Ab initio Gibbs ensemble Monte Carlo simulations of the liquid-vapor equilibrium and the critical point of sodium.

The ab initio (ai) Gibbs ensemble (GE) Monte Carlo (MC) method coupled with Kohn-Sham density functional theory is successful in predicting the liquid-vapour equilibrium of insulating systems. Here we show that the aiGEMC method can be used to study also metallic systems, where the excited electronic states play an important role and cannot be neglected. For this we include the electronic free energy in the formulation of the effective energy of the system to be used in the acceptance criteria for the MC moves. The application of this aiGEMC method to sodium yields a good agreement with available experimental data on the liquid-vapour equilibrium densities. We predict a critical point for sodium at 2338 ± 108 K and 0.24 ± 0.03 g cm-3. The liquid structure stemming from aiGEMC simulations is very similar to the one from ab initio molecular dynamics. Since this method can determine phase transition without computing the Gibbs free energy, it may offer a new possibility to study other materials with a reasonable computational cost.

Superionic-Superionic Phase Transitions in Body-Centered Cubic H_{2}O Ice.

From first-principles molecular dynamics, we investigate the relation between the superionic proton conduction and the behavior of the O─H⋯O bond (ice VII^{'} to ice X transition) in body-centered-cubic (bcc) H_{2}O ice between 1300 and 2000 K and up to 300 GPa. We bring evidence that there are three distinct phases in the superionic bcc stability field. A first superionic phase characterized by extremely fast diffusion of highly delocalized protons (denoted VII^{''} hereinafter) is stable at low pressures. A first-order transition separates this phase from a superionic VII^{'}, characterized by a finite degree of localization of protons along the nonsymmetric O─H⋯O bonds. The transition is identified in structural, energetic, and elastic analysis. Upon further compression a second-order phase transition leads to the superionic ice X with symmetric O─H─O bonds.

Ferroelectricity in high-density H2O ice.

The origin of longstanding anomalies in experimental studies of the dense solid phases of H2O ices VII, VIII, and X is examined using a combination of first-principles theoretical methods. We find that a ferroelectric variant of ice VIII is energetically competitive with the established antiferroelectric form under pressure. The existence of domains of the ferroelectric form within anti-ferroelectric ice can explain previously observed splittings in x-ray diffraction data. The ferroelectric form is stabilized by density and is accompanied by the onset of spontaneous polarization. The presence of local electric fields triggers the preferential parallel orientation of the water molecules in the structure, which could be stabilized in bulk using new high-pressure techniques.

Earth's volatile depletion trend is consistent with a high-energy Moon-forming impact.

The abundance of volatile elements in the silicate Earth relative to primitive chondrites provides an important constraint on the thermochemical evolution of the planet. However, an overabundance of indium relative to elements with similar nebular condensation temperatures is a source of debate. Here we use ab initio molecular dynamics simulations to explore the vaporization behavior of indium from pyrolite melt at conditions of the early magma ocean just after the Moon-forming impact. We then compare this to the vaporization behavior of other minor elements. When considering the volatility of the elements from the magma ocean in the absence of the solar nebula gas, we find that there is no overabundance of indium. On the contrary, there is a slight deficit in the abundance of indium, which is consistent with its moderately siderophile nature. Thus, we propose that a high-energy Moon-forming impact may have had a more significant contribution to volatile depletion than previously believed.

Stability of high-temperature salty ice suggests electrolyte permeability in water-rich exoplanet icy mantles.

Electrolytes play an important role in the internal structure and dynamics of water-rich satellites and potentially water-rich exoplanets. However, in planets, the presence of a large high-pressure ice mantle is thought to hinder the exchange and transport of electrolytes between various liquid and solid deep layers. Here we show, using first-principles simulations, that up to 2.5 wt% NaCl can be dissolved in dense water ice at interior conditions of water-rich super-Earths and mini-Neptunes. The salt impurities enhance the diffusion of H atoms, extending the stability field of recently discovered superionic ice, and push towards higher pressures the transition to the stiffer ice X phase. Scaling laws for thermo-compositional convection show that salts entering the high pressure ice layer can be readily transported across. These findings suggest that the high-pressure ice mantle of water-rich exoplanets is permeable to the convective transport of electrolytes between the inner rocky core and the outer liquid layer.

