“…Firstprinciple electronic band structure calculations of Fe-alloys accounting for the saturation theory suggested values ranging from 0.58-0.74 µΩm for Fe-(5.4 to 31.6 wt%)Ni at CMB conditions (Gomi and Yoshino, 2018). In agreement with these studies, Zidane et al (2020) also used first-principle calculations based on the Kubo-Greenwood relation and reported values of 0.62-1.22 µΩm for Fe-Ni with 2.7-37.7 wt% light elements (O, Si, S) at ICB conditions (5,500 K, 360 GPa).…”
Section: Electrical Resistivity Of the Cores Of Terrestrial-type Bodies Earthsupporting
There is a considerable amount of literature on the electrical resistivity of iron at Earth’s core conditions, while only few studies have considered iron and iron-alloys at other planetary core conditions. Much of the total work has been carried out in the past decade and a review to collect data is timely. High pressures and temperatures can be achieved with direct measurements using a diamond-anvil cell, a multi-anvil press or shock compression methods. The results of direct measurements can be used in combination with first-principle calculations to extrapolate from laboratory temperature and pressure to the relevant planetary conditions. This review points out some discrepancies in the electrical resistivity values between theoretical and experimental studies, while highlighting the negligible differences arising from the selection of pressure and temperature values at planetary core conditions. Also, conversions of the reported electrical resistivity values to thermal conductivity via the Wiedemann-Franz law do not seem to vary significantly even when the Sommerfeld value of the Lorenz number is used in the conversion. A comparison of the rich literature of electrical resistivity values of pure Fe at Earth’s core-mantle boundary and inner-core boundary conditions with alloys of Fe and light elements (Si, S, O) does not reveal dramatic differences. The scarce literature on the electrical resistivity at the lunar core suggests the effect of P on a wt% basis is negligible when compared to that of Si and S. On the contrary, studies at Mercury’s core conditions suggest two distinct groups of electrical resistivity values but only a few studies apply to the inner-core boundary. The electrical resistivity values at the Martian core-mantle boundary conditions suggest a negligible contribution of Si, S and O. In contrast, Fe-S compositions at Ganymede’s core-mantle boundary conditions result in large deviations in electrical resistivity values compared to pure Fe. Contour maps of the reported values illustrate ρ(P, T) for pure Fe and its alloys with Ni, O and Si/S and allow for estimates of electrical resistivity at the core-mantle boundary and inner-core boundary conditions for the cores of terrestrial-like planetary bodies.
“…Firstprinciple electronic band structure calculations of Fe-alloys accounting for the saturation theory suggested values ranging from 0.58-0.74 µΩm for Fe-(5.4 to 31.6 wt%)Ni at CMB conditions (Gomi and Yoshino, 2018). In agreement with these studies, Zidane et al (2020) also used first-principle calculations based on the Kubo-Greenwood relation and reported values of 0.62-1.22 µΩm for Fe-Ni with 2.7-37.7 wt% light elements (O, Si, S) at ICB conditions (5,500 K, 360 GPa).…”
Section: Electrical Resistivity Of the Cores Of Terrestrial-type Bodies Earthsupporting
There is a considerable amount of literature on the electrical resistivity of iron at Earth’s core conditions, while only few studies have considered iron and iron-alloys at other planetary core conditions. Much of the total work has been carried out in the past decade and a review to collect data is timely. High pressures and temperatures can be achieved with direct measurements using a diamond-anvil cell, a multi-anvil press or shock compression methods. The results of direct measurements can be used in combination with first-principle calculations to extrapolate from laboratory temperature and pressure to the relevant planetary conditions. This review points out some discrepancies in the electrical resistivity values between theoretical and experimental studies, while highlighting the negligible differences arising from the selection of pressure and temperature values at planetary core conditions. Also, conversions of the reported electrical resistivity values to thermal conductivity via the Wiedemann-Franz law do not seem to vary significantly even when the Sommerfeld value of the Lorenz number is used in the conversion. A comparison of the rich literature of electrical resistivity values of pure Fe at Earth’s core-mantle boundary and inner-core boundary conditions with alloys of Fe and light elements (Si, S, O) does not reveal dramatic differences. The scarce literature on the electrical resistivity at the lunar core suggests the effect of P on a wt% basis is negligible when compared to that of Si and S. On the contrary, studies at Mercury’s core conditions suggest two distinct groups of electrical resistivity values but only a few studies apply to the inner-core boundary. The electrical resistivity values at the Martian core-mantle boundary conditions suggest a negligible contribution of Si, S and O. In contrast, Fe-S compositions at Ganymede’s core-mantle boundary conditions result in large deviations in electrical resistivity values compared to pure Fe. Contour maps of the reported values illustrate ρ(P, T) for pure Fe and its alloys with Ni, O and Si/S and allow for estimates of electrical resistivity at the core-mantle boundary and inner-core boundary conditions for the cores of terrestrial-like planetary bodies.
