scholarly journals Thermal Equation of State of Fe3C to 327 GPa and Carbon in the Core

Minerals ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 744 ◽  
Author(s):  
Suguru Takahashi ◽  
Eiji Ohtani ◽  
Daijo Ikuta ◽  
Seiji Kamada ◽  
Tatsuya Sakamaki ◽  
...  
Keyword(s):  
High Temperature ◽  
Equation Of State ◽  
Inner Core ◽  
Velocity Structure ◽  
Light Element ◽  
Scale Model ◽  
Earth Model ◽  
Thermal Equation ◽  
The Core ◽  
Pressure Scale

The density and sound velocity structure of the Earth’s interior is modeled on seismological observations and is known as the preliminary reference Earth model (PREM). The density of the core is lower than that of pure Fe, which suggests that the Earth’s core contains light elements. Carbon is one plausible light element that may exist in the core. We determined the equation of state (EOS) of Fe3C based on in situ high-pressure and high-temperature X-ray diffraction experiments using a diamond anvil cell. We obtained the P–V data of Fe3C up to 327 GPa at 300 K and 70–180 GPa up to around 2300 K. The EOS of nonmagnetic (NM) Fe3C was expressed by two models using two different pressure scales and the third-order Birch–Murnaghan EOS at 300 K with the Mie–Grüneisen–Debye EOS under high-temperature conditions. The EOS can be expressed with parameters of V0 = 148.8(±1.0) Å3, K0 = 311.1(±17.1) GPa, K0′ = 3.40(±0.1), γ0 = 1.06(±0.42), and q = 1.92(±1.73), with a fixed value of θ0 = 314 K using the KBr pressure scale (Model 1), and V0 = 147.3(±1.0) Å3, K0 = 323.0(±16.6) GPa, K0′ = 3.43(±0.09), γ0 = 1.37(±0.33), and q = 0.98(±1.01), with a fixed value of θ0 = 314 K using the MgO pressure scale (Model 2). The density of Fe3C under inner core conditions (assuming P = 329 GPa and T = 5000 K) calculated from the EOS is compatible with the PREM inner core.

scholarly journals Thermal equation of state of cubic boron nitride: Implications for a high-temperature pressure scale

2007 ◽  
Vol 75 (22) ◽  
Author(s):  
Alexander F. Goncharov ◽  
Jonathan C. Crowhurst ◽  
John K. Dewhurst ◽  
Sangeeta Sharma ◽  
Chrystele Sanloup ◽  
...  
Keyword(s):  
High Temperature ◽  
Equation Of State ◽  
Boron Nitride ◽  
Cubic Boron Nitride ◽  
Thermal Equation ◽  
Thermal Equation Of State ◽  
Pressure Scale

Density and sound velocity of liquid Fe-S alloys at Earth's outer core P-T conditions

2020 ◽  
Vol 105 (9) ◽  
pp. 1349-1354
Author(s):  
Jie Fu ◽  
Lingzhi Cao ◽  
Xiangmei Duan ◽  
Anatoly B. Belonoshko
Keyword(s):  
Sound Velocity ◽  
Inner Core ◽  
Light Element ◽  
Outer Core ◽  
Earth Model ◽  
Thermal Equation ◽  
Fundamental Parameters ◽  
Core Boundary ◽  
Core Conditions ◽  
Dynamics Simulations

Abstract Pressure-temperature-volume (P-T-V) data on liquid iron-sulfur (Fe-S) alloys at the Earth's outer core conditions (~136 to 330 GPa, ~4000 to 7000 K) have been obtained by first-principles molecular dynamics simulations. We developed a thermal equation of state (EoS) composed of Murnaghan and Mie-Grüneisen-Debye expressions for liquid Fe-S alloys. The density and sound velocity are calculated and compared with Preliminary Reference Earth Model (PREM) to constrain the S concentration in the outer core. Since the temperature at the inner core boundary (TICB) has not been measured precisely (4850~7100 K), we deduce that the S concentration ranges from 10~14 wt% assuming S is the only light element. Our results also show that Fe-S alloys cannot satisfy the seismological density and sound velocity simultaneously and thus S element is not the only light element. Considering the geophysical and geochemical constraints, we propose that the outer core contains no more than 3.5 wt% S, 2.5 wt% O, or 3.8 wt% Si. In addition, the developed thermal EoS can be utilized to calculate the thermal properties of liquid Fe-S alloys, which may serve as the fundamental parameters to model the Earth's outer core.

