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The strikingly low luminosity of Uranus (Teff ~ Teq) constitutes along-standing challenge to our understanding of Ice Giant planets. Here wepresent the first Uranus structure and evolution models that are constructed toagree with both the observed low luminosity and the gravity field data. Ourmodels make use of modern ab initio equations of state at high pressures forthe icy components water, methane, and ammonia. Proceeding step by step, weconfirm that adiabatic models yield cooling times that are too long, even whenuncertainties in the ice:rock ratio (I:R) are taken into account. We then arguethat the transition between the ice/rock-rich interior and the H/He-rich outerenvelope should be stably stratified. Therefore, we introduce a simple thermalboundary and adjust it to reproduce the low luminosity. Due to this thermalboundary, the deep interior of the Uranus models are up to 2--3 warmer thanadiabatic models, necessitating the presence of rocks in the deep interior witha possible I:R of $1\times$ solar. Finally, we allow for an equilibriumevolution (Teff ~ Teq) that begun prior to the present day, which wouldtherefore no longer require the current era to be a "special time" in Uranus'evolution. In this scenario, the thermal boundary leads to more rapid coolingof the outer envelope. When Teff ~ Teq is reached, a shallow, subadiabatic zonein the atmosphere begins to develop. Its depth is adjusted to meet theluminosity constraint. This work provides a simple foundation for future IceGiant structure and evolution models, that can be improved by properly treatingthe heat and particle fluxes in the diffusive zones.

Laser-driven dynamic compression experiments of plastic materials have found surprisingly fast formation of nanodiamonds (ND) via X-ray probing. This mechanism is relevant for planetary models, but could also open efficient synthesis routes for tailored NDs. We investigate the release mechanics of compressed NDs by molecular dynamics simulation of the isotropic expansion of finite size diamond from different P-T states. Analysing the structural integrity along different release paths via molecular dynamic simulations, we found substantial disintegration rates upon shock release, increasing with the on-Hugnoiot shock temperature. We also find that recrystallization can occur after the expansion and hence during the release, depending on subsequent cooling mechanisms. Our study suggests higher ND recovery rates from off-Hugoniot states, e.g., via double-shocks, due to faster cooling. Laser-driven shock compression experiments of polyethylene terephthalate (PET) samples with in situ X-ray probing at the simulated conditions found diamond signal that persists up to 11 ns after breakout. In the diffraction pattern, we observed peak shifts, which we attribute to thermal expansion of the NDs and thus a total release of pressure, which indicates the stability of the released NDs., (© 2024. The Author(s).)

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.

We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

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., (© 2023. The Author(s).)

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

The determination of the ionization of a system in the hot dense regime is a long standing issue. Recent studies have shown inconsistencies between standard predictions using average atom models and evaluations deduced from electronic transport properties computed with quantum molecular dynamics simulations [Bethkenhagen et al., Phys. Rev. Res. 2, 023260 (2020)]2643-156410.1103/PhysRevResearch.2.023260. Here, we propose a definition of the ionization based on its effect on the plasma structure as given by the pair distribution function (PDF), and on the concept of effective one-component plasma (eOCP). We also introduce a definition based on the total pressure and on a modelization of the electronic pressure. We show the equivalence of these definitions on two studies of carbon along the 100 eV isotherm and the 10 g/cm^{3} isochor. Simulations along the 100 eV isotherm are obtained with the newly implemented Ext. First principles molecular dynamics (Fpmd) method in Abinit for densities ranging from 1 to 500 g/cm^{3}and along the 10 g/cm^{3} isochor with the recently published Spectral quadrature DFT (Sqdft) simulations, between 8 and 860 eV. The resulting ionizations are compared to the predictions of the average-atom code Qaam which is based on the muffin-tin approximation. A disagreement between the eOCP and the actual PDFs (non-OCP behavior) is interpreted as the onset of bonding in the system.

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 H 2 O systems, respectively. Here, we investigate a stoichiometric mixture of C and H 2 O 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 H 2 O 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.

Most experimentally known high-pressure ice phases have a body-centred cubic (bcc) oxygen lattice. Our large-scale molecular-dynamics simulations with a machine-learning potential indicate that, amongst these bcc ice phases, ices VII, VII' and X are the same thermodynamic phase under different conditions, whereas superionic ice VII″ has a first-order phase boundary with ice VII'. Moreover, at about 300 GPa, the transformation between ice X and the Pbcm phase has a sharp structural change but no apparent activation barrier, whilst at higher pressures the barrier gradually increases. Our study thus clarifies the phase behaviour of the high-pressure ices and reveals peculiar solid-solid transition mechanisms not known in other systems., (© 2022. The Author(s).)

We investigate the thermopower and Lorenz number of hydrogen with Kohn-Sham density functional theory (DFT) across the plasma plane toward the near-classical limit, i.e., weakly degenerate and weakly coupled states. Our results are in concordance with certain limiting values for the Lorentz plasma, a model system which only considers electron-ion scattering. Thereby, we clearly show that the widely used method of calculating transport properties via the Kubo-Greenwood (KG) formalism does not capture electron-electron scattering processes. Our discussion also addresses the inadequateness of assuming a Drude-like frequency behavior for the conductivity of nondegenerate plasmas by revisiting the relaxation time approximation within kinetic theory.

We use a nonrelativistic average-atom model to calculate carbon ionization at megabar and gigabar pressures. The pressure is calculated using the stress-tensor method. The electronic electrical conductivity is also considered using the Kubo-Greenwood approach. Comparisons are made with quantum molecular dynamic simulations. A good agreement is obtained for the pressure between the average-atom model and the quantum molecular dynamic simulations in the regime of gigabar pressures. However, the discrepancy already seen with the PURGATORIO code for the average ionization deduced from the quantum molecular dynamic simulations is also observed here with the present average-atom model. Excellent agreement with the PURGATORIO code is found for the average ionization.

We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from six to three quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ∼0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

We have performed finite-temperature density functional theory molecular dynamics simulations on dense methane, ammonia, and water mixtures (CH4:NH3:H2O) for various compositions and temperatures (2000 K ≤ T ≤ 10,000 K) that span a set of possible conditions in the interiors of ice-giant exoplanets. The equation-of-state, pair distribution functions, and bond autocorrelation functions (BACF) were used to probe the structure and dynamics of these complex fluids. In particular, an improvement to the choice of the cutoff in the BACF was developed that allowed analysis refinements for density and temperature effects. We note the relative changes in the nature of these systems engendered by variations in the concentration ratios. A basic tenet emerges from all these comparisons that varying the relative amounts of the three heavy components (C,N,O) can effect considerable changes in the nature of the fluid and may in turn have ramifications for the structure and composition of various planetary layers.

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.

We present an equation of state as well as a phase diagram of ammonia at high pressures and high temperatures derived from ab initio molecular dynamics simulations. The predicted phases of ammonia are characterized by analyzing diffusion coefficients and structural properties. Both the phase diagram and the subsequently computed Hugoniot curves are compared to experimental results. Furthermore, we discuss two methods that allow us to take into account nuclear quantum effects, which are of considerable importance in molecular fluids. Our data cover pressures up to 330 GPa and a temperature range from 500 K to 10,000 K. This regime is of great interest for interior models of the giant planets Uranus and Neptune, which contain, besides water and methane, significant amounts of ammonia.