Structure and electronic transport properties of metallic liquids at conditions of planetary cores

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Electrical conductivity is a key parameter in models of magnetic field generation in planetary interiors through magneto-hydrodynamic convection. Measurements of this key material parameter of liquid metals is not possible to date by experiments at relevant conditions, and dynamo models rely on extrapolations from low pressure/temperature experiments, or more recently on ab-initio calculations combining molecular dynamics and linear response calculations, using the Kubo-Greenwood formulation of transport coefficients. Such calculations have been performed for Fe, Fe-alloys, H, He and H-He mixtures to cover the interior of terrestrial and giant gas planets. These simulations are computationally expensive, and an efficient accurate scheme to determine electrical conductivities is desirable.Here we propose a model that can, at much lower computational costs, provide this information. It is based on Ziman theory of electrical conductivity that uses information on the liquid structure, combined with an internally consistent model of potentials for the electron-electron, electron-atom, and atom-atom interactions. In the proposal we formulate the theory and expand it to multi-component systems. We point out that fitting the liquid structure factor is the critical component in the process, and devise strategies on how this can be done efficiently. Fitting the structure factor in a thermodynamically consistent way and having a transferable electron-atom potential we can then relatively cheaply predict the electrical conductivity for a wide range of conditions. Only limited molecular dynamics simulations to obtain the structure factors are required.In the proposed project we will test and advance this model for liquid aluminum, a free-electron like metal, that we have studied with the Kubo-Greenwood method previously. We will then be able to predict the conductivities of Fe, Fe-light elements and H, He, as well as the H-He system that are relevant to the planetary interiors of terrestrial and giant gas planets, respectively.