water, ammonia, and methane. Here, we discuss results from first-principles molecular dynamics simulations up to 500 GPa and 7000 K for four different ammonia-water mixtures that correspond to the stable stoichiometries found in solid ammonia hydrates. We show that all mixtures support the formation of plastic and superionic phases at elevated pressures and temperatures, before eventually melting into molecular or ionic liquids. All mixtures' melting lines are found to be close to the isentropes of Uranus and Neptune. Through local structure analyses we trace and compare the evolution of chemical composition and longevity of chemical species across the thermally activated states. Under specific conditions we find that protons can be less mobile in the fluid state than in the (colder, solid) superionic regime.

Multicomponent mutual diffusion in the warm, dense matter regime

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Laser-driven shock compression of "synthetic planetary mixtures" of water, ethanol, and ammonia

Water, methane, and ammonia are commonly considered to be the key components of the interiors of Uranus and Neptune. Modelling the planets' internal structure, evolution, and dynamo heavily relies on the properties of the complex mixtures with uncertain exact composition in their deep interiors. Therefore, characterising icy mixtures with varying composition at planetary conditions of several hundred gigapascal and a few thousand Kelvin is crucial to improve our understanding of the ice giants. In this work, pure water, a water-ethanol mixture, and a water-ethanol-ammonia "synthetic planetary mixture" (SPM) have been compressed through laser-driven decaying shocks along their principal Hugoniot curves up to 270, 280, and 260 GPa, respectively. Measured temperatures spanned from 4000 to 25000 K, just above the coldest predicted adiabatic Uranus and Neptune profiles (3000-4000 K) but more similar to those predicted by more recent models including a thermal boundary layer (7000-14000 K). The experiments were performed at the GEKKO XII and LULI2000 laser facilities using standard optical diagnostics (Doppler velocimetry and optical pyrometry) to measure the thermodynamic state and the shock-front reflectivity at two different wavelengths. The results show that water and the mixtures undergo a similar compression path under single shock loading in agreement with Density Functional Theory Molecular Dynamics (DFT-MD) calculations using the Linear Mixing Approximation (LMA). On the contrary, their shock-front reflectivities behave differently by what concerns both the onset pressures and the saturation values, with possible impact on planetary dynamos.

Evidence for Crystalline Structure in Dynamically-Compressed Polyethylene up to 200 GPa

We investigated the high-pressure behavior of polyethylene (CH₂) by probing dynamically-compressed samples with X-ray diffraction. At pressures up to 200 GPa, comparable to those present inside icy giant planets (Uranus, Neptune), shock-compressed polyethylene retains a polymer crystal structure, from which we infer the presence of significant covalent bonding. The A2/m structure which we observe has previously been seen at significantly lower pressures, and the equation of state measured agrees with our findings. This result appears to contrast with recent data from shock-compressed polystyrene (CH) at higher temperatures, which demonstrated demixing and recrystallization into a diamond lattice, implying the breaking of the original chemical bonds. As such chemical processes have significant implications for the structure and energy transfer within ice giants, our results highlight the need for a deeper understanding of the chemistry of high pressure hydrocarbons, and the importance of better constraining planetary temperature profiles.