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

导电性是行星内部通过磁流体动力对流产生磁场模型中的一个关键参数。在相关条件下的实验无法测量液态金属的这一关键材料参数，而发电机模型依赖于低压/低温实验的外推，或者最近使用Kubo-Greenwood输运系数公式结合分子动力学和线性响应计算的从头算计算。这样的计算已经在覆盖类地行星和巨型气体行星内部的铁、铁合金、氢、氦和氢-氦混合物中进行了。这些模拟在计算上是昂贵的，并且需要一个有效准确的方案来确定电导率。在这里，我们提出了一个模型，它可以以更低的计算成本提供这些信息。它基于齐曼电导率理论，利用液体结构的信息，结合内部一致的电子-电子、电子-原子和原子-原子相互作用的电位模型。在该方案中，我们阐述了该理论并将其扩展到多组件系统中。我们指出，拟合液体结构因素是该过程中的关键组成部分，并就如何有效地完成这一工作制定了策略。以热力学一致的方式拟合结构因子，并具有可转移的电子-原子势，我们可以相对便宜地预测各种条件下的电导率。只需要有限的分子动力学模拟来获得结构因子。在提议的项目中，我们将测试和推进液态铝的模型，液态铝是一种类似自由电子的金属，我们之前用Kubo-Greenwood方法研究过。然后，我们将能够预测Fe、Fe轻元素和H、He的电导率，以及分别与类地行星和巨型气体行星内部相关的H-He系统。

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.