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Abstract Many planets in the solar system and across the Galaxy have hydrogen-rich atmospheres overlying more heavy element-rich interiors with which they interact for billions of years. Atmosphere–interior interactions are thus crucial to understanding the formation and evolution of these bodies. However, this understanding is still lacking in part because the relevant pressure–temperature conditions are extreme. We conduct molecular dynamics simulations based on density functional theory to investigate how hydrogen and water interact over a wide range of pressure and temperature, encompassing the interiors of Neptune-sized and smaller planets. We determine the critical curve at which a single homogeneous phase exsolves into two separate hydrogen-rich and water-rich phases, finding good agreement with existing experimental data. We find that the temperature along the critical curve increases with increasing pressure and shows the influence of a change in fluid structure from molecular to atomic near 30 GPa and 3000 K, which may impact magnetic field generation. The internal temperatures of many exoplanets, including TOI-270 d and K2-18 b, may lie entirely above the critical curve: the envelope is expected to consist of a single homogeneous hydrogen–water fluid, which is much less susceptible to atmospheric loss as compared with a pure hydrogen envelope. As planets cool, they cross the critical curve, leading to rainout of water-rich fluid and an increase in internal luminosity. Compositions of the resulting outer, hydrogen-rich and inner, water-rich envelopes depend on age and instellation and are governed by thermodynamics. Rainout of water may be occurring in Uranus and Neptune at present. 

Abstract Mineral phase transitions can either hinder or accelerate mantle flow. In the present day, the formation of the bridgmanite + ferropericlase assemblage from ringwoodite at 660 km depth has been found to cause weak and intermittent layering of mantle convection. However, for the higher temperatures in Earth's past, different phase transitions could have controlled mantle dynamics. We investigate the potential changes in convection style during Earth's secular cooling using a new numerical technique that reformulates the energy conservation equation in terms of specific entropy instead of temperature. This approach enables us to accurately include the latent heat effect of phase transitions for mantle temperatures different from the average geotherm, and therefore fully incorporate the thermodynamic effects of realistic phase transitions in global‐scale mantle convection modeling. We set up 2‐D models with the geodynamics softwareAspect, using thermodynamic properties computed by HeFESTo, while applying a viscosity profile constrained by the geoid and mineral physics data and a visco‐plastic rheology to reproduce plate‐like behavior and Earth‐like subduction morphologies. Our model results reveal the layering of plumes induced by the wadsleyite to garnet (majorite) + ferropericlase endothermic transition (between 450 and 590 km depth and over the 2000–2500 K temperature range). They show that this phase transition causes a large‐scale and long‐lasting temperature elevation in a depth range of 500–650 km depth if the potential temperature of the mantle is higher than 1800 K, indicating that mantle convection may have been partially layered in Earth's early history. 

Abstract We investigate the consequences of nonideal chemical interaction between silicate and overlying hydrogen-rich envelopes for rocky planets using basic tenets of phase equilibria. Based on our current understanding of the temperature and pressure conditions for complete miscibility of silicate and hydrogen, we find that the silicate-hydrogen binary solvus will dictate the nature of atmospheres and internal layering in rocky planets that garnered H₂-rich primary atmospheres. The temperatures at the surfaces of supercritical magma oceans will correspond to the silicate-hydrogen solvus. As a result, the radial positions of supercritical magma ocean–atmosphere interfaces, rather than their temperatures and pressures, should reflect the thermal states of these planets. The conditions prescribed by the solvus influence the structure of the atmosphere, and thus the transit radii of sub-Neptunes. Separation of iron-rich metal to form metal cores in sub-Neptunes and super-Earths is not assured due to prospects for neutral buoyancy of metal in silicate melt induced by dissolution of H, Si, and O in the metal at high temperatures. 

Abstract The bulk of Uranus consists of a rock–ice core, but the relative proportions of rock and ice are unknown. Radioactive decay of potassium in the silicates produces⁴⁰Ar. If transport of argon from the core to the gaseous envelope is efficient, a measurement of⁴⁰Ar in the envelope will provide a direct constraint on the rock mass present (assuming a chondritic rock composition). The expected⁴⁰Ar concentrations in this case would be readily detectable by a mass spectrometer carried by a future atmospheric probe. For a given envelope concentration there is a trade-off between the rock mass present and the transport efficiency; this degeneracy could be overcome by making independent determinations of the rock mass (e.g., by gravity and seismology). Primordial⁴⁰Ar is a potential confounding factor, especially if Ar/H₂is significantly enhanced above solar or if degassing of radiogenic⁴⁰Ar were inefficient. Unfortunately, the primordial⁴⁰Ar/³⁶Ar ratio is very uncertain; better constraints on this ratio through measurement or theory would be very helpful. Pollution of the envelope by silicates is another confounding factor but can be overcome by a measurement of the alkali metals in the envelope. 