“…A multi-variable linear regression analysis of the ρ values in the solid state from this study provides the following model of solid k e ( T , P ): Figure 4 ( a ) Thermal conductivity of Fe10Ni10Si as a function of T . Results are compared with Fe at 7 GPa 57 , solid Fe11.9Ni13.4Si at 140 GPa 65 , solid Fe11.7Ni10Si at 330 GPa 66 , and solid Fe9Si at 136–183 GPa 67 . Equation ( 4 ) is used to calculate k e of solid Fe10Ni10Si, as shown by the black triangles, at the P , T conditions of Zidane et al 66 and Zhang et al 67 , shown with black and blue stars respectively.…”
Electrical resistivity measurements of Fe–10wt%Ni–10wt%Si have been performed in a multi-anvil press from 3 to 20 GPa up to 2200 K. The temperature and pressure dependences of electrical resistivity are analyzed in term of changes in the electron mean free path. Similarities in the thermal properties of Fe–Si and Fe–Ni–Si alloys suggest the effect of Ni is negligible. Electrical resistivity is used to calculate thermal conductivity via the Wiedemann–Franz law, which is then used to estimate the adiabatic heat flow. The adiabatic heat flow at the top of Earth’s core is estimated to be 14 TW from the pressure and temperature dependences of thermal conductivity in the liquid state from this study, suggesting thermal convection may still be an active source to power the dynamo depending on the estimated value taken for the heat flow through the core mantle boundary. The calculated adiabatic heat flux density of 22.7–32.1 mW/m2 at the top of Mercury’s core suggests a chemically driven magnetic field from 0.02 to 0.21 Gyr after formation. A thermal conductivity of 140–148 Wm−1 K−1 is estimated at the center of a Fe–10wt%Ni–10wt%Si Venusian core, suggesting the presence of a solid inner core and an outer core that is at least partially liquid.
“…Such a high thermal conductivity reduces the amount of heat that can be transported by convective flow ( 11 ) and raises a question as to what powered the convection prior to inner core growth over Earth’s history [the so-called new core paradox ( 24 )]. Thus far, several hypotheses have been proposed to reconcile this paradox, including a possible large conductivity reduction due to nickel and light elements ( 25 – 28 ), a rapid core cooling rate ( 29 ), or exsolution of chemically saturated species from the core to the lowermost mantle, such as MgO, SiO 2 , or FeO (e.g., refs. 30 – 32 ).…”
Light elements in Earth’s core play a key role in driving convection and influencing geodynamics, both of which are crucial to the geodynamo. However, the thermal transport properties of iron alloys at high-pressure and -temperature conditions remain uncertain. Here we investigate the transport properties of solid hexagonal close-packed and liquid Fe-Si alloys with 4.3 and 9.0 wt % Si at high pressure and temperature using laser-heated diamond anvil cell experiments and first-principles molecular dynamics and dynamical mean field theory calculations. In contrast to the case of Fe, Si impurity scattering gradually dominates the total scattering in Fe-Si alloys with increasing Si concentration, leading to temperature independence of the resistivity and less electron–electron contribution to the conductivity in Fe-9Si. Our results show a thermal conductivity of ∼100 to 110 W⋅m−1⋅K−1 for liquid Fe-9Si near the topmost outer core. If Earth’s core consists of a large amount of silicon (e.g., > 4.3 wt %) with such a high thermal conductivity, a subadiabatic heat flow across the core–mantle boundary is likely, leaving a 400- to 500-km-deep thermally stratified layer below the core–mantle boundary, and challenges proposed thermal convection in Fe-Si liquid outer core.
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