Session S2: Materials in Extremes IX

Ab initio equation of states for planetary and exoplanetary modeling

Using ab initio molecular dynamics simulations, we recently calculated equations of state for the main constituents of planetary interiors: H, He, H2O, MgSiO3(MgO,SiO2) and Fe. These equations of states are multi-phases, include liquid and solid phases, and aim at building planetary and exoplanetary interior models solely based on ab initio predictions. This talk will concentrate on Jupiter. We will review how our current understanding of the behavior of these basic constituents at extreme density temperature conditions has modified our current understanding of Jupiter interior, not only for the envelop where metallization of hydrogen and hydrogen-helium demixing is the issue but also for the core where the high pressure melting properties of iron, water and silicates bring a new understanding on the nature of giant planet cores. This work is supported in part by the French Agence National de la Recherche under contract PLANETLAB ANR-12-BS04-0015.   

Spin crossover in (Mg,Fe$^{3+}$)(Si,Fe$^{3+}$)O$_3$ bridgmanite: effects of disorder, iron concentration, and temperature

The spin crossover of iron in Fe$^{3+}$-bearing bridgmanite, the most abundant mineral of the Earth's lower mantle, is by now a well-established phenomenon, though several aspects of this crossover remain unclear. Here we investigate effects of disorder, iron concentration, and temperature on this crossover using ab initio LDA + U$_{SC}$ calculations. Disorder and concentration effects are addressed using complete statistical samplings of coupled substituted configurations up to 80 atoms supercells, while the vibrational effects using the quasiharmonic approximation. Our calculated compression curves for iron-free and iron-bearing bridgmanite compare well with the latest experimental measurements. The comparison also suggests that in a closed system, Fe$^{2+}$ present in the sample may transform into Fe$^{3+}$ by introduction of Mg and O vacancies with increasing pressure. As in the spin crossover in ferropericlase, this crossover in bridgmanite is accompanied by a clear volume reduction and an anomalous softening of the bulk modulus throughout the crossover pressure range. Though the concentration of [Fe$^{3+}$]$_{Si}$ in bridgmanite may be small, related elastic anomalies may impact the interpretation of radial and lateral velocity structures of the Earth's lower mantle.   

Impact of ferropericlase’ spin crossover on the Earth's lower mantle temperature profile

The pressure induced iron spin crossover in ferropericlase, the second most important lower mantle phase, introduces anomalies in its thermodynamics and thermoelastic properties. Here we investigate how these anomalies can affect the Earth's lower mantle adiabatic temperature profile. The effect is examined in likely lower mantle aggregates consisting of mixtures of Mg$_{1-x}$Fe$_x$SiO$_3$ perovskite (bridgmanite), Mg$_{1-x}$Fe$_x$O (ferropericlase), and CaSiO$_3$ perovskite, at different Mg/Si ratios varying from harzburgitic to perovskitic (Mg/Si $\sim$ 1.5 to 0.8). We find that the anomalies introduced by the spin crossover increase the isentropic temperature gradient and thus the geotherm proportionally to the amount of ferropericlase. The geotherms can be as much as $\sim$ 200K hotter than the conventional adiabatic geotherm [1] at deep lower mantle conditions ($\sim$ 125GPa). Aggregate elastic moduli and seismic velocities are also sensitive to the spin crossover and the geotherm, which impacts analyses of lower mantle velocities and composition. [1] J.M. Brown and T.J. Shankland, Geophys. J. R. Int., 66, 579 (1981).   

Phase equilibria and velocity discontinuities across the post-perovskite transition in (Mg,Fe)SiO$_3$

The enigmatic nature of the region above the Earth's core-mantle boundary known as the D" region, is often characterized by a significant contrast in seismic wave velocities. The perovskite (Pv) to post-perovskite (PPv) transition in bridgmanite ((Mg,Fe)SiO$_3$ perovskite) is one of the keys for understanding this region. In this study, we present DFT + U$_{SC}$ calculations of phase equilibria in bridgmanite across the post-perovskite transition. Thermal effects are addressed within the quasi-harmonic approximation. By computing high-pressure and high-temperatures elastic/acoustic properties of Pv and PPv phases, we also investigate seismic signature of the PPv-transition, believed to cause the D" discontinuity. Aggregate elastic moduli and sound velocities for the Mg-end member are successfully compared with limited experimental data available. Predicted velocity discontinuities across the PPv transition are consistent with seismic observations in some places of the global D" discontinuity. Our robust estimates of the phase boundary and elastic properties of the perovskite and post-perovskite phases will help to clarify the origin of lateral velocity variations in the deep lower mantle region and constrain its composition and thermal structure.   