Buoyancy and Structure of Volatile-Rich Silicate Melts.

The early Earth was marked by at least one global magma ocean. Melt buoyancy played a major role for its evolution. Here we model the composition of the magma ocean using a six-component pyrolite melt, to which we add volatiles in the form of carbon as molecular CO or CO2 and hydrogen as molecular H2O or through substitution for magnesium. We compute the density relations from first-principles molecular dynamics simulations. We find that the addition of volatiles renders all the melts more buoyant compared to the reference volatile-free pyrolite. The effect is pressure dependent, largest at the surface, decreasing to about 20 GPa, and remaining roughly constant to 135 GPa. The increased buoyancy would have enhanced convection and turbulence, and thus promoted the chemical exchanges of the magma ocean with the early atmosphere. We determine the partial molar volume of both H2O and CO2 throughout the magma ocean conditions. We find a pronounced dependence with temperature at low pressures, whereas at megabar pressures the partial molar volumes are independent of temperature. At all pressures, the polymerization of the silicate melt is strongly affected by the amount of oxygen added to the system while being only weakly affected by the specific type of volatile added.

Genesis of a CO2-rich and H2O-depleted atmosphere from Earth's early global magma ocean.

The magma ocean was a important reservoir for Earth's primary volatiles. Understanding the volatile fluxes between the early atmosphere and the magma ocean is fundamental for quantifying the volatile budget of our planet. Here we investigate the vaporization of carbon and hydrogen at the boundary between the magma ocean and the thick, hot early atmosphere using first-principles molecular dynamics calculations. We find that carbon is rapidly devolatilized, while hydrogen mostly remains dissolved in the magma during the existence of a thick silicate-bearing atmosphere. In the early stages of the magma ocean, the atmosphere would have contained significantly more carbon than hydrogen, and the high concentrations of carbon dioxide would have prolonged the cooling time of early Earth.

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package.

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package is best suited for applications on natural systems, like silicate and oxide melts, water-based fluids, and various supercritical fluids. The package is a collection of Python scripts that include two major libraries dealing with file formats and with crystallography. All the scripts are run at the command line. We propose a simplified format to store the atomic trajectories and relevant thermodynamic information of the simulations, which is saved in UMD files, standing for Universal Molecular Dynamics. The UMD package allows the computation of a series of structural, transport and thermodynamic properties. Starting with the pair-distribution function it defines bond lengths, builds an interatomic connectivity matrix, and eventually determines the chemical speciation. Determining the lifetime of the chemical species allows running a full statistical analysis. Then dedicated scripts compute the mean-square displacements for the atoms as well as for the chemical species. The implemented self-correlation analysis of the atomic velocities yields the diffusion coefficients and the vibrational spectrum. The same analysis applied on the stresses yields the viscosity. The package is available via the GitHub website and via its own dedicated page of the ERC IMPACT project as open-access package.

The Critical Point and the Supercritical State of Alkali Feldspars: Implications for the Behavior of the Crust During Impacts.

The position of the vapor-liquid dome and of the critical point determine the evolution of the outermost parts of the protolunar disk during cooling and condensation after the Giant Impact. The parts of the disk in supercritical or liquid state evolve as a single thermodynamic phase; when the thermal trajectory of the disk reaches the liquid-vapor dome, gas and melt separate leading to heterogeneous convection and phase separation due to friction. Different layers of the proto-Earth behaved differently during the Giant Impact depending on their constituent materials and initial thermodynamic conditions. Here we use first-principles molecular dynamics to determine the position of the critical point for NaAlSi3O8 and KAlSi3O8 feldspars, major minerals of the Earth and Moon crusts. The variations of the pressure calculated at various volumes along isotherms yield the position of the critical points: 0.5-0.8 g cm-3 and 5500-6000 K range for the Na-feldspar, 0.5-0.9 g cm-3 and 5000-5500 K range for the K-feldspar. The simulations suggest that the vaporization is incongruent, with a degassing of O2 starting at 4000 K and gas component made mostly of free Na and K cations, O2, SiO and SiO2 species for densities below 1.5 g cm-3. The Hugoniot equations of state imply that low-velocity impactors (<8.3 km s-1) would at most melt a cold feldspathic crust, whereas large impacts in molten crust would see temperatures raise up to 30000 K.

