DI41A-0339
The equation of state and structure stability of elemental metal vanadium under high pressure -from experiments to theories
The EOS of elemental metal vanadium was measured using diamond anvil cell and synchrotron x-ray powder diffraction techniques up to 1.5 Mbar. A phase transition was observed at 63-69 GPa and room temperature in vanadium. The transition is characterized as a rhombohedral lattice distortion of the body-centered cubic vanadium without a discontinuity in the pressure-volume data, thus representing a novel type of transition that has never been observed in elements. The first principles calculations of electronic structure and lattice dynamics indicate that, instead of driven by the conventional s-d electronic transition mechanism, the phase transition is associated with the softening of C44 trigonal elasticity tensor that originates from the combination of Fermi surface nesting, band Jahn-Teller distortion and electronic topological transition. Major references related to this work, (1) Yang Ding et al , Structural Phase Transition of Vanadium at 69 GPa Phys. Rev. Lett. 98, 085502 (2007). (2)Wei Luo, Rajeev Ahuja, Yang Ding, and Ho-kwang Mao, "Unusual lattice dynamics of Vanadium under high pressure", submitted to PNAS. (3) Byeongchan Lee et al., "Theoretical confirmation of a high-pressure rhombohedral phase in vanadium metal", Phys. Rev. B 75, 180101 (R) (2007)
DI41A-0340
New P-V-T equation of state is proposed and tested against experiments on perovskite and epsilon iron
The volume is not an independent variable and must be broken down into its fundamental components when the relationships to the pressure and temperature are defined. Using absolute reference frame (zero pressure and temperature) three initial parameters, the volume at zero pressure and temperature, the bulk modulus at zero temperature, and the volume coefficient of thermal expansion at zero pressure are defined. It is assumed that the temperature derivative of the bulk modulus is zero, and that the pressure derivative of the volume coefficient of thermal expansion is constant. The pressure dependence of the bulk modulus is described by linear and exponential factors and linear change for the temperature derivative of the volume coefficient of thermal expansion is assumed. Based on these assumptions a new EoS consisting seven parameters is derived. The new EoS is tested against the experiments on perovskite and epsilon iron. The Root-mean-square- deviations (RMSD) of the residuals of the molar volume, pressure, and temperature are 0.043 cm3, 0.8 GPa, and 128 K for perovskite and 0.018 cm3, 1.7 GPa, and 117 K for iron respectively. The RMSD values indicate that the new EOS is able to reproduce the data within the uncertainties of the experiments. Separating the experiments into 200 K ranges the new EoS was compared to the most widely used finite strain, interatomic potential, and empirical isothermal EoSs such the Birch-Murnaghan, the Vinet, and the Roy-Roy respectively. Correlation coefficients, RMSD of the residuals and Akaike Information Criteria are used to evaluate the fit. Based on these fitting parameters the new p-V-T EoS is superior in every temperature range to all of the investigated conventional isothermal EoSs for both perovskite and epsilon iron. The new EoS of epsilon iron reproduces the PREM densities at 4400 K indicating that the melting temperature of iron is around 4400 K at the outer-inner core boundary and that presence of light elements might not be necessary to explain the inner core densities. http://www.garai-research.com
DI41A-0341
Pressure-Volume-Temperature Equation of State for alpha-FeOOH Using X-ray Diffraction
Hydrogen strongly influences the physical properties of mantle materials. Understanding the stability and properties of simple hydroxides at high pressures and temperatures offers an important first step toward quantifying more complex hydrogen-bearing compounds relevant to the Earth's interior. We focus on iron-oxy- hydroxide because Fe is a major chemical component of the deep Earth, with valence (hence chemical-bonding properties) dependent on pressure. Powder x-ray diffraction measurements on goethite (α-FeOOH), collected at combined pressures and temperatures of 0-35 GPa and 23°-400°C, and fit to a third- order Birch-Murnaghan equation of state, yield a zero-pressure isothermal bulk modulus and pressure derivative of K0T = 124 (±3) GPa and K'0T = 4 (±1). We measure the zero-pressure thermal expansivity of goethite, finding α = 2.3 (±0.6) x 10-5K-1 between 23 and 400°C. These thermoelastic parameters are compatible with the values for diaspore (AlOOH), an isostructural analogue that forms a continuous solid solution with goethite (its high-pressure phase, δ-AlOOH, is thought to be a dehydration product of lawsonite in the transition zone). And at even higher pressures, ~50 GPa or more, where the mechanical and coulombic energy densities are comparable to major electronic transitions, we expect a change in Fe-(OH) interaction. Finally, we propose that a high- to low-spin transition in trivalent iron could result in a significant molar-volume reduction, manifesting itself as a first-order phase transition at high pressures.