Fate of MgSiO3 Post-Perovskite at Terapascal Pressures

Understanding the fate of MgSiO$_{\mathrm{3}}$ post-perovskite (ppv) under TPa pressures should provide insights into the nature of the interiors of Super-Earths-type exoplanets. The prediction that ppv should dissociate into the elementary oxides MgO and SiO$_{\mathrm{2}}$ at TPa pressures has been confirmed by all ab initio computational studies so far. The most recent high pressure and high temperature (PT) studies agree that at \textasciitilde 2.2 TPa the dissociation process should be completed. These studies also agree that the final dissociation phase boundary has a negative Clapeyron slope, irrespective of the dissociation paths, suggesting a barrier to whole mantle convection possibly leading to chemical stratification in the deep mantle of these planets. The dissociation paths identified more recently involve partial dissociation into MgO, SiO$_{\mathrm{2}}$, and Mg- and Si-rich intermediate compounds whose compositions are temperature dependent. Here we re-investigate the high PT phase diagram of the MgO-SiO$_{\mathrm{2}}$ system and identify novel phase fields and dissociation paths that push the final dissociation boundary to \textasciitilde 3 TPa.   

Ab-initio calculations of the sound velocities of iron at high pressure and temperature.

By means of \textit{ab initio}molecular dynamics calculations and the temperature dependent effective potential method (TDEP) we have calculated the vibrational properties of hcp iron as a function of density and temperature. From the interatomic force constants we derived the elastic constants and the compressional and shear velocities. We compare our results with the experimental data in the range of densities and temperatureswhere they are available and to previous theoretical work. We show that our data respect the Birch's law with a linear dependence in density at any fixed temperature and we give a fit of our values covering a large scale of densities and temperatures (10-14g/cc, 0-7000K). We also compare our results with the Preliminary Reference Earth Model (PREM) and we discuss the effect of light elements on the sound velocities of iron.   

Mechanism of the body-centered cubic iron stabilization under the Earth core conditions

The Earth solid inner core is mostly iron, therefore, the question -- what is the structure of iron in the Earth inner core -- is central to our understanding of the Core. However, the stable phase of iron in the Core is still unknown. Currently, two major candidates are considered -- hexagonal close-packed (hcp) and body centered cubic (bcc) structures. Neither of these structures received unanimous support. We demonstrate stability of the bcc phase under conditions in the center of the Core by performing constant pressure-temperature ab initio molecular dynamics simulations with varying shape and volume of the computational cell. The bcc phase is stabilized by the discovered unique diffusion mechanism that originates in the low temperature dynamical instability of the bcc phase. It appears that the bcc phase has already been observed in the recent experiments, however, the experimental data was misinterpreted. The diffusion of iron atoms in solid state is quite unique and might allow us to explain both the anisotropy and the low shear modulus of the inner Core.   

Synthesis of novel materials via useful hard x-ray photochemistry.

h $-abstract-$\backslash $pard We discuss an effort to synthesize higher oxidation forms of cesium fluoride by pressurizing cesium fluoride in a fluorine rich environment created via the x-ray decomposition of potassium tetrafluoroborate. This was done in order to confirm recent theoretical predictions of higher oxidation forms of CsFn (n\textgreater 1) under extreme conditions. We discusses the development of a technique to produce molecular fluorine in situ via useful hard x-ray photochemistry, and the attempt to utilize this technique to form higher oxidation states of cesium fluoride. In order to verify the formation of the novel stoichiometric species of CsFn, we used X-ray Absorption Near Edge Spectroscopy (XANES) centered on the cesium K-edge to probe the formal oxidation state of cesium as well as the local molecular coordination. We present evidence of the formation of CsF3.$\backslash $-/abstract-$\backslash $\tex   