SUMMARY We expand the scope of HeFESTo by encompassing the rich physics of iron in the mantle, including the existence of multiple valence and spin states. In our previous papers, we considered iron only in its most common state in the mantle: the high-spin divalent (ferrous) cation. We now add ferric iron end-members to six phases, as well as the three phases of native iron. We also add low-spin states of ferrous and ferric iron and capture the behaviour of the high-spin to low-spin transition. Consideration of the multi-state nature of iron, unique among the major elements, leads to developments of our theory, including generalization of the chemical potential to account for the possibility of multiple distinguishable states of iron co-existing on a single crystallographic site, the effect of the high-spin to low-spin transition on seismic wave velocities in multiphase systems, and computation of oxygen fugacity. Consideration of ferric iron also motivates the addition of the chromia component to several phases, so that we now consider the set of components: Ca, Na, Fe, Mg, Al, Si, O and Cr (CNFMASO+Cr). We present the results of a new global inversion of mineral properties and compare our results to experimental observations over the entire pressure–temperature range of the mantle and over a wide range of oxygen fugacity. Applications of our method illustrate how it might be used to better understand the seismic structure, dynamics and oxygen fugacity of the mantle. 

Abstract The contrasting internal luminosity of Uranus and Neptune present a challenge to our understanding of the origin and evolution of these bodies, as well as extra-solar ice giants. The thermal evolution of Neptune is known to be nearly consistent with an entirely fluid interior, but this is not a unique solution, and does not account for the tidal dissipation required by the migration of its moons. We examine a model that has been previously shown to explain the thermal and tidal evolution of Uranus: one that features a growing, frozen core. The core traps heat in the interior, affecting the cooling time scale, and provides a source of tidal dissipation. We review the growing, frozen core model, and the computation of thermal and tidal evolution. We then apply this model to Neptune. We find that the growing frozen core model can account for the observed internal luminosity of Neptune and the migration of its moons, in the form of resonances that were either encountered or avoided in the past. We discuss prospects for observational tests of the growing frozen core model and possible implications for understanding the gas giants. 

Abstract We focus on the ferric end-member of phase H: ε-FeOOH using density functional theory at the PBEsol+U level. At 300 K, we find that ε-FeOOH undergoes a hydrogen bond symmetrization at 37 GPa and a sharp high-spin to low-spin transition at 45 GPa. We find excellent agreement with experimental measurements of the equation of state, lattice parameters, atomic positions, vibrational frequencies, and optical properties as related to the band gap, which we find to be finite and small, decreasing with pressure. The hydrogen bond symmetrization transition is neither first-nor second-order, with no discontinuity in volume or any of the elastic moduli. Computed IR and Raman frequencies and intensities show that vibrational spectroscopy may provide the best opportunity for locating the hydrogen bond symmetrization transition experimentally. We find that ε-FeOOH is highly anisotropic in both longitudinal- and shear-wave velocities at all pressures, with the shear wave velocity varying with propagation and polarization direction by as much as 24% at zero pressure and 43% at 46 GPa. The shear and bulk elastic moduli increase by 18% across the high-spin to low-spin transition. 

Abstract The evolution of the magma ocean that occupied the early Earth is influenced by the buoyancy of crystals in silicate liquid. At lower mantle pressures, silicate crystals are denser than the iso‐chemical liquid, but heavy elements like iron can cause crystals to float if they partition into the liquid phase. Crystal flotation allows for a basal magma ocean, which might explain geochemical anomalies in mantle‐derived magmas, seismic anomalies in the lower mantle, and the source of the Earth's early magnetic field. To examine whether a basal magma ocean is gravitationally stable, we investigate the degree of iron partitioning between (Mg,Fe)SiO₃liquid and bridgmanite. By utilizing ab initio molecular dynamics simulations coupled with thermodynamic integration, we find that iron partitions into the liquid, and increasingly so with increasing pressure. Bridgmanite crystals are found to be buoyant at lower mantle conditions, stabilizing the basal magma ocean.