DI41A-0342
High-Pressure Phase Diagram of TiO2 as Determined by Experiment and Theory
We have investigated the high-pressure phase diagram and determined the equations of state (EOS) of TiO2 using high-resolution synchrotron x-ray diffraction and complementary ab-initio computations. The phase sequence we observe experimentally is as follows: rutile → columbite → baddeleyite → orthorhombic I (OI), and additional high-pressure structures. Upon compression at room temperature, rutile was observed to be stable up to about 17 GPa, but reflections from baddeleyite were observed at about 12 GPa and persisted to 50 GPa. Upon decompression from 17 GPa (without heating), the baddeleyite phase transformed to columbite at ~ 8 GPa. Columbite remained stable as the pressure was decreased further. Additionally, we have heated our sample at pressures 30, 35, 40, and 50 GPa to ~ 1800 K and found that baddeleyite transforms to OI at 30 and 35 GPa. Finally, the EOS's determined experimentally will be compared with those determined computationally.
DI41A-0343
In situ diffraction studies of magnesium silicate liquids and glasses under extremes of temperature and pressure.
Recently, there has been increasing interest in the structure of the liquid and glassy state at high pressure. Maxima in the melting temperature and corresponding negative melt slopes with pressure have now been reported in many systems which implies that both density and entropy increase with increasing pressure. In some cases, changes in amorphous structure with pressure can be abrupt and these changes are used to suggest that there may be first-order transitions between stable or metastable low and high density liquids at high pressure. Most evidence for this type of behaviour is indirect and is based on the changes in thermodynamic and other structure-related properties with pressure. Diffraction studies of liquids and amorphous materials at high pressure and temperature are therefore desirable and in this presentation we will discuss the results of X- ray and neutron scattering methods applied to silicate liquids and glasses that reveal details of structural changes that occur as a function of both pressure and temperature. Liquids in the MgO-SiO2 system provide a good approximation for the liquids that are produced when the mantle minerals from planetary interiors melt. Their structures are however poorly understood because the liquids are refractory and do not form glasses particularly easily. Containerless synthesis techniques have been used to make glasses ranging in composition from the minerals enstatite to forsterite. Combined neutron and X- ray diffraction studies show a jump in the Mg-O coordination number between 38 and 33 Mole % SiO2, this is interpreted as reflecting a limit to the formation of a polymerised silicate network. In-situ studies of these liquids using combined containerless and high energy X-ray diffraction techniques suggest that the limit to network formation is encountered at higher silica content in the liquids, and a change in the structure and structure-related properties such as the liquid viscosity, occurs when the liquids are cooled. The high temperature studies were carried out at ambient pressure; in situ diffraction studies of the glass structure can be made however and are used to identify related changes in structure. Neutron diffraction studies of a single composition magnesium silicate glass from ambient pressure to 9 GPa show changes in the amorphous structure. We identify changes in the Mg-O and O-O which suggest pressure-induced changes in the local environment of magnesium. Experimentally both the high temperate and high pressure experiments are challenging, although these in- situ studies reveal a wealth of structural complexity. As new facilities become commissioned and new techniques are developed, studies of these and similar liquids at elevated pressures and temperatures will soon be achievable.
DI41A-0344
Self-Consistent Thermodynamic Description of Silicate Liquids
Describing the thermodynamic properties of dense liquids at extreme pressure and temperature is crucial to our understanding of planetary processes including deep melting, magma ocean dynamics and lunar formation. The functional form chosen to represent the equation of state should ideally depend on only a few parameters and correctly account for kinetic and electronic contributions to the free energy at extreme conditions. High pressure equation of state data for terrestrial liquids have mostly been fit to functional forms used for solids, such as the high temperature form of the Mie-Grüneisen equation, which assumes a constant thermal pressure coefficient (α KT). This approach is flawed since Maxwell relations require (∂ α KT / ∂ T)V = (∂ CV / ∂ V)T and we have found in first principles molecular dynamics studies of magnesiosilicate liquids at high pressure that the isochoric heat capacity (CV) varies significantly with volume. Moreover, the Mie-Grüneisen equation of state does not yield the correct (ideal gas) behavior in the limit of infinite temperature. Finally we have found that electronic contributions to thermodynamic properties are non-negligible. With these constraints in mind, we develop a number of approaches to expressing the Helmholtz potential over a large range of volume and temperature, including potential, kinetic and electronic contributions to the free energy. From these expressions for the fundamental relation, internally consistent equilibrium thermodynamic properties are derived by derivatives and Legendre transformations, which may be applied to the exploration of a large array of problems in planetary science.
DI41A-0345
Equation of state of MgSiO3-perovskite
In-situ X-ray diffraction measurements of MgSiO3-perovskite were performed in the pressure range of 27-61 GPa and temperature of 300-1500 K using Kawai-type multi-anvil apparatus with sintered diamond anvils, in a synchrotron radiation facility. Mg2SiO4-forsterite was used as a starting material, and MgSiO3-perovskite was synthesized during heating period. XRD measurements were carried out in cooling cycle of each experiment. Au was used as an internal pressure standard, which was mixed with the starting material. In addition, MgO was used another pressure standard, which was synthesized from the decomposition of the starting material. Temperature was successfully measured using W3Re-W25Re thermocouple in every experiment, and temperature fluctuations were less than 1 K for XRD measurements of 60 minutes. Errors in volume determination of each phase were about 0.5 %, and typical error in pressure calculation was 0.2 GPa. In this study, we can provide internally consistent and precisely determined P-V-T data set of MgSiO3-perovskite, MgO, and Au to mid lower mantle condition, which be a primary reference in the study of the lower mantle.
