Session P42: Focus Session: Planetary Materials III

Dissociation of CaIrO$_3$-type MgSiO$_3$ in the gas giants

CaIrO$_3$-type MgSiO$_3$ is the planet-forming silicate stable at pressures and temperatures (PTs) beyond those of Earth's core-mantle boundary. We have found using first principles quasiharmonic free energy computations that this mineral dissociates into MgO and SiO$_2$ at PTs expected to occur in the cores of the gas giants ($>\sim$10 Mbar, 10,000 K). This transformation should be important also for modeling the internal structure of two recently discovered terrestrial exoplanets: a dense Saturn orbiting HD149026b and a super Earth orbiting GJ876d. We propose a low pressure route experiment to confirm this dissociation.   

Thermal Electrons and Thermal Conductivity in Oxide Minerals at P and T Relevant to Terrestrial Exoplanets

The recent discovery of an extrasolar planet, with 7.5 times the mass of the Earth, has prompted investigation of a new range of parameter space, 3 times higher in temperature T and 10 times higher in pressure P than the Earth's mantle. We estimate thermal conductivity k(T) of minerals under these extreme conditions. The radiative portion of k(T) is large above the mid-lower post-perovskite mantle, where T reaches 5000-6000K. At T higher than 5000 K, free electron carriers are thermally activated with the population n(T) increasing as exp(-E*/2kT), where E* is the band gap energy of around 5 eV. Free carriers damp electromagnetic waves at frequencies below the plasma frequency, estimated to be close to 1 eV, shutting down radiative heat transport. Although thermal holes have low mobility, we find that thermal electrons are quite mobile, with small effective masses and weak scattering. Therefore, they become dominant carriers of heat. We predict electrical resistivity as low as 1000 micro-ohm cm.   

Elasticity of MgO Under Direct Pressure Measurement: Insights on Current Pressure Scales.

Recent high pressure studies indicated that the inaccuracy and inconsistency of the pressure scales used for pressure determination in different studies might be an importance source that gives rise to the apparent discrepancy in the derived phase equilibrium and physical properties for mantle minerals. In this study, P and S wave velocities and unit cell parameters (density) of MgO are measured simultaneously up to 11 GPa 1073K using combined ultrasonic interferometry and in-situ X-ray diffraction techniques, from which the elastic bulk and shear moduli as well as their and temperature pressure derivatives are obtained independent of pressure. These properties are subsequently used to calculate the primary pressures at the observed strains for comparison with those derived from previous proposed MgO pressure scales. Additionally, a comparison of the primary pressure obtained from MgO with those inferred from the enclosed internal pressure calibrant (NaCl) gives an opportunity to evaluate the Decker NaCl scale as well. Our results suggest that current pressure scales may bear larger uncertainties than originally claimed.   

A high PT scale based on density functional calculations of MgO

In situ crystallography based on diamond anvil cells have recently been extended to the multi-Mbar regime. Temperatures in these experiments have crossed the 2,000 K mark. Yet, current high PT standards of calibration produce too large uncertainties to the point of inhibiting clear conclusions regarding the importance of certain phenomena for planetary processes at these high PTs, e.g., the post-perovskite transition in Earth’s mantle. We propose a calibration based on thermal equations of state (EoS) of MgO obtained from LDA quasiharmonic (QHA) calculations. These EoSs agree very well with several calibrations at relatively low PTs. This gives further support to our predictions made within the range of validity of the QHA.   

Phase stability and elasticity of CaSiO$_3$ perovskite at high pressure and high temperature from Ab inito molecular dynamic calculations

We report the dynamics of the structure and elastic properties of CaSiO3 perovskite from \textit{ab initio }molecular dynamics (AIMD) calculations at high pressure (P up to 130 GPa) and high temperature (T up to 5000K). Our calculations indicate three separate stability fields: metrically orthorhombic, tetragonal and cubic, with the tetragonal phase dominating the pressure and temperature region between room temperature and 4000K. The cubic phase is not entirely stabilized even at temperatures of the Earth's lower mantle. Calculated X-ray diffraction patterns indicate small super- lattice reflections that could result from the octahedral rotations throughout the P-T region investigated. The calculated elastic constants and velocities are independent of temperature at constant volume. Referenced to room pressure and 2000K, we find: Gr\^{u}neisen parameter is $\gamma $(V) = $\gamma $0(V/V0)q with $\gamma $0 = 1.53 and q = 1.02(5), and the Anderson Gr\^{u}neisen parameter is given by ($\alpha $/ $\alpha $0) = (V/V0)$\delta $T in which $\alpha $0 = 2.89 x 10-5 K-1 and $\delta $T = 4.09(5). Using the third order Birch Murnaghan equation of state to fit our data, we have for ambient P and T, K$_{0}$ = 236.6(8) GPa, K$_{0}$' = 3.99(3), and V$_{0}$ = 729.0(6) {\AA}3.   

