Electrical and thermal conductivity of Al liquid at high pressures and temperatures fromab initiocomputations

We performed first-principles calculations to obtain values of electrical (σ) and thermal conductivity (κ) for compressed aluminum liquid at temperatures and pressures up to 8000 K and 110 GPa. To do this we apply the Kubo-Greenwood formula via density functional perturbation theory to phase trajectories generated using first-principles molecular dynamics. Our results are consistent with measurements at low pressures, and indicate that electronic transport coefficients σ and κ increase under compression; with increasing temperature σ decreases and κ increases. Behavior in response to compression and heating are explained in terms of changes in occupation of conduction bands by thermally excited electrons. Based on the frequency dependence of σ, we further show that liquid aluminum is well described by the Drude picture over a wide range of conditions, confirming its free-electron nature. At high P and T, our computed σ and κ yield Lorenz numbers up to 7$%$ lower than the theoretical value, indicating that the Wiedemann-Franz law remains approximately satisfied at extreme conditions. Using an electronically simple metal such as liquid Al as a guide to the behavior of more complex metals, we infer that present extrapolation-based estimates of σ and κ for the Earth's outer core may be 3--4 times too low.