Fig. 1: Electrical conductivity.
The electronic σel (red), ionic σion (blue), and total σtotal = σel + σion (green) electrical conductivity along the magma ocean isentrope37 (black) for low-spin (top of range shown) and high-spin (bottom of range) results. Along the magma ocean isentrope, the electrical conductivity increases with depth because the effects of increasing temperature outweigh the effects of increasing pressure. Inset. The electrical conductivity of the bulk silicate Earth liquid from our simulations, including the electronic (large symbols) and ionic (small symbols with 1σ uncertanties) contributions at 6000 K (red) and 4000 K (purple) in spin-polarized (diamonds) and non-spin-polarized (squares) calculations. Lines are best fits to the form \(\sigma = \sigma _0T^{ - 1}\exp \left[ { - \left( {E^\ast + PV^\ast } \right)/RT} \right]\) for the electronic non-spin-polarized results (σ0 = 1.994e9 S/m, E* = 108.6 kJ/mol, V* = 0.0611 cm3/mol, light solid lines) and shifted uniformly downward to account for spin-polarization (σ0 = 1.754e9 S/m, bold solid lines), and to the ionic contribution (σ0 = 1.0811e9 S/m, E* = 131.0 kJ/mol, V* = 0.437 cm3/mol, dashed lines).
