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

<p>Recent theoretical studies have tried to constrain Mercury’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<sub>el</sub>), a lower bound for thermal conductivity. Direct measurements of electrical resistivity (ρ) of Fe-8.5wt%Si at core conditions can be related to k<sub>el</sub> 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 ρ at melting seem to remain constant at 127 µΩ·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’s core-mantle boundary is estimated between 21.8-29.5 mWm<sup>-2</sup>, 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’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.</p>

The Thermal Conductivity of Earth's Core: A Key Geophysical Parameter's Constraints and Uncertainties

2018 ◽  
Vol 46 (1) ◽  
pp. 47-66 ◽  
Author(s):  
Q. Williams
Keyword(s):  
Thermal Conductivity ◽  
High Pressures ◽  
Inner Core ◽  
Thermal Evolution ◽  
Magnetic Moments ◽  
Earth’S Core ◽  
Earth's Core ◽  
Current State ◽  
Core Conditions

The thermal conductivity of iron alloys at high pressures and temperatures is a critical parameter in governing ( a) the present-day heat flow out of Earth's core, ( b) the inferred age of Earth's inner core, and ( c) the thermal evolution of Earth's core and lowermost mantle. It is, however, one of the least well-constrained important geophysical parameters, with current estimates for end-member iron under core-mantle boundary conditions varying by about a factor of 6. Here, the current state of calculations, measurements, and inferences that constrain thermal conductivity at core conditions are reviewed. The applicability of the Wiedemann-Franz law, commonly used to convert electrical resistivity data to thermal conductivity data, is probed: Here, whether the constant of proportionality, the Lorenz number, is constant at extreme conditions is of vital importance. Electron-electron inelastic scattering and increases in Fermi-liquid-like behavior may cause uncertainties in thermal conductivities derived from both first-principles-associated calculations and electrical conductivity measurements. Additional uncertainties include the role of alloying constituents and local magnetic moments of iron in modulating the thermal conductivity. Thus, uncertainties in thermal conductivity remain pervasive, and hence a broad range of core heat flows and inner core ages appear to remain plausible.

On the possibility of anisotropic heat flow in the inner core

2001 ◽  
Vol 38 (6) ◽  
pp. 975-982 ◽  
Author(s):  
R A Secco ◽  
P S Balog
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
High Temperature ◽  
Heat Flow ◽  
Seismic Anisotropy ◽  
Inner Core ◽  
Elevated Pressure ◽  
Conductivity Anisotropy ◽  
Anisotropic Thermal Conductivity ◽  
Thermally Driven

We consider the possibility of anisotropic heat flow in the inner core by examining the potential for anisotropic thermal conductivity of hexagonal close-packed (hcp-)Fe. Because hcp-Fe exists only at pressures above 13 GPa at room temperature, we investigate thermal conductivity anisotropy in analog material Gd by measuring the electrical conductivity and applying the Wiedemann–Franz Law to determine thermal conductivity (k). The electrical conductivity anisotropy of Gd was measured at pressures up to 1.4 GPa and temperatures up to 873 K in the hcp phase range. At elevated pressure, the variation with temperature of anisotropic thermal conductivity of Gd single crystal resembles the anisotropic behavior at high temperature and 1 atm observed in earlier work. The temperature range of anisotropy of thermal conductivity of Gd, where kc > ka, is extended by pressure, but the anisotropy disappears before the high temperature hcp[Formula: see text]bcc (body-centered cubic) transformation. Our results on hcp-Gd lead us to raise the question of the possibility of hcp-Fe exhibiting anisotropy of thermal conductivity. Together with the known seismic anisotropy of the inner core, and the inferred textural alignment of hcp crystals causing it, we suggest some implications that an anisotropy of thermal conductivity of hcp-Fe, and a concomitant anisotropy of inner core heat flow, could have on thermally driven core processes.

scholarly journals Mantle-induced temperature anomalies do not reach the inner core boundary

2019 ◽  
Vol 219 (Supplement_1) ◽  
pp. S21-S32 ◽  
Author(s):  
Christopher J Davies ◽  
Jon E Mound
Keyword(s):  
Heat Flow ◽  
Numerical Simulations ◽  
Inner Core ◽  
Liquid Core ◽  
Temperature Variations ◽  
Temperature Anomalies ◽  
Longitudinal Temperature ◽  
Core Boundary ◽  
Core Conditions ◽  
Heat Flow Variations

SUMMARY Temperature anomalies in Earth’s liquid core reflect the vigour of convection and the nature and extent of thermal core–mantle coupling. Numerical simulations suggest that longitudinal temperature anomalies forced by lateral heat flow variations at the core–mantle boundary (CMB) can greatly exceed the anomalies that arise in homogeneous convection (i.e. with no boundary forcing) and may even penetrate all the way to the inner core boundary. However, it is not clear whether these simulations access the relevant regime for convection in Earth’s core, which is characterized by rapid rotation (low Ekman number E) and strong driving (high Rayleigh number Ra). We access this regime using numerical simulations of non-magnetic rotating convection with imposed heat flow variations at the outer boundary (OB) and investigate the amplitude and spatial pattern of thermal anomalies, focusing on the inner and outer boundaries. The 108 simulations cover the parameter range 10−4 ≤ E ≤ 10−6 and Ra = 1−800 times the critical value. At each Ra and E we consider two heat flow patterns—one derived from seismic tomography and the hemispheric $Y_1^1$ spherical harmonic pattern—with amplitudes measured by the parameter q⋆ = 2.3, 5 as well as the case of homogeneous convection. At the OB the forcing produces strong longitudinal temperature variations that peak in the equatorial region. Scaling relations suggest that the longitudinal variations are weakly dependent on E and Ra and are much stronger than in homogeneous convection, reaching O(1) K at core conditions if q⋆ ≈ 35. At the inner boundary, latitudinal and longitudinal temperature variations depend weakly on Ra and q⋆ and decrease strongly with E, becoming practically indistinguishable between homogeneous and heterogeneous cases at E = 10−6. Interpreted at core conditions our results suggest that heat flow variations on the CMB are unlikely to explain the large-scale variations observed by seismology at the top of the inner core.

