Thermal and electrical conductivity of solid iron and iron–silicon mixtures at Earth's core conditions

Monica Pozzo,Chris Davies,David Gubbins,Dario Alfè

doi:10.1016/j.epsl.2014.02.047

Abstract

We report on the thermal and electrical conductivities of solid iron and iron–silicon mixtures (Fe0.92Si0.08 and Fe0.93Si0.07), representative of the composition of the Earth's solid inner core at the relevant pressure–temperature conditions, obtained from density functional theory calculations with the Kubo–Greenwood formulation. We find thermal conductivities k=232(237) Wm−1K−1, and electrical conductivities σ=1.5(1.6)×106 Ω−1m−1 at the top of the inner core (centre of the Earth). These values are respectively about 45–56% and 18–25% higher than the corresponding conductivities in the liquid outer core. The higher conductivities are due to the solid structure and to the lower concentration of light impurities. These values are much higher than those in use for previous inner core studies, k by a factor of four and σ by a factor of three. The high thermal conductivity means that heat leaks out by conduction almost as quickly as the inner core forms, making thermal convection unlikely. The high electrical conductivity increases the magnetic decay time of the inner core by a factor of more than three, lengthening the magnetic diffusion time to 10 kyr and making it more likely that the inner core stabilises the geodynamo and reduces the frequency of reversals.

Highlights

This paper follows previous articles (Pozzo et al, 2012, 2013), in which we reported on the electrical and thermal conductivities of liquid iron and iron mixtures at Earth’s outer core conditions computed with density functional theory (DFT) and the Kubo–Greenwood (KG) relation
The values for the electrical and thermal conductivities in pure solid iron are in the range 1.76–1.97 × 106 −1 m−1 and 286–330 W m−1 K−1, respectively, with the low/high values corresponding to inner core boundary (ICB)/Earth’s centre pressure–temperature conditions
For all other thermodynamic states, we only considered one single trajectory, in which the distribution of the Si atoms was obtained from a Monte Carlo simulation as described above

Summary

Introduction

This paper follows previous articles (Pozzo et al, 2012, 2013), in which we reported on the electrical and thermal conductivities of liquid iron and iron mixtures at Earth’s outer core conditions computed with density functional theory (DFT) and the Kubo–Greenwood (KG) relation We extend those results to the Earth’s solid inner core. To extrapolate their results to core temperatures they combined their measurements with the saturation resistivity model, which says that the resistivity of a material stops increasing with temperature once the mean free path of the electrons becomes of the order of the interatomic distance (Gunnarsson et al, 2003) Within this model, their extrapolated values for the electrical and thermal conductivity of Fe78Si22 at T = 3750 (4971) K and P = 135 (330) GPa, representative of inner core (outer core) boundary conditions, were 0.98 (1.22) × 106 −1 m−1 and 90 (148) W m−1 K−1, respectively.

Techniques

Results

Iron–silicon mixtures

Implications for the Earth

Conclusions