Session B23: Focus Session: High Pressure II - Earth and Planetary Materials

High-pressure investigations of Earth's interior

In the first half of the talk, the electronic structure of iron in ferromagnesium silicate perovskite will be discussed. Knowledge of iron valences and spin states in silicate perovskite is relevant to our understanding of the physical and chemical properties of Earth's lower mantle such as transport properties, mechanical behavior, and element partitioning. In this study, we have measured the electronic structure of the iron component of an aluminous Fe-bearing silicate perovskite sample, (Mg$_{0.88}$Fe$_{0.09})$(Si$_{0.94}$Al$_{0.10})$O$_{3}$, close to a pyrolite composition, using synchrotron M\"{o}ssbauer spectroscopy (SMS) and laser heated diamond anvil cells at high-pressure and temperatures at beamline 3-ID of the Advanced Photon Source. Evaluation of the spectra provided the isomer shift and the quadrupole splitting of the iron component in silicate perovskite, which gives information on valence and spin states under lower mantle conditions. In the second half of the talk, experiments on the melting curve of iron at high-pressures will be presented. Seismological observations indicate that Earth's iron-dominated core consists of a solid inner region surrounded by a liquid outer core. Previously, melting studies of iron metal at high-pressures and temperatures were performed by shock-compression, resistive- and laser-heating in diamond anvil cells using visual observations or synchrotron x-ray diffraction and theoretical methods. However, the melting curve of iron is still controversial. Here, we will present a new method of detecting the solid-liquid phase boundary of iron at high-pressure using $^{57}$Fe SMS. The characteristic SMS time signature is observed by fast detectors and vanishes suddenly when melting occurs. This process is described by the Lamb-M\"{o}ssbauer factor $f$ = exp(-$k^{2}<$x$^{2}>)$, where $k$ is the wave number of the resonant x-rays and $<$x$^{2}>$ is the mean-square displacement of the iron atoms.   

Infrared Reflectance of Magnesiowustite(Mg$_{1-x}$Fe$_{x}$O): Experiment and Theory

We measured the optical reflectance spectra(0$\sim $32300 cm$^{-1})$ of magnesiowustite(Mg$_{1-x}$Fe$_{x}$O, x=0.06, x=0.27) at 6K and 295K, using a Bruker IFS 113v spectrometer. Kramers-Kronig relations are used to extract the corresponding dielectric functions. The Infrared parts of the spectra resemble those of pure MgO, while showing much smaller temperature dependence. There are two factors determining the structure of dielectric functions: a) anharmonic phonon-phonon interactions, b) disorder scattering. A breathing-shell model is used to evaluate factor a) in pure MgO, and a supercell is built to estimate the influence of factor b) in Fe doped MgO. Our results will be useful for computing the heat conductivity of magnesiowustite in the earth's lower mantle.   

Dynamical mean-field theory study of the high pressure behavior of FeO

First-principles calculations have an important part in the development of our understanding of Earth's interior, including geophysical and geochemical phenomena. Proper treatment of iron bearing minerals is fundamental in this respect. Unfortunately standard density functional theory (DFT) approaches such as the local density (LDA) or the generalized gradient approximations (GGA) fail in describing qualitative features of simple iron containing minerals; for example the insulating nature and magnetic structure of many metal oxides such as FeO. The LDA+U approximation, self-interaction correction (SIC), and dynamical mean-field theory (DMFT) have demonstrated significant improvement in the physical description of transition metal and rare earth compounds. Presented results will focus on theoretical predictions obtained with the DMFT method. The high pressure behavior and high-spin-low-spin phase transition for iron oxide in the distorted rocksalt (B1) structure.   

Elastic Signature of the High-Spin to Low-Spin Transition in Magnesiow\"{u}stite

It has been reported that the high to low-spin spin transition in ferrous iron in magnesiow\"{u}stite (Mw) under pressure is accompanied by considerable volume reduction and changes in elastic properties. Using an LDA+U method with consistently calculated U, we investigate the elastic signature of this transition. We confirm that there is large contrast in elasticity across this transition. However, this contrast is temperature sensitive. We address the geophysical signature of this phenomenon.   

\textit{Ab initio} Study of the Composition Dependence of the Pressure-Induced Spin Transition in Perovskite (Mg,Fe)SiO$_{3}$

We present \textit{ab initio} calculations of the zero-temperature compositional dependent spin transition in (Mg,Fe)SiO$_{3}$ perovskite at pressures relevant to Earth's lower mantle. Equations of state are fit for a range of compositions and used to predict the Fe$^{2+}$ high- to low-spin transition pressure and associated changes in volume and bulk modulus. We predict a relatively constant transition pressure for x $<$ 0.25, but a significant decrease for higher Fe concentrations, contrary to the trend for rocksalt (Mg,Fe)O, suggesting the mechanism for spin transition is highly dependent on the structural environment of Fe. The spin transition is dominated by both the spin flip energy and the change in volume from high- to low-spin. Furthermore, volume trends show that high-spin Fe$^{2+}$ is larger than Mg$^{2+}$ even under pressure, but low-spin Fe$^{2+}$ is smaller at ambient conditions and approximately the same size as Mg$^{2+}$ under pressure, which has implications for correctly calculating Fe partitioning coefficients in the lower mantle. We also find the spin transition pressure differs between Fe$^{2+}$ and Fe$^{3+}$; therefore the coupling behavior of these two species must be examined closely.   

