Equation of state and phase diagram of ammonia at high pressures from ab initio simulations

Double superionicity in icy compounds at planetary interior conditions

The elements hydrogen, carbon, nitrogen and oxygen are assumed to comprise the bulk of the interiors of the ice giant planets Uranus, Neptune, and sub-Neptune exoplanets. The details of their interior structures have remained largely unknown because it is not understood how the compounds H2O, NH3 and CH4 behave and react once they have been accreted and exposed to high pressures and temperatures. Here we study thirteen H-C-N-O compounds with ab initio computer simulations and demonstrate that they assume a superionic state at elevated temperatures, in which the hydrogen ions diffuse through a stable sublattice that is provided by the larger nuclei. At yet higher temperatures, four of the thirteen compounds undergo a second transition to a novel doubly superionic state, in which the smallest of the heavy nuclei diffuse simultaneously with hydrogen ions through the remaining sublattice. Since this transition and the melting transition at yet higher temperatures are both of first order, this may introduce additional layers in the mantle of ice giant planets and alter their convective patterns.

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.

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.

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.

Compressive behavior and electronic properties of ammonia ice: a first-principles study

We performed systematic ab initio calculations to explore the structures and electronic properties of ammonia ice by hydrostatic compression.

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.

Structural and transport properties of ammonia along the principal Hugoniot

We investigate, via quantum molecular dynamics simulations, the structural and transport properties of ammonia along the principal Hugoniot for temperatures up to 10 eV and densities up to 2.6 g/cm³. With the analysis of the molecular dynamics trajectories by use of the bond auto-correlation function, we identify three distinct pressure-temperature regions for local chemical structures of ammonia. We derive the diffusivity and viscosity of strong correlated ammonia with high accuracy through fitting the velocity and stress-tensor autocorrelation functions with complex functional form which includes structures and multiple time scales. The statistical error of the transport properties is estimated. It is shown that the diffusivity and viscosity behave in a distinctly different manner at these three regimes and thus present complex features. In the molecular fluid regime, the hydrogen atoms have almost the similar diffusivity as nitrogen and the viscosity is dominated by the kinetic contribution. When entering into the mixture regime, the transport behavior of the system remarkably changes due to the stronger ionic coupling, and the viscosity is determined to decrease gradually and achieve minimum at about 2.0 g/cm³ on the Hugoniot. In the plasma regime, the hydrogen atoms diffuse at least twice as fast as the nitrogen atoms.

Stabilization of ammonia-rich hydrate inside icy planets

The interior structure of the giant ice planets Uranus and Neptune, but also of newly discovered exoplanets, is loosely constrained, because limited observational data can be satisfied with various interior models. Although it is known that their mantles comprise large amounts of water, ammonia, and methane ices, it is unclear how these organize themselves within the planets-as homogeneous mixtures, with continuous concentration gradients, or as well-separated layers of specific composition. While individual ices have been studied in great detail under pressure, the properties of their mixtures are much less explored. We show here, using first-principles calculations, that the 2:1 ammonia hydrate, (H₂O)(NH₃)₂, is stabilized at icy planet mantle conditions due to a remarkable structural evolution. Above 65 GPa, we predict it will transform from a hydrogen-bonded molecular solid into a fully ionic phase O^2-([Formula: see text])₂, where all water molecules are completely deprotonated, an unexpected bonding phenomenon not seen before. Ammonia hemihydrate is stable in a sequence of ionic phases up to 500 GPa, pressures found deep within Neptune-like planets, and thus at higher pressures than any other ammonia-water mixture. This suggests it precipitates out of any ammonia-water mixture at sufficiently high pressures and thus forms an important component of icy planets.

Ab initio calculation of thermodynamic potentials and entropies for superionic water

We construct thermodynamic potentials for two superionic phases of water [with body-centered cubic (bcc) and face-centered cubic (fcc) oxygen lattice] using a combination of density functional theory (DFT) and molecular dynamics simulations (MD). For this purpose, a generic expression for the free energy of warm dense matter is developed and parametrized with equation of state data from the DFT-MD simulations. A second central aspect is the accurate determination of the entropy, which is done using an approximate two-phase method based on the frequency spectra of the nuclear motion. The boundary between the bcc superionic phase and the ices VII and X calculated with thermodynamic potentials from DFT-MD is consistent with that directly derived from the simulations. Differences in the physical properties of the bcc and fcc superionic phases and their impact on interior modeling of water-rich giant planets are discussed.

Superionic Phases of the 1:1 Water-Ammonia Mixture

We report four structures for the 1:1 water-ammonia mixture showing superionic behavior at high temperature with the space groups P4/nmm, Ima2, Pma2, and Pm, which have been identified from evolutionary random structure search calculations at 0 K. Analyzing the respective pair distribution functions and diffusive properties the superionic phase is found to be stable in a temperature range between 1000 and 6000 K for pressures up to 800 GPa. We propose a high-pressure phase diagram of the water-ammonia mixture for the first time and compare the self-diffusion coefficients in the mixture to the ones found in water and ammonia. Finally, possible implications on the interior structure of the giant planets Uranus and Neptune are discussed.

Effect of correlation on viscosity and diffusion in molecular-dynamics simulations

In the warm dense matter (WDM) regime, material properties like diffusion and viscosity can be obtained from lengthy quantum molecular dynamics simulations, where the quantum behavior of the electrons is represented using either Kohn-Sham or orbital-free density functional theory. To reduce the simulation duration, we fit the time dependence of the autocorrelation functions (ACFs) and then use the fit to find values of the diffusion and viscosity. This fitting procedure avoids noise in the long time behavior of the ACFs. We present a detailed analysis of the functional form used to fit the ACFs, which is always a more efficient means to obtain mass transport properties. We use the fits to estimate the statistical error of the transport properties. We apply this methodology to a dense correlated plasma of copper and a mixture of carbon and hydrogen. Both systems show structure in their ACFs and exhibit multiple time scales. The mixture contains different structural forms of the ACFs for each component in the mixture.