Carbon sequestration during core formation implied by complex carbon polymerization.

Current estimates of the carbon flux between the surface and mantle are highly variable, and the total amount of carbon stored in closed hidden reservoirs is unknown. Understanding the forms in which carbon existed in the molten early Earth is a critical step towards quantifying the carbon budget of Earth's deep interior. Here we employ first-principles molecular dynamics to study the evolution of carbon species as a function of pressure in a pyrolite melt. We find that with increasing pressure, the abundance of CO2 and CO3 species decreases at the expense of CO4 and complex oxo-carbon polymers (CxOy) displaying multiple C-C bonds. We anticipate that polymerized oxo-carbon species were a significant reservoir for carbon in the terrestrial magma ocean. The presence of Fe-C clusters suggests that upon segregation, Fe-rich metal may partition a significant fraction of carbon from the silicate liquid, leading to carbon transport into the Earth's core.

Compressional pathways of α-cristobalite, structure of cristobalite X-I, and towards the understanding of seifertite formation.

In various shocked meteorites, low-pressure silica polymorph α-cristobalite is commonly found in close spatial relation with the densest known SiO2 polymorph seifertite, which is stable above ∼80 GPa. We demonstrate that under hydrostatic pressure α-cristobalite remains untransformed up to at least 15 GPa. In quasi-hydrostatic experiments, above 11 GPa cristobalite X-I forms-a monoclinic polymorph built out of silicon octahedra; the phase is not quenchable and back-transforms to α-cristobalite on decompression. There are no other known silica polymorphs, which transform to an octahedra-based structure at such low pressures upon compression at room temperature. Further compression in non-hydrostatic conditions of cristobalite X-I eventually leads to the formation of quenchable seifertite-like phase. Our results demonstrate that the presence of α-cristobalite in shocked meteorites or rocks does not exclude that materials experienced high pressure, nor is the presence of seifertite necessarily indicative of extremely high peak shock pressures.

Dynamical instabilities of ice X.

Water ice X is stable in the 120-400 GPa pressure range, as obtained from lattice dynamical calculations performed using the density-functional theory. Below 120 GPa, it is characterized by one unstable flat phonon band, which generates the disordered ice X structure. Above 400 GPa, ice X has an unstable phonon mode in M, which leads to the Pbcm orthorhombic structure obtained in previous molecular-dynamics calculations [M. Benoit, M. Bernasconi, P. Focher, and M. Parrinello, Phys. Rev. Lett. 76, 2934 (1996)10.1103/PhysRevLett.76.2934]. Therefore, based on lattice dynamics, we propose that the high-pressure low-temperature phase-transition sequence in H2O ice is ice VIII-disordered ice X-ordered ice X-ice Pbcm.

Raman spectra and lattice dynamics of cubic gauche nitrogen.

The lattice dynamical properties of the cubic gauche phase of nitrogen are computed using density functional perturbation theory. The structure is found to be stable up to at least 250 GPa. Based on the dynamical data we derive the thermodynamical properties. We also determine the Raman spectra with both peak position and intensity and find excellent agreement with the experimental data, with the A mode dominating the spectra at all pressures.

Theoretical determination of the structures of CaSiO3 perovskites.

Density functional theory is used to determine the possible crystal structure of the CaSiO3 perovskites and their evolution under pressure. The ideal cubic perovskite is considered as a starting point for studying several possible lower-symmetry distorted structures. The theoretical lattice parameters and the atomic coordinates for all the structures are determined, and the results are discussed with respect to experimental data.

Iron-rich silicates in the Earth's D'' layer.

High-pressure experiments and theoretical calculations demonstrate that an iron-rich ferromagnesian silicate phase can be synthesized at the pressure-temperature conditions near the core-mantle boundary. The iron-rich phase is up to 20% denser than any known silicate at the core-mantle boundary. The high mean atomic number of the silicate greatly reduces the seismic velocity and provides an explanation to the low-velocity and ultra-low-velocity zones. Formation of this previously undescribed phase from reaction between the silicate mantle and the iron core may be responsible for the unusual geophysical and geochemical signatures observed at the base of the lower mantle.