The Earth's core and the phase diagram of iron

1982 ◽  
Vol 306 (1492) ◽  
pp. 21-35 ◽  
Keyword(s):  
Shock Wave ◽  
Phase Diagram ◽  
Inner Core ◽  
Temperature Drop ◽  
Melting Curve ◽  
Outer Core ◽  
Melting Point Depression ◽  
The Core ◽  
Wave Measurements ◽  
Thermally Driven

The phase diagram of iron is presented for P < 330 GPa. The melting curve is derived from Stevenson’s generalized form of Lindemann’s law, successfully connecting the low-pressure (5-20 GPa) measurements to the new shock-wave measurements of 250 GPa. The isothermal equation of state of e-iron (h.c.p.) and y-iron (f.c.c.), indicate that the inner core density is that of pure solid iron. The present experiments cannot distinguish between the e or y phase for the inner core, but preference is given to y-iron. From these constructions, it is concluded that the melting temperature of iron at the inner core - outer core boundary pressure, T (i.c.b.), is 5200-6600 K. A likely model of the outer core temperature is presented by taking 5800 K as the probable value of T (i.c.b.), and assuming a temperature drop of 1000 K due to chemically induced melting point depression. This yields 3620 K for the T of the core side of the core-mantle boundary (c.m.b.). This model results in a large AjT(D"), (700 K), at the c.m.b., but the shock-wave data also allow other models where A!T(D") is less. A numerical experiment reveals that the value for A T(D") of 700 K does not lead to distortion of the density profile. The (y-8-liquid) triple point is beyond the i.c.b. Thus, diluted y-iron in the liquid phase constitutes the outer core. The experiments support a thermally driven model of the geomagnetic dynamo, and further support a model of a slowly freezing inner core for the energy source.

scholarly journals High Pressure and High Temperature Equation-of-State of Gamma and Liquid Iron

1997 ◽  
Vol 499 ◽  
Author(s):  
George Q. Chen ◽  
Thomas J. Ahrens
Keyword(s):  
Shock Wave ◽  
Equation Of State ◽  
Sound Velocity ◽  
Liquid Iron ◽  
Inner Core ◽  
Melting Curve ◽  
Outer Core ◽  
Pressure Derivative ◽  
Longitudinal Sound Velocity ◽  
Core Boundary

ABSTRACTShock-wave experiments on pure iron preheated to 1573 K were conducted in the 17–73 GPa range. The shock-wave equation of state of γ-iron at an initial temperature of 1573 K can be fit with us = 4.102 (0.015) km/s + 1.610(0.014) up with ρo = 7.413±0.012 Mg/m3 We obtain for γ-iron's bulk modulus and pressure derivative the values: 124.7±1.1 GPa and 5.44±0.06, respectively.We present new data for sound velocities in the γ- and liquid-phases. In the γ-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = −3.13 (0.72) + 1.119(0.084) p(units for Vp and p are km/s and Mg/m3, respectively). Melting was observed in the highest pressure (about 70–73 GPa) experiments at a calculated shock temperature of 2775±160 K. This result is consistent with a previously calculated melting curve (for ε-iron) which is close to those measured by Boehler [1] and Saxena et al. [2]. The liquid iron sound velocity data yields a Grüneisen parameter value of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity γρ is 15.2±2.6 Mg/m3, which agrees with the uncertainty bounds of Brown and McQueen [3] (13.3–19.6 Mg/m3). Based on upward pressure and temperature extrapolation of the melting curve of γ-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is 3930±630 K.

Thermodynamics from first principles: temperature and composition of the Earth’s core

2003 ◽  
Vol 67 (1) ◽  
pp. 113-123 ◽  
Author(s):  
D. Alfé ◽  
M. J. Gillan ◽  
G. D. Price
Keyword(s):  
Melting Temperature ◽  
First Principles ◽  
Inner Core ◽  
Melting Curve ◽  
Outer Core ◽  
Earth’S Core ◽  
Earth's Core ◽  
The Core ◽  
Core Conditions ◽  
Main Ideas

AbstractWe summarize the main ideas used to determine the thermodynamic properties of pure systems and binary alloys from first principles calculations. These are based on the ab initio calculations of free energies. As an application we present the study of iron and iron alloys under Earth,s core conditions. In particular, we report the whole melting curve of iron under these conditions, and we put constraints on the composition of the core. We found that iron melts at 6350士600 K at the pressure corresponding to the boundary between the solid inner core and the liquid outer core (ICB). We show that the core could not have been formed from a binary mixture of Fe with S, Si or O and we propose a ternary or quaternary mixture with 8—10% of S/Si in both liquid and solid and an additional ~8% of oxygen in the liquid. Based on this proposed composition we calculate the shift of melting temperature with respect to the melting temperature of pure Fe of ~—700 K, so that our best estimate for the temperature of the Earth's core at ICB is 5650±600 K.