Computational study of the pressure behavior of post-perovskite phases

The recent discovery of the post-perovskite phase transition (CaIrO$_3$ structure) in MgSiO$_3$ has lead to theoretical and experimental investigations of silicates, germanates and oxides that could take this structure. We have employed density functional-theory to explore a series of new compounds with the post-perovskite structure under pressure. We analyze the effects of the Si substitution by tetravalent cations on the perovskite-to-post-perovskite transition and on the crystal structure of post-perovskite. Cations Ti$^{4+}$ and Zr$^{4+}$ prefer the post-perovskite structure. We also explore the sesquioxides Al$_2$O$_3$ and Rh$_2$O$_3$ and compare their structural evolution with the one of MgSiO$_3$. For Rh$_2$O$_3$ we observe an enhancement of the ionic character of the type II structure with pressure.   

Thermodynamics of Mg$_2$SiO$_4$ liquid from first principles molecular dynamics simulations

As the main medium through which planetary differentiation occurs, silicate liquids have a central role in the study of the Earth. We determine the structural and thermodynamic properties of Mg$_2$SiO$_4$ liquid using first principles molecular dynamics in the framework of density functional theory and the local density approximation (LDA). Calculations, performed in the canonical ensemble with a Nose thermostat, span a range of pressures (0 - 150 GPa) and temperatures (3000 - 6000 K). Simulations are performed over 3000 time steps (femto seconds), yielding the total energy and average pressure from which the equation of state, heat capacity and Gruneisen parameter are determined. Preliminary results show that, in addition to the increase in Si coordination with pressure, about one third of the O atoms are not bound to Si at low pressure, a fraction which vanishes with increased Si coordination.   

Dissociation of Ringwoodite investigated by first principles

The dissociation of Ringwoodite, Mg$_2$SiO$_4$ gamma-spinel, into MgO and MgSiO$_3$ perovskite is believed to be associated with the 660-km discontinuity in Earth's mantle. Details of this transition are important to clarify its effect on mantle convection: it is believed to inhibit flow across the ``660'' discontinuity. We have investigated the phase boundary using quasiharmonic free energy computations within the LDA and GGA. Once more the GGA transition pressure, P$_{tr}$, is higher and in much better agreement with the limited experiments available. The higher GGA P$_{tr}$ can be rationalized by close inspection of the relationship between GGA and LDA functional forms. Our predictions of density, bulk modulus, and bulk velocity jumps across the transition are consistent with seismic observations.   

Structure and freezing of MgSiO$_3$ liquid in Earth's interior

Silicate liquids are primary agents of mass and heat transport, yet little is known of their physical properties or structure over most of the mantle pressure regime. We have applied density functional theory within the local density approximation to the study of silicate liquids via Born-Oppenheimer first principles molecular dynamics. The simulations are performed in the NVT ensemble with a Nose thermostat. We find that over the pressure regime of Earth's mantle the mean Si-O coordination number increases nearly linearly with compression from four-fold to six-fold. The Gr\"uneisen parameter of the liquid increases markedly on compression, in contrast to the behavior of mantle crystalline phases, and in accord with expectations based on the pressure-induced change in structure of the liquid. The density contrast between liquid and crystal decreases nearly five-fold over the mantle pressure regime and is 4 \% at the core-mantle boundary. The melting curve, obtained via integration of the Claussius-Clapeyron equation yields a melting temperature of $5400 \pm 600$ K at the core mantle boundary. Our results support the notion of buoyantly stable silicate melts at the core-mantle boundary.   

A laboratory method for modeling synthesis of coesite in the earth's surface by combining local mechanical collision with shear stress and high static pressure.

