Heat Flow in Earth's Core From Invariant Electrical Resistivity of Fe‐Si on the Melting Boundary to 9 GPa: Do Light Elements Matter?

Abstract

The electrical resistivity and thermal conductivity of liquid Fe alloys are the least constrained parameters in Earth's outer core (OC). These parameters are important as they modulate energy budget available for the geodynamo and affect the spatiotemporal evolution of the core. We report results of electrical resistivity measurements on solid and liquid Fe‐4.5 wt%Si from 3–9 GPa using a large volume multianvil press. The internally modified 18/11 octahedron cell was used to maintain the geometry of the liquid sample and to delay the onset of contamination. Electrical resistivity of solid Fe‐4.5Si decreases steadily with pressure and is very sensitive to increasing temperature‐driven onset of phase transitions. Along the melting boundary and within error, electrical resistivity remains constant and assumes the same value of 120 μΩcm as observed in pure liquid Fe. The results are interpreted in the context of icosahedral short‐range order (ISRO) structures that exhibit higher concentration with increasing pressure. Along the melting line, the increasing concentration of ISROs reduces charge carrier mean free path and prevents decrease of electrical resistivity with increasing pressure as seen in liquid metals, Cu, Ag, and Au, which do not have ISROs. In light of recent developments in understanding of the structure and dynamics of liquid transition metals and alloys, we postulate that our findings are applicable to other Fe alloys in the OC with small light element (C, S, and O) content. We calculated an adiabatic heat flow of 9.4–12 TW at the OC‐CMB interface, which admits thermal convection.

A Joint Experimental‐Modeling Investigation of the Effect of Light Elements on Dynamos in Small Planets and Moons

“…The electrical resistivity of all investigated alloys at 10 GPa and 1200-1850 K varies from~3 × 10 −6 to 15 × 10 −6 ohm-m (or 300 to 1,500 microhm-cm) ( Figure 3) and is highly sensitive to bulk composition (Figures 3 and 4). The strong dependence of resistivity to chemistry is in agreement with previous studies of Fe, Fe-S, Fe-Si, and Fe-P alloys under a pressure of a few GPa and confirms that adding light elements to pure iron increases resistivity (Deng et al, 2013;Manthilake et al, 2019;Pommier, 2018;Pommier et al, 2019;Silber et al, 2019;Yin et al, 2019). The alloys in our study all contain 5 wt.% S (Table 1) and their resistivities are higher than the ones measured for FeS 5 at 8 GPa and up to 1573 K (<1 × 10 −6 ohm-m, or 100…”

“…Several studies have measured or computed the electrical resistivity and thermal conductivity of core analogues under pressure and temperature conditions. However, these investigations have focused mostly on systems that do not combine several light elements, considering either pure iron (e.g., de Koker et al, 2012; Pozzo et al, 2012 for computational studies, and Deng et al, 2013; Ohta et al, 2016; Konôpková et al, 2016; Silber et al, 2018 for laboratory studies) or binary systems such as Fe‐S, Fe‐Si, and Fe‐O (e.g., de Koker et al, 2012; Pozzo et al, 2013; Wagle et al, 2019 for computational studies, and Gomi et al, 2013, 2016; Pommier, 2018; Silber et al, 2019 for laboratory studies). As pointed out by Wagle et al (2019) using simulations at temperature ranging from 2000 to 8000 K and pressure from 23 up to >300 GPa, light elements do not affect electrical resistivity and thermal resistivity the same way: both S and Si atoms substitute for Fe in the molten state, but S atoms tend to distribute more evenly in liquid iron than Si atoms.…”

Electrical Resistivity Measurements of Fe‐Si With Implications for the Early Lunar Dynamo

“…For Fe17Si, the analyses showed much less diffusion of 1.3–3.8 wt%W from the discs into the central part of the sample after exposure to a T of approximately 59 K above the liquidus. Silber et al (2019) confirmed on Fe4.5Si that there is no W contamination after exposure to T at or just above the liquidus and so the electrical resistivity data collected up to these T are robust. Contrary to the Fe2Si at 3 GPa, the other data sets do not show a decrease of ρ total at high T , suggesting the W contribution to ρ total several degrees past the liquidus T is not significant.…”

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

“…4) to the core temperatures (>4000 K) would not change it much, while the thermal conductivity of a material in molten phase that lacks crystallinity for heat conduction is typically smaller than in solid phase. For Fe and Fe-light element alloys, the effect of melting is expected to reduce the thermal conductivity of the solid phase by ≈20% or less 15,18,[20][21][22][34][35][36][37] . For instance, Silber et al 36 recently reported that at pressures from 3 to 9 GPa the electrical resistivity (inversely proportional to the electronic thermal conductivity using WF law) of Fe alloyed with 4.5 wt% Si abruptly increases by~10 −7 Ω m (~10%) or less as it undergoes a solid-to-liquid transition, and such increase in resistivity is expected to be also present at higher pressures 18 .…”