scholarly journals Thermal Analysis, Compressibility, and Decomposition of Synthetic Bastnäsite-(La) to Lanthanum Oxyfluoride

Minerals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 212
Author(s):  
Richard L. Rowland ◽  
Barbara Lavina ◽  
Kathleen E. Vander Kaaden ◽  
Lisa R. Danielson ◽  
Pamela C. Burnley
Keyword(s):  
High Temperature ◽  
Equation Of State ◽  
Ambient Temperature ◽  
Evolved Gas Analysis ◽  
Ambient Pressure ◽  
Basic Material ◽  
X Ray Diffraction ◽  
Scanning Calorimetry ◽  
Thermal Equation ◽  
X Ray

Understanding basic material properties of rare earth element (REE) bearing minerals such as their phase stability and equations of state can assist in understanding how economically viable deposits might form. Bastnäsite is the most commonly mined REE bearing mineral. We synthesized the lanthanum-fluoride end member, bastnäsite-(La) (LaCO3F), and investigated its thermal behavior and decomposition products from 298 K to 1173 K under ambient pressure conditions through thermogravimetric analysis, differential scanning calorimetry, evolved gas analysis, and high temperature powder X-ray diffraction. We also investigated the compressibility of bastnäsite-(La) via single crystal X-ray diffraction in diamond anvil cells at an ambient temperature up to 11.3 GPa and from 4.9 GPa to 7.7 GPa up to 673 K. At ambient pressure, bastnäsite-(La) was stable up to 598 K in air, where it decomposed into CO2 and tetragonal γ-LaOF. Above 948 K, cubic α-LaOF is stable. High temperature X-ray diffraction data were used to fit the Fei thermal equation of state and the thermal expansion coefficient α298 for all three materials. Bastnäsite-(La) was fit from 298 K to 723 K with V0 = 439.82 Å3, α298 = 4.32 × 10−5 K−1, a0 = −1.68 × 10−5 K−1, a1 = 8.34 × 10−8 K−1, and a2 = 3.126 K−1. Tetragonal γ-LaOF was fit from 723 K to 948 K with V0 = 96.51 Å3, α298 = 2.95×10−4 K−1, a0 = −2.41×10−5 K−1, a1 = 2.42×10−7 K−1, and a2 = 41.147 K−1. Cubic α-LaOF was fit from 973 K to 1123 K with V0 = 190.71 Å3, α298 = −1.12×10−5 K−1, a0 = 2.36×10−4 K−1, a1 = −1.73 × 10−7 K−1, and a2 = −17.362 K−1. An ambient temperature third order Birch–Murnaghan equation of state was fit with V0 = 439.82 Å3, K0 = 105 GPa, and K’ = 5.58.

scholarly journals Axial Compressibility and Thermal Equation of State of Hcp Fe–5wt% Ni–5wt% Si

Minerals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 98
Author(s):  
Eric Edmund ◽  
Francesca Miozzi ◽  
Guillaume Morard ◽  
Eglantine Boulard ◽  
Alisha Clark ◽  
...  
Keyword(s):  
Equation Of State ◽  
Ambient Temperature ◽  
Inner Core ◽  
Equations Of State ◽  
Axial Ratio ◽  
Seismic Velocities ◽  
X Ray Diffraction ◽  
Thermal Equation ◽  
Planetary Cores ◽  
Ni Addition

