Electrical resistivity of liquid Fe to 12 GPa: Implications for heat flow in cores of terrestrial bodies

Measuring the Electrical Resistivity of Liquid Iron to 1.4 Mbar

We determined the electrical resistivity of liquid Fe to 135 GPa and 6680 K using a four-probe method in a diamond-anvil cell combined with two novel techniques: (i) enclosing a molten Fe in a sapphire capsule, and (ii) millisecond time-resolved simultaneous measurements of the resistance, x-ray diffraction, and temperature of instantaneously melted Fe. Our results show the minimal temperature dependence of the resistivity of liquid Fe and its anomalous resistivity decrease around 50 GPa, likely associated with a gradual magnetic transition, both in agreement with previous ab initio calculations.

Electrical resistivity of the Fe–Si–S ternary system: implications for timing of thermal convection shutdown in the lunar core

The composition of the lunar core has been suggested to be Fe-rich with varying amounts of lighter elements, such as Si and S. Presence of Si and S affects electrical and thermal transport properties and thus influences core thermal processes and evolution. Paleomagnetic observations constrain a high intensity magnetic field that ceases shortly after formation of the moon (~ 3.5–4.2 Ga year ago), and thermal convection in the core may contribute to generation of this field. In this study, the electrical resistivity of Fe-14 wt% Si-3 wt% S was measured in both solid and molten states at pressures up to 5 GPa and thermal conductivity was calculated via the Wiedemann–Franz Law from the electrical measurements. The results were used to estimate the adiabatic conductive heat flux of a molten Fe-14 wt% Si-3 wt% S lunar core and compared to a Fe-2-17 wt% Si lunar core, which showed that thermal convection of either core composition shuts down within the duration of the high intensity magnetic field: (1) 3.17–3.72 Ga year ago for a Fe-14 wt% Si-3 wt% S core; and (ii) 3.38–3.86 Ga years ago for a Fe-2-17 wt% Si core. Results favouring compatibility of these core compositions with paleomagnetic observations are strongly dependent on the temperature of the core-mantle boundary and time-dependent mantle-side heat flux.

Resistivity of solid and liquid Fe-Ni-Si with applications to the cores of Earth, Mercury and Venus

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.

In situ measurements of electrical resistivity of metals in a cubic multi-anvil apparatus by van der Pauw method

On the basis of the van der Pauw method, we developed a new technique for measuring the electrical resistivity of metals in a cubic multi-anvil high-pressure apparatus. Four electrode wires were introduced into the sample chamber and in contact with the pre-pressed metal disk on the periphery. The sample temperature was measured with a NiCr-NiSi (K-type) thermocouple, which was separated from the sample by a thin hexagonal boron nitride layer. The electrodes and thermocouple were electrically insulated from each other and from the heater by an alumina tube as well. Their leads were in connection with cables through the gap between the tungsten carbide anvils. We performed experiments to determine the temperature dependence of electrical resistivity of pure iron at 3 and 5 GPa. The experiments produce reproducible measurements and the results provide an independent check on electrical resistivity data produced by other methods. The new technique provides reliable electrical resistivity measurements of metallic alloys and compounds at high pressure and temperature.

Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo

We measure the electrical resistivity of hcp iron up to ∼170  GPa and ∼3000  K using a four-probe van der Pauw method coupled with homogeneous flattop laser heating in a DAC, and compute its electrical and thermal conductivity by first-principles molecular dynamics including electron-phonon and electron-electron scattering. We find that the measured resistivity of hcp iron increases almost linearly with temperature, and is consistent with our computations. The results constrain the resistivity and thermal conductivity of hcp iron to ∼80±5  μΩ cm and ∼100±10  W m^{-1} K^{-1}, respectively, at conditions near the core-mantle boundary. Our results indicate an adiabatic heat flow of ∼10±1  TW out of the core, supporting a present-day geodynamo driven by thermal and compositional convection.

Low thermal conductivity of iron-silicon alloys at Earth's core conditions with implications for the geodynamo

Earth’s core is composed of iron (Fe) alloyed with light elements, e.g., silicon (Si). Its thermal conductivity critically affects Earth’s thermal structure, evolution, and dynamics, as it controls the magnitude of thermal and compositional sources required to sustain a geodynamo over Earth’s history. Here we directly measured thermal conductivities of solid Fe and Fe–Si alloys up to 144 GPa and 3300 K. 15 at% Si alloyed in Fe substantially reduces its conductivity by about 2 folds at 132 GPa and 3000 K. An outer core with 15 at% Si would have a conductivity of about 20 W m⁻¹ K⁻¹, lower than pure Fe at similar pressure–temperature conditions. This suggests a lower minimum heat flow, around 3 TW, across the core–mantle boundary than previously expected, and thus less thermal energy needed to operate the geodynamo. Our results provide key constraints on inner core age that could be older than two billion-years.

Thermal conductivity of Earth’s core affects Earth’s thermal structure, evolution and dynamics. Based on thermal conductivity measurements of iron–silicon alloys at high pressure and temperature conditions, the authors here propose Earth’s inner core could be older than previously expected.

Technique, cell assembly, and measurement of T-dependent electrical resistivity of liquid Fe devoid of contamination at P, T conditions

Since the cores of rocky planetary bodies are mainly Fe in composition, the understanding of the electrical resistivity and thermal conductivity of solid and molten Fe at pressure and temperature conditions is vital in placing a constraint on the quantity of heat flux from the cores of these planets. We develop an experimental technique and cell design to measure the temperature-dependent electrical resistivity of solid and molten Fe and other transition metals under high pressure. This addresses the problem of metal sample contamination encountered in designs that used W/Re, W, and Mo in direct contact with the sample. At first, we attempted to improve these pre-existing designs by testing the suitability of Hf and Zr metals to serve as a mechanical barrier between the electrodes and the sample. Unfortunately, our result shows that solid Hf and Zr dissolve in molten Fe and are not suitable for this purpose. Next, we adopt the same sample material, Fe, for electrodes and leads while the thermocouple leads are taken through the gasket and protected against frequent mechanical breakage using the shielding technique. The recovered Fe samples compressed at various pressure conditions and heated up to 200 K above the melting temperature show no trace of contamination. As anticipated, the resistivity increases and decreases with increasing temperature and pressure, respectively. Thus, to closely measure the electrical resistivity of molten Fe and other similar metals at extreme conditions, it is necessary to ensure liquid containment, eliminate biased voltage through the current reversal technique, and ensure the use of the same material for the electrode and sample while monitoring the sample temperature using a thermocouple placed close to but not in contact with the sample. Our developed technique provides the highly demanding technique for investigating the temperature-dependent electrical resistivity of Fe and other similar metals devoid of contamination at extreme conditions. This progress will accelerate studies which will provide a detailed understanding of the electrical and heat transport properties of Fe as it applies to the core of rocky planetary bodies.

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

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.