DI41A-0346
Lattice Dynamics and Thermal Equation of State of Platinum
Platinum is widely used as a pressure calibration standard for in situ high-pressure and high-temperature experiments. However, the isothermal EOS reduced from shock Hugoniot has uncertainties. It appears that it seriously overestimates pressure in the high pressure range. This has also been suggested by recent DAC experiments. We use density functional theory to calculate the thermal equation of state of platinum, up to 600 GPa and 5000K. The static lattice energy is computed by using the LAPW method, with LDA, PBE, and the recently proposed WC functional. The electronic thermal free energy is evaluated using the Mermin functional. The vibrational part is computed within the quasi-harmonic approximation using density functional perturbation theory and pseudopotentials. Special attention is paid to the influence of the electronic temperature to the phonon frequencies. A theoretical Hugoniot is obtained by solving the Rankine-Hugoniot equation. We find that in overall LDA results agree best with the experimental ones, while the new WC functional shows much improved results than PBE. After correcting the calculated equilibrium volume to the experimental one, the room temperature isothermal EOS agrees with the new DAC data, and confirms that the previous standard overestimates pressure. The calculated thermodynamic properties agree reasonably well with experiments. We further compare our thermal EOS with the previous ones based on empirical models. Research supported by NSF/EAR and NSF/ITR
DI41A-0347 INVITED
PVT relations in MgO: a ultra-high PT scale for planetary sciences applications
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 forbidding clear conclusions regarding the significance 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 by combining LDA quasiharmonic (QHA) calculations up to ultrahigh PTs and experimental data at moderately high PTs. Within the range of validity of the QHA the resulting EoSs agree very well with shock data. They have been used here to reinvestigate the post-spinel and post-perovskite transitions. Research supported by NSF/EAR and NSF/ITR (VLab)
DI41A-0348
Molybdenum and Tantalum at High Pressure and Temperature: Melting from Another Solid Phase
Considerable controversy exists as regards the interpretation of the melting of Mo and Ta in shock wave (SW) and diamond anvil cell (DAC) experiments. While SW experiments find a solid-solid phase transition in Mo, DAC experiments do not. We resolve this controversy by demonstrating from first principles phonon calculations within the quasiharmonic approximation that at higher pressure Mo, being stable in body-centered cubic (bcc) structure at low temperature, transforms into face centered cubic (fcc) structure on heating. This transformation occurs before melting, which is demonstrated by ab initio molecular dynamics (AIMD) simulations. Although Mo may not melt from fcc, if there is yet another more stable structure than fcc, Mo does certainly not melt from bcc. SW experiments in Ta suggest a solid-solid transformation before melting, as well as in Mo. Our AIMD simulations demonstrate that at higher pressure fcc is a more stable structure than bcc in Ta at high temperature, and therefore, like Mo, Ta does not melt from bcc. These findings suggest that DAC experiments do not correctly identify the high-pressure melting of both Mo and Ta.
DI41A-0349
Constraining Parameters of the Reciprocal K-Primed Equation of State Using Normal Modes
Most equations of state predict that K', the pressure derivative of bulk modulus, K, decreases with pressure, but there is considerable variation in the infinite pressure limit, K'infinity. Although this limit can never be attained physically, since phase transitions as pressure increases invalidates the use of a single EOS, K'infinity represents a fitting constant for EOS valid over pressure ranges where the material has constant phase. Thermodynamic arguments have been used to place constraints on K'infinity. The reciprocal K-primed equation of state RKp_EOS (GJI 143, 621-628, 2000; PEPI 142, 137-184, 2004) relates K' to the variation of P (normalized by K) by two parameters K'0 and K'infinity, with density, ρ, variation governed a third parameter, ρ0. It describes a smooth decrease of K' and ρ with pressure, and the limit satisfies the thermodynamic constraint, and so is useful for determining other thermodynamic parameters that require (smooth) higher order derivatives. The parameters of the RKp-EOS are determined by fitting to standard Earth models such as PREM. However the PREM K' variation does not exhibit smooth decrease in K' with P and so the fit has been through a widely fluctuating curve. This fluctuation not unexpected, as the PREM parameters were expressed in polynomial expansions of radial distance adjusted to fit seismic data with no constraints on smoothness of K'. In order to estimate the RKp_EOS parameters in the outer core, we use non-linear least squares to fit spheroidal mode frequencies using the PREM polynomial expansion in the mantle and inner core, but the RKp_EOS parameters in the outer core. The resulting constants give a core EOS that satisfies the mode data, the thermodynamic constraint, and smooth decrease of K' with P.