First-principles investigation of the spin state of ferrous iron in MgSiO$_3$ under pressure

We present a density functional study of the pressure induced spin transition in ferrous iron in MgSiO$_3$ perovskite and post-perovskite. We address the influence of iron concentration and configuration (structural and magnetic), as well as technical issues such as the nature of the exchange correlation (XC) functional (LDA versus PBE-GGA) on the spin transition pressure. Supercells containing up to 160 atoms were adopted to tackle these issues. We show that there are preferred configurations for high-spin and low-spin iron and that the spin transition pressure depends strongly on iron concentration and XC functionals. We also address the possibility of a structural change accompanying the spin transition.   

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.   

Consequences of the Quasiharmonic Approximation: Tests and Predictions

The quasiharmonic approximation (QHA) is extremely useful since it allows the computation of thermodynamic properties if one knows the volume dependence of the vibrational density of states. It has an important consequence: the structure and vibrational properties of the solid depend on volume alone. The temperature dependence occurs via extrinsic volumetric effects. We present here a criterion to determine the pressure- temperature range of validity of the QHA, apply it to and test it in MgSiO3-perovskite, and inspect the possibility of a simple volumetric depended of other properties such as acoustic velocities, i.e., ``Birch's Law.''   

Quantum Monte Carlo Benchmarks Functionals for Silica Polymorphs

For many silica polytypes, the local density approximation (LDA) does a better job than the generalized gradient approximation (GGA) in predicting structural properties and bulk moduli. However, gradient corrections to the charge density are necessary for accurate phase energy differences \footnote[1]{Th. Demuth et al., J. Phys.: Cond. Matter 11, 3833 (1999).}. Functionals that go beyond GGA may improve the accuracy of both structures and energies. For example, a meta-GGA functional, TPSS, and hybrid functionals B3LYP and HSE \footnote[2]{J. Heyd et al., J. Chem. Phys. 121, 1187 (2004).} have shown improvement in other systems \footnote[3]{E. R. Batista et al., Phys. Rev. B 74, 121102(R) (2006).}. We compare results from these functionals for structural properties, energy differences, and bulk moduli for a few high pressure phases of silica, and benchmark the results with Quantum Monte Carlo (QMC). Preliminary QMC results indicate that careful wavefunction optimization and finite size effects are of particular importance in obtaining accurate silica phase properties. Supported by DOE(DE-FG02-99ER45795), NSF (EAR-0530301, DMR-0205328), and Sandia National Laboratory. Computation at OSC and NERSC.   

Quantum Monte Carlo Simulations of the Quartz to Stishovite Transition in SiO$_2$

The quartz-stishovite transition has been a long standing problem for density functional theory (DFT). Although conventional DFT computations within the local density approximation (LDA) give reasonably good properties of silica phases individually, they do not give the energy difference between quartz and stishovite accurately. The LDA gives stishovite as a lower energy structure than quartz at zero pressure, which is incorrect. The generalized gradient approximation (GGA) has been shown to give the correct energy difference between quartz and stishovite (about 0.5 eV/formula unit) (Hamann, PRL 76, 660, 1996; Zupan et al., PRB 58, 11266, 1998), and it was generally thought that the GGA was simply a better approximation than the LDA. However, closer inspection shows that other properties are not better for the GGA than the LDA, so there is room for improvement. A new density functional that is an improvement for most materials unfortunately does not improve the quartz-stishovite transition (Wu and Cohen, PRB 73, 235116, 2006). We are performing QMC computations using the CASINO code to obtain the accurate energy difference between quartz and stishovite to obtain more accurate high pressure properties, and to better understand the errors on DFT and how DFT can be improved.   

First-principles calculations of thermodynamic properties and phase transitions in Al$_{2}$O$_{3}$ and Ga$_{2}$O$_{3}$ at high temperature and high pressure

Using \textit{ab initio} density functional theory and statistical quasi-harmonic approximation theory, we have calculated thermodynamic potentials of mineral Al$_{2}$O$_{3}$ materials and the related Ga$_{2}$O$_{3}$ materials over a wide range of temperature and pressure (T-P) conditions. The equilibrium T-P phase diagrams are predicted to understand the trend of pressure induced phase transitions in group IIIB oxides. Furthermore, we theoretically explored the possible new high-pressure structures of Ga$_{2}$O$_{3}$. Finally, we derived experimentally measurable thermal properties, such as lattice thermal expansion, heat capacity, and isothermal compressibility. Our calculated thermal properties are in excellent agreement with available experiments.   

Proton behaviour, structure and elasticity of serpentine at high-pressure

Serpentine occurs in oceanic crust as the alteration product of ultramafic rocks and is a possible candidate for carrying water to the deep earth. The presence of sub-surface serpentine may be manifested by mud volcanoes, high electrical conductivities, and seismic anomalies. Using density functional theory, we predict a phase transition in serpentine near 22 GPa. The phase transition is caused by a re-orientation of the hydroxyl vector coupled with changes in the di-trigonal rings of SiO$_{4}$ tetrahedra. The symmetry of the crystal-structure remains unaffected. Evidence of pressure-induced hydrogen bonding is absent in serpentine, as evident from the reduction of O-H bond length upon compression. Results of compression for the low-pressure phase is well represented by a fourth order Birch-Murnaghan finite strain expression with $K_O $= 63 GPa, ${K}'_O $= 10.2 and $K_O {K}''_O $ = -120, where $K$ is the bulk modulus, prime indicates pressure derivatives, and O refers to zero pressure. At low pressures, the elastic constant tensor is highly anisotropic with $C_{11}^o \sim 2.4\times C_{33}^o $, and becomes more isotropic with compression. We find an elastic instability near 36 GPa that may be related to experimentally observed amorphization.