scholarly journals Stability of body-centered cubic iron–magnesium alloys in the Earth's inner core

2009 ◽  
Vol 106 (37) ◽  
pp. 15560-15562 ◽  
Author(s):  
Krisztina Kádas ◽  
Levente Vitos ◽  
Börje Johansson ◽  
Rajeev Ahuja
Keyword(s):  
Inner Core ◽  
The Body ◽  
Mg Alloys ◽  
Functional Study ◽  
Body Centered Cubic ◽  
Calculated Density ◽  
The Core ◽  
Earth’S Inner Core ◽  
Core Conditions ◽  
Bcc Phase

The composition and the structure of the Earth's solid inner core are still unknown. Iron is accepted to be the main component of the core. Lately, the body-centered cubic (bcc) phase of iron was suggested to be present in the inner core, although its stability at core conditions is still in discussion. The higher density of pure iron compared with that of the Earth's core indicates the presence of light element(s) in this region, which could be responsible for the stability of the bcc phase. However, so far, none of the proposed composition models were in full agreement with seismic observations. The solubility of magnesium in hexagonal Fe has been found to increase significantly with increasing pressure, suggesting that Mg can also be an important element in the core. Here, we report a first-principles density functional study of bcc Fe–Mg alloys at core pressures and temperatures. We show that at core conditions, 5–10 atomic percent Mg stabilizes the bcc Fe both dynamically and thermodynamically. Our calculated density, elastic moduli, and sound velocities of bcc Fe–Mg alloys are consistent with those obtained from seismology, indicating that the bcc-structured Fe–Mg alloy is a possible model for the Earth's inner core.

scholarly journals Thermal Convection in the Core of Ganymede Inferred from Liquid Eutectic Fe-FeS Electrical Resistivity at High Pressures

Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 875
Author(s):  
Joshua A. H. Littleton ◽  
Richard A. Secco ◽  
Wenjun Yong
Keyword(s):  
Electrical Resistivity ◽  
Thermal Convection ◽  
High Pressures ◽  
Freezing Point ◽  
Thermal Evolution ◽  
Significant Proportion ◽  
Freezing Point Depression ◽  
The Core ◽  
Liquid Transition ◽  
End Members

The core of Ganymede is suggested to be mainly Fe but with a significant proportion of S. Effects of S as a core constituent are freezing-point depression, allowing for a molten core at relatively low core temperatures, and modification of transport properties that can influence the dynamo and thermal evolution. The electrical resistivity of solid and liquid Fe-FeS (~24–30 wt.% S) was measured up to 5 GPa and thermal conductivity was calculated using the Wiedemann–Franz law. These first well-constrained experimental data on near eutectic Fe-FeS compositions showed intermediate values of electrical and thermal conductivities compared to the end-members. Eutectic temperatures were delineated from the solid to liquid transition, inferred from sharp changes in electrical resistivity, at each pressure. Combined with thermal models, our calculated estimates of the adiabatic heat flow of a molten Fe-FeS eutectic composition core model of Ganymede showed that thermal convection is permissible.

scholarly journals Fe Melting Transition: Electrical Resistivity, Thermal Conductivity, and Heat Flow at the Inner Core Boundaries of Mercury and Ganymede

Crystals ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 359 ◽  
Author(s):  
Innocent C. Ezenwa ◽  
Richard A. Secco
Keyword(s):  
Thermal Conductivity ◽  
Electrical Resistivity ◽  
Heat Flow ◽  
Inner Core ◽  
Outer Core ◽  
Melting Transition ◽  
Planetary Bodies ◽  
Core Boundary ◽  
The Difference ◽  
Electronic Scattering

The electrical resistivity and thermal conductivity behavior of Fe at core conditions are important for understanding planetary interior thermal evolution as well as characterizing the generation and sustainability of planetary dynamos. We discuss the electrical resistivity and thermal conductivity of Fe, Co, and Ni at the solid–liquid melting transition using experimental data from previous studies at 1 atm and at high pressures. With increasing pressure, the increasing difference in the change in resistivity of these metals on melting is interpreted as due to decreasing paramagnon-induced electronic scattering contribution to the total electronic scattering. At the melting transition of Fe, we show that the difference in the value of the thermal conductivity on the solid and liquid sides increases with increasing pressure. At a pure Fe inner core boundary of Mercury and Ganymede at ~5 GPa and ~9 GPa, respectively, our analyses suggest that the thermal conductivity of the solid inner core of small terrestrial planetary bodies should be higher than that of the liquid outer core. We found that the thermal conductivity difference on the solid and liquid sides of Mercury’s inner core boundary is ~2 W(mK)−1. This translates into an excess of total adiabatic heat flow of ~0.01–0.02 TW on the inner core side, depending on the relative size of inner and outer core. For a pure Fe Ganymede inner core, the difference in thermal conductivity is ~7 W(mK)−1, corresponding to an excess of total adiabatic heat flow of ~0.02 TW on the inner core side of the boundary. The mismatch in conducted heat across the solid and liquid sides of the inner core boundary in both planetary bodies appears to be insignificant in terms of generating thermal convection in their outer cores to power an internal dynamo suggesting that chemical composition is important.

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.

Sign in / Sign up

Export Citation Format

Share Document