Adiabatic Heat Flow in Mercury with a Fe-8.5wt%Si Core

2021 ◽  
Author(s):  
Meryem Berrada ◽  
Richard Secco ◽  
Wenjun Yong
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Internal Structure ◽  
High Pressures ◽  
Inner Core ◽  
Thermal Evolution ◽  
The Core ◽  
Thermally Driven ◽  
Wire Method ◽  
Core Conditions

&lt;p&gt;Recent theoretical studies have tried to constrain Mercury&amp;#8217;s internal structure and composition using thermal evolution models. The presence of a thermally stratified layer of Fe-S at the top of an Fe-Si core has been suggested, which implies a sub-adiabatic heat flow on the core side of the CMB. In this work, the adiabatic heat flow at the top of the core was estimated using the electronic component of thermal conductivity (k&lt;sub&gt;el&lt;/sub&gt;), a lower bound for thermal conductivity. Direct measurements of electrical resistivity (&amp;#961;) of Fe-8.5wt%Si at core conditions can be related to k&lt;sub&gt;el&lt;/sub&gt; using the Wiedemann-Franz law. Measurements were carried out in a 3000 ton multi-anvil press using a 4-wire method. The integrity of the samples at high pressures and temperatures was confirmed with electron-microprobe analysis of quenched samples at various conditions. Unexpected behaviour at low temperatures between 6-8 GPa may indicate an undocumented phase transition. Measurements of &amp;#961; at melting seem to remain constant at 127 &amp;#181;&amp;#937;&amp;#183;cm from 10-24 GPa, on both the solid and liquid side of the melting boundary. The adiabatic heat flow at the core side of Mercury&amp;#8217;s core-mantle boundary is estimated between 21.8-29.5 mWm&lt;sup&gt;-2&lt;/sup&gt;, considerably higher than most models of an Fe-S or Fe-Si core yet similar to models of an Fe core. Comparing these results with thermal evolution models suggests that Mercury&amp;#8217;s dynamo remained thermally driven up to 0.08-0.22 Gyr, at which point the core became sub-adiabatic and stimulated a change from dominant thermal convection to dominant chemical convection arising from the growth of an inner core. Simply considering the internal structure of Mercury, these results support the capture of Mercury into a 3:2 resonance orbit during the thermally driven era of the dynamo.&lt;/p&gt;

Multiple inner core reflections from a Novaya Zemlya explosion

1972 ◽  
Vol 62 (4) ◽  
pp. 1063-1071 ◽  
Author(s):  
R. D. Adams
Keyword(s):  
Lower Bound ◽  
Inner Core ◽  
Nuclear Explosion ◽  
Outer Core ◽  
Low Velocity ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
Novaya Zemlya ◽  
The Core ◽  
Velocity Channel

Abstract The phases P2KP, P3KP, and P4KP are well recorded from the Novaya Zemlya nuclear explosion of October 14, 1970, with the branch AB at distances of up to 20° beyond the theoretical end point A. This extension is attributed to diffraction around the core-mantle boundary. A slowness dT/dΔ = 4.56±0.02 sec/deg is determined for the AB branch of P4KP, in excellent agreement with recent determinations of the slowness of diffracted P. This slowness implies a velocity of 13.29±0.06 km/sec at the base of the mantle, and confirms recent suggestions of a low-velocity channel above the core-mantle boundary. There is evidence that arrivals recorded before the AB branch of P2KP may lie on two branches, with different slownesses. The ratio of amplitudes of successive orders of multiple inner core reflections gives a lower bound of about 2200 for Q in the outer core.