Knowledge of the elastic properties and equations of state of iron and iron alloys are of fundamental interest in Earth and planetary sciences as they are the main constituents of telluric planetary cores. Here, we present results of X-ray diffraction measurements on a ternary Fe–Ni–Si alloy with 5 wt% Ni and 5 wt% Si, quasi-hydrostatically compressed at ambient temperature up to 56 GPa, and under simultaneous high pressure and high temperature conditions, up to 74 GPa and 1750 K. The established pressure dependence of the c/a axial ratio at ambient temperature and the pressure–volume–temperature (P–V–T) equation of state are compared with previous work and literature studies. Our results show that Ni addition does not affect the compressibility and axial compressibility of Fe–Si alloys at ambient temperature, but we suggest that ternary Fe–Ni–Si alloys might have a reduced thermal expansion in respect to pure Fe and binary Fe–Si alloys. In particular, once the thermal equations of state are considered together with velocity measurements, we conclude that elements other than Si and Ni have to be present in the Earth’s inner core to account for both density and seismic velocities.

Dynamics of the liquid core of the Earth

1972 ◽  
Vol 273 (1233) ◽  
pp. 237-260 ◽  
Keyword(s):  
Boundary Layer ◽  
Inner Core ◽  
Liquid Core ◽  
Stable Stratification ◽  
Earth Model ◽  
Unstable Stratification ◽  
The Core ◽  
Long Period ◽  
Love Numbers ◽  
Neutral Equilibrium

An asymptotic theory is developed for the long-period bodily tides in an Earth model having a liquid core. The yielding inside the core is found to be different in the case of a stable density stratification from the case of an unstable stratification. In the latter case, a boundary layer is formed in which the stress decreases exponentially with depth below the core surface, the scale length of the exponent being proportional to the frequency. In the limit of vanishing frequency the stress tends to zero through most of the liquid core, except near the boundary layer at the surface, where it grows to a finite value. In case of a stable stratification, the stress oscillates with depth below the surface of the core with a wavelength which is proportional to frequency. An infinite number of 'core oscillations' with indefinitely increasing periods exist in a liquid core with stable stratification, but in the case of an unstable stratification, none exist above the fundamental spheroidal oscillation (53.7 min) for n — 2. The assertion made that a liquid core must be in neutral equilibrium is not true. The displacements and stresses within a liquid core in long-period tidal yielding are determinate, even in the static limit, and are not arbitrary. Love numbers are derived for uniformly stable, neutral, and unstable liquid cores, as well as for a model with a rigid inner core.

scholarly journals Delamination in Tibet: Deriving constraints from the density of eclogite

2021 ◽  
Author(s):  
Zhilin Ye ◽  
Dawei Fan ◽  
Bo Li ◽  
Qizhe Tang ◽  
Jingui Xu ◽  
...  
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Equation Of State ◽  
Lower Crust ◽  
Gravitational Instability ◽  
Volume Data ◽  
Thermal Equation ◽  
Pressure Derivative ◽  
Temperature Conditions ◽  
Slab Breakoff

Abstract. Tibet, which is characterized by collisional orogens, has undergone the process of delamination or convective removal. The lower crust and mantle lithosphere appear to have been removed through delamination during orogenic development. Numerical and analog experiments demonstrate that the metamorphic eclogitized oceanic subduction slab or lower crust may promote gravitational instability due to its increased density. The eclogitized oceanic subduction slab or crustal root is believed to be denser than the underlying mantle and tends to sink. However, the density of eclogite under high-pressure and high-temperature conditions and density differences from the surrounding mantle is not preciously constrained. Here, we offer new insights into the derivation of eclogite density with a single experiment to constrain delamination in Tibet. Using in situ synchrotron X-ray diffraction combined with diamond anvil cell, experiments focused on minerals (garnet, omphacite, and epidote) of eclogite are conducted under simultaneous high-pressure and high-temperature conditions, which avoids systematic errors. Fitting the pressure-temperature-volume data with the third-order Birch-Murnaghan equation of state, the thermal equation of state (EoS) parameters, including the bulk modulus (KT0), its pressure derivative (KT0′), the temperature derivative ((KT/T)P), and the thermal expansion coefficient (α0), are derived. The densities of rock-forming minerals and eclogite are modeled along with the geotherms of two types of delamination. The delamination processes of subduction slab breakoff and the removal of the eclogitized lower crust in Tibet are discussed. The Tibetan eclogite which containing 40–60 vol. % garnet and 37–64 % degrees of eclogitization can promote the delamination of slab break-off in Tibet. Our results indicate that eclogite is a major controlling factor in the initiation of delamination. A high abundance of garnet, a high Fe-content, and a high degree of eclogitization are more conducive to instigating the delamination.