A laboratory method of combining the high-energy mechanical ball milling and high static pressure has been suggested for modeling synthesis of coesite in the earth's surface. A window of milling time, a mechanical collision-induced intermediate phase of $\alpha $-quartz and its condition of easily crystallizing into coesite induced by high static pressure 3.0 GPa, 923 K, $<$ 1.0 min have been discovered. The condition has a much shorter synthesizing time and lower synthesizing critical pressure than that obtained before. The Raman spectrum for the coesite synthesized by the present method has the biggest number of peaks, and have covered over the information of those natural and synthesized coesite reported before. Here We clarify the implications of the coesite synthesized by this method in geo-science, and suggest another possible formation mechanism of coesite in the earth's surface, which is different from the hypothesis of plate subduction-exhumation in the earth that was based on the coesite formation condition of high static pressure in laboratory.   

Novel Perovskite Compounds Synthesized under Elevated High Pressure.

High pressure synthesis is very powerful to stabilize new compounds with perovskite-like structure, as it has been very well established in the studies of Earth mantle. This has been widely demonstrated in the research of transition metal oxides. Here we introduce some new transition metal compounds that have been recently synthesized under elevated high pressure.   

Structure of MgO(MgSiO$_{3})_{n}$ in Earth's Lower Mantle: ab initio calculations

Ruddlesden-Popper (RP) compounds are composed of alternating perovskite-type and rocksalt-type structural elements. MgSiO$_{3}$ and MgO are found as separate phases in Earth's lower mantle. Both structural elements occur also in the hypothetical RP-series MgO(MgSiO$_{3})_{n}$. It is interesting to explore the high pressure-high temperature stability of such RP-structures. Using the augmented plane wave implementation of Density Functional Theory we investigate the structural stability at lower mantle conditions of the member with $n$ = 1 e.g. Mg$_{2}$SiO$_{4}$. The goal of the present calculations is to test the stability of this Ruddlesden-Popper phase relative to $\gamma$-(Mg,Fe)$_{2}$SiO$_{4}$ and the assemblage MgSiO$_{3}$-perovskite + MgO magnesiow\"{u}stite. We will present our results of this study.   

Heat capacity measurements of sub-milligram quantities of mantle minerals

Knowledge of heat capacities and standard entropies of mantle minerals is necessary for thermodynamic modeling of high P-T equilibria. However many of these materials can only be prepared in milligram quantities in a multianvil apparatus or in microgram quantities in a diamond anvil cell. This eliminates traditional adiabatic calorimetry techniques for Cp measurements. Our microcalorimeters have been used to successfully measure thin films, multilayers, and magnetic single crystals. Using these ``calorimeters on a chip'', we are measuring the heat capacity of the Fe$_{2}$SiO$_{4}$ olivine and spinel polymorphs from 2 K to room temperature. This will provide a direct measurement of the entropy of the olivine-spinel transition and will uncover possible magnetic phase transitions at low temperature in the spinel phase. We would like to thank the DOE for funding this research.   

Carbon under extreme conditions: phase boundaries from first-principles theory

We present predictions of diamond and BC8 melting lines and their phase boundary in the solid phase, as obtained from first principles calculations. Maxima are found in both melting lines, with a triple point located at $\sim 850~\rm GPa$ and $\sim 7400~\rm K$. Our results show that hot, compressed diamond is a semiconductor which undergoes metalization upon melting. On the contrary, in the stability range of BC8, an insulator to metal transition is likely to occur in the solid phase. Close to the diamond/ and BC8/liquid boundaries, molten carbon is a low-coordinated metal retaining some covalent character in its bonding up to extreme pressures. Our data provide constraints to the carbon equation of state, which is of critical importance to devise models of, e.g., Neptune, Uranus and white dwarf stars, as well as of extra-solar carbon planets. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

Synthesis of New Cubic C$_{3}$N$_{4}$ Phase under High Pressure and High Temperature

Synchrotron-based X-ray diffraction studies were carried out on a graphite-like C$_{3}$N$_{4}$ ($g$- C$_{3}$N$_{4})$ phase subjected to high pressures up to 38 GPa and high temperatures of up to 3000 K using the laser-heated diamond-anvil cell. Laser-heating the sample to 1800 K at pressure between 20 and 38 GPa, a new set of diffraction pattern appeared, showing positively that a high-pressure phase was formed. Upon decompression of the post-lasered sample to 1 atmospheric pressure, the X-ray diffraction peaks of high-pressure phase were replaced completely by a new pattern, thus demonstrating a new metastable phase was formed retrogressively. X-ray diffraction data on the recovered phase show that it is a new cubic phase that does not match to any high-pressure phases in C$_{3}$N$_{4}$ predicted theoretically.