Analytical Evaluation of Core Bowing Reactivity in the 4S Reactor

2009 ◽  
Author(s):  
Satoshi Nishimura ◽  
Hirokazu Ohta ◽  
Nobuyuki Ueda
Keyword(s):  
Fast Reactor ◽  
Radial Displacement ◽  
Inner Core ◽  
Structural Characteristics ◽  
Outer Core ◽  
Radial Expansion ◽  
Neutron Absorption ◽  
Analytical Evaluation ◽  
Life Condition ◽  
The Core

The 4S (super-safe, small and simple) reactor is a sodium-cooled small fast reactor. The core reactivity is controlled by moving the reflectors installed around the core, and the reactor has a fixed absorber at the core center to accomplish a long core lifetime. To evaluate core bowing behavior and the resulting reactivity feedback in the 4S reactor, an analytical evaluation was conducted under various core power to flow ratios (P/F). The core bowing reactivity under the BOC (beginning of core life) condition becomes increasingly negative with increasing P/F up to 2.0, then becomes less negative with increasing P/F from 2.0 to 3.0, and finally becomes positive at P/F = 3.0. The bowing reactivity under the EOC (end of core life) condition becomes increasingly negative with increasing P/F up to 1.5, then becomes less negative then positive with increasing P/F from 1.5 to 3.0; the core bowing reactivity is positive when P/F ≥ 2.0. These results are mainly caused by the following two mechanisms originating from the structural characteristics of the 4S reactor: - a decrease in neutron absorption by the fixed absorber due to the radial displacement of the inner core subassemblies (under the BOC condition); - a decrease in neutron streaming caused by the small gaps between the outer core subassemblies and the reflectors due to core radial expansion (under the EOC condition).

Viscous drag and the differential rotation of the Earth's core

1997 ◽  
Vol 57 (1) ◽  
pp. 231-233
Author(s):  
DAVID L. BOOK ◽  
J. A. VALDIVIA
Keyword(s):  
Simple Model ◽  
Differential Rotation ◽  
Dynamic Viscosity ◽  
Inner Core ◽  
Outer Core ◽  
Viscous Drag ◽  
Earth’S Rotation ◽  
The Core ◽  
The Earth ◽  
Earth’S Inner Core

It is proposed that the differential rotation of the Earth's inner core deduced by Song and Richards is due to a combination of the deceleration of the Earth's rotation and the viscous drag between the Earth's inner and outer cores. If this model is correct then the dynamic viscosity in the outer core of the Earth can be estimated to be μ≈104 poise. Besides providing a novel way of determining the viscosity of the core, this simple model suggests some new tests and shows how astronomical effects can influence geological phenomena.

scholarly journals Analysis of the Structure and Biosynthesis of the Lipopolysaccharide Core Oligosaccharide of Pseudomonas syringae pv. tomato DC3000

2021 ◽  
Vol 22 (6) ◽  
pp. 3250
Author(s):  
Alexander Kutschera ◽  
Ursula Schombel ◽  
Dominik Schwudke ◽  
Stefanie Ranf ◽  
Nicolas Gisch
Keyword(s):  
Pseudomonas Syringae ◽  
Species Complex ◽  
Inner Core ◽  
Divalent Cations ◽  
Membrane Integrity ◽  
Outer Core ◽  
Core Oligosaccharide ◽  
Structure Information ◽  
The Core ◽  
Genetic Components

Lipopolysaccharide (LPS), the major component of the outer membrane of Gram-negative bacteria, is important for bacterial viability in general and host–pathogen interactions in particular. Negative charges at its core oligosaccharide (core-OS) contribute to membrane integrity through bridging interactions with divalent cations. The molecular structure and synthesis of the core-OS have been resolved in various bacteria including the mammalian pathogen Pseudomonas aeruginosa. A few core-OS structures of plant-associated Pseudomonas strains have been solved to date, but the genetic components of the underlying biosynthesis remained unclear. We conducted a comparative genome analysis of the core-OS gene cluster in Pseudomonas syringae pv. tomato (Pst) DC3000, a widely used model pathogen in plant–microbe interactions, within the P. syringae species complex and to other plant-associated Pseudomonas strains. Our results suggest a genetic and structural conservation of the inner core-OS but variation in outer core-OS composition within the P. syringae species complex. Structural analysis of the core-OS of Pst DC3000 shows an uncommonly high phosphorylation and presence of an O-acetylated sugar. Finally, we combined the results of our genomic survey with available structure information to estimate the core-OS composition of other Pseudomonas species.

scholarly journals Incommensurate Crystallization of Neutron Matter in Neutron Stars