scholarly journals Constraints on Earth’s inner core composition inferred from measurements of the sound velocity of hcp-iron in extreme conditions

2016 ◽  
Vol 2 (2) ◽  
pp. e1500802 ◽  
Author(s):  
Tatsuya Sakamaki ◽  
Eiji Ohtani ◽  
Hiroshi Fukui ◽  
Seiji Kamada ◽  
Suguru Takahashi ◽  
...  
Keyword(s):  
Sound Velocity ◽  
Inner Core ◽  
Earth Model ◽  
Light Elements ◽  
Earth’S Core ◽  
Heated Sample ◽  
Earth's Core ◽  
The Core ◽  
Core Composition ◽  
Earth’S Inner Core

Hexagonal close-packed iron (hcp-Fe) is a main component of Earth’s inner core. The difference in density between hcp-Fe and the inner core in the Preliminary Reference Earth Model (PREM) shows a density deficit, which implies an existence of light elements in the core. Sound velocities then provide an important constraint on the amount and kind of light elements in the core. Although seismological observations provide density–sound velocity data of Earth’s core, there are few measurements in controlled laboratory conditions for comparison. We report the compressional sound velocity (VP) of hcp-Fe up to 163 GPa and 3000 K using inelastic x-ray scattering from a laser-heated sample in a diamond anvil cell. We propose a new high-temperature Birch’s law for hcp-Fe, which gives us the VP of pure hcp-Fe up to core conditions. We find that Earth’s inner core has a 4 to 5% smaller density and a 4 to 10% smaller VP than hcp-Fe. Our results demonstrate that components other than Fe in Earth’s core are required to explain Earth’s core density and velocity deficits compared to hcp-Fe. Assuming that the temperature effects on iron alloys are the same as those on hcp-Fe, we narrow down light elements in the inner core in terms of the velocity deficit. Hydrogen is a good candidate; thus, Earth’s core may be a hidden hydrogen reservoir. Silicon and sulfur are also possible candidates and could show good agreement with PREM if we consider the presence of some melt in the inner core, anelasticity, and/or a premelting effect.

scholarly journals The Effect of General Relativity and Equation of State on the Adiabatic Collapse and Explosion of a Stellar Core

1988 ◽  
Vol 108 ◽  
pp. 417-419
Author(s):  
N. Sack ◽  
I. Lichtenstadt
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Inner Core ◽  
Massive Stars ◽  
Iron Core ◽  
Nuclear Density ◽  
Type Ii ◽  
Velocity Difference ◽  
Initial Strength ◽  
The Core

The collapse of the iron core of massive stars ( M ≥ 8 MO) is initiated by photodissociation and electron capture. The collapse of the inner core proceeds homologously until it is stopped by the stiffness of the equation of state (hereafter EOS) at nuclear density and it stops or rebounds. A shock forms at the edge of homology. The initial strength of the shock increases with the velocity difference between the inner and outer cores, i.e. it increases with a larger rebound of the inner core. The uniterrupted propagation of this prompt shock through the remainder of the core to the stellar mantle, where it can deliver enough energy to blow off the loosely bound outer layers, has long been proposed as the mechanism of type II supernovae explosions. However most authors did not get an explosion as a result of the prompt mechanism. Recently Baron et al. (1985) reported that the combination of General Relativity (GR) with a relatively soft EOS at nuclear densities leads to a much greater blow off than they got with Newtonian hydrodynamics. In order to see where purely hydrodynamical effects are important, namely for what EOS the GR outburst is greater than the Newtonian, we did a set of pure hydrodynamical adiabatic calculations (complete neutrino trapping) with different EOS above nuclear densities, turning the GR terms on and off. Neutrino leakage, which we do not incorporate, usually leads to harmful energy losses.

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