Resistivity saturation in liquid iron–light-element alloys at conditions of planetary cores from first principles computations

Abstract

We present a comprehensive analysis of electrical resistivity for liquid Fe–Si, Fe–S, and Fe–O alloys from first principles computations, covering the pressure/temperature conditions and major light element candidates inside the cores of terrestrial planets. By fitting optical conductivity with the Drude formula, we explicitly calculate the effective electron mean free path, and show that it becomes comparable to the interatomic distance for high densities and Si/S concentrations (Ioffe–Regel criterion). In approaching the Ioffe–Regel criterion, the temperature coefficient of resistivity decreases with compression for all compositions, eventually vanishes (Fe–Si), or even changes sign (Fe–S). Differences in resistivity and the degree of saturation between the iron alloys studied are explained in terms of iron–light element coordination numbers and their density dependence. Due to competing temperature and pressure effects, resistivity profiles along proposed core adiabats exhibit a small negative pressure gradient.