2020 ◽  
Keyword(s):  
Neutron Star ◽  
Neutron Stars ◽  
Specific Heat ◽  
Inner Core ◽  
Surface Region ◽  
Outer Core ◽  
Neutron Matter ◽  
High Mass ◽  
The Core ◽  
Gravitational Stress

The composition of the neutron stars from its surface region, outer-core, inner-core, and to its center is still being investigated. One can only surmise on the properties of neutron stars from the spectroscopic data that may be available from time to time. A few models have suggested that the matter at the surface region of the neutron star is composed of atomic nuclei that get crushed under extremely large pressure and gravitational stress, and this leads to the creation of solid lattice with a sea of electrons, and perhaps some protons, flowing through the gaps between them. Nuclei with high mass numbers, such as ferrous, gold, platinum, uranium, may exist in the surface region or in the outer-core region. It is found that the structure of the neutron star changes very much as one goes from the surface to the core of the neutron star. The surface region is extremely hard and very smooth. Surface irregularities are hardly of the order of 5 mm, whereas the interior of the neutron star may be superfluid and composed of neutron-degenerate matter. However, the neutron star is highly compact crystalline systems, and in terrestrial materials under pressure, many examples of incommensurate phase transitions have been discovered. Consequently, the properties of incommensurate crystalline neutron star have been studied. The composition of the neutron stars in the super dense state remains uncertain in the core of the neutron star. One model describes the core as superfluid neutron-degenerate matter, mostly, composed of neutrons , and a small percentage of protons and electrons More exotic forms of matter are possible, including degenerate strange matter. It could also be incommensurate crystalline neutron matter that could be BCC or HCP. Using principles of quantum statistical mechanics, the specific heat and entropy of the incommensurate crystalline neutron star has been calculated assuming that the temperature of the star may vary between to . Two values for the temperature T that have been arbitrarily chosen for which the calculations have been done are and . The values of specific heat and entropy decrease as the temperature increases, and also, their magnitudes are very small. This is in line with the second law of thermodynamics.

The constitution of the core: seismological evidence

1982 ◽  
Vol 306 (1492) ◽  
pp. 11-20 ◽  
Keyword(s):  
Inner Core ◽  
Outer Core ◽  
Body Waves ◽  
P Wave ◽  
Necessary Condition ◽  
Strong Increase ◽  
Linear Perturbation ◽  
The Core ◽  
Rate Of Increase ◽  
Seismic Quality Factor

The present best estimates of seismic velocities in the core are compared with the 1939 solution of Jeffreys, with emphasis on the remaining uncertainties and present resolution capability. The relative contributions of measurements of seismic body waves and terrestrial eigenspectra to the inverse problem of the determination of elastic parameters, density and damping in the core are compared. Linear perturbation algorithms and smoothing functions used with the spectral data reduce their capacity for fine structural definition. Between radii of 1400 and 3300 km (shell E), the outer core appears to be substantially homogeneous and non-stratified, with small or zero rigidity and a dimensionless seismic quality factor, Q ,of order 10 4 . It is a sufficient but still not a necessary condition that density p follows precisely the Adams-Williamson equation in E; for an averaging interval of 400 km, estimates of have a standard error there of about 0.2 g cm -3 . There is as yet no unequivocal seismological evidence for or against a boundary shell (thickness less than about 200 km) at the top of the liquid outer core. At the bottom of the outer core, the evidence is becoming stronger that any reduction in the rate of increase with depth of P wave velocity is confined to a minor transition layer little more than 100 km thick. The inner core has a sharp outer boundary at about 1216 km radius, but below it only average physical properties are estimated with any confidence. The average seismic compressions and shear velocities are about — 11.2 and /? — 3.5 km s -1 and 12.5 < p < 13.6 g cm-3, yielding a peculiar mean Poisson ratio of 0.44 or greater. At the inner core boundary, jumps in parameters are: A « 0.65, A/? — 2.0- 3.0 km s-1 and A p» 1.0 g cm -3 . Recent travel-time and waveform synthetics suggest a strong increase of P (and perhaps S) velocity in the upper 300 km of the inner core, which could be interpreted as a mixing or melting effect. Damping properties in the inner core may have an unusual dependence on wave frequency with an order of magnitude increase in Q from 1 Hz to 4 mHz vibrations.

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