Thermal and electrical conductivity of solid iron and iron–silicon mixtures at Earthʹs core conditions

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 Earthʹs 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 ) W m − 1 K − 1 , and electrical conductivities σ = 1.5 ( 1.6 ) × 10 6   Ω − 1 m − 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.