Discovery of pyrite-structured FeO$_{2}$ at high pressure

We conducted x-ray diffraction experiment and first-principles simulation on the assemblage of ferric iron oxide and oxygen. The sample was compressed up to one megapressure (100 GPa) and heated by a double-sided laser to above 2000 K. We identified a previous predicted but not experimentally observed FeO$_{2}$ phase and solve the structure by multigrain single crystal method. Iron peroxide is energetically stable above 75 GPa and holds greater amount of oxygen than any other iron oxides. We further recognized this phase also relates to the decomposition of iron oxy-hydroxide at high pressure. The extreme stability of FeO$_{2}$ can result in accumulating high-density iron peroxide at mantle basal and ascending hydrogen to the crust. This work suggests a new paradigm in the research of Fe-O-H ternary system under extreme conditions.   

Modeling Thermodynamics of High-Pressure Liquids with Application to MgSiO3 for Understanding Magma Ocean Evolution

Accurately modeling high pressure thermodynamic properties for liquids is challenging due to the intimate link between liquid structure and thermodynamics. In the geological sciences, this issue arises for the early formation stages of rocky planets. Cooling and crystallization of magma oceans are dominated by the thermodynamics of high-pressure silicate melts. Even first-order properties like adiabats and melting curves are poorly understood, with strong disagreements between studies [e.g. Stixrude 2005, 2009; Mosenfelder 2009; Fiquet 2010; Andrault 2011]. We develop a new equation of state for compressed liquids and apply it to MgSiO3 melt. The High-Pressure Rosenfeld-Tarazona (RTpress) model extends the original Rosenfeld-Tarazona EOS by coupling it to physical compression models. We fit a new MgSiO3 melt EOS based on molecular dynamics simulations [Spera 2011], and show that it compares well with first-principles simulations and shock data. The relative slopes of the melting curve and liquid adiabat determine the crystallization depth of the magma ocean. Our model produces highly concave melting curves, consistent with recent experimental analog studies of MgSiO3 glass compression [Petitgirard 2015], and support the more complex center-outwards style of crystallization.   

First-principles Raman spectroscopy of dissolved carbon in water under extreme conditions

The aqueous properties of dissolved carbon at extreme conditions are of great importance to the carbon cycle in the deep Earth, which substantially influences the carbon budget near the Earth's surface, and in turn global climate change. We carried out first-principles simulations that showed that, contrary to the assumptions of many geochemical models, carbon dissolved in water-rich fluids at the bottom of the Earth's upper mantle is not in the form of CO$_2$(aq) but rather in carbonate and bicarbonate ions [1]. We also calculated the Raman spectra of (bi)carbonate aqueous solutions at supercritical conditions, and obtained the Raman scattering cross sections of carbon species at high pressures and high temperatures from first principles. We will discuss how to use our results to interpret and guide spectroscopic measurements. [1]D. Pan and G. Galli, Sci. Adv. 2, e1601278(2016)   

Signatures of Water Dissociation at Extreme Conditions in Vibrational Spectra and Ionic Conductivity from ab initio Simulations

Predicting the properties of water at high pressure and~temperature is critical to understanding hydrogen bonding, charge transport, and phase stability of aqueous media in the Earth and outer planets. Here we employed ab initio molecular dynamics and density functional perturbation theory, as implemented in the Qbox code [1] to study ionic conductivity and infrared and Raman spectra of water at 10 and 20 GPa and 1000 K, as well as those of an amorphous solid phase at 16 GPa, and 500K. We identified specific signatures of proton hopping and molecular dissociation in the IR spectra at 20 GPa, which may be used to guide future experiments, as well as signatures of molecular diffusivity in the low frequency portion of Raman spectra, which help discern between amorphous and liquid phases at high pressure. We also computed ionic conductivities using~maximally localized Wannier functions. We used our results at~ 20 GPa and~ 1000 K to address the existence of possible plastic and~ amorphous ice phases, recently proposed to potentially mediate the ice VII melting line. \newline [1] http://qboxcode.org