Electrical conductivity of Iron under Earth core conditions using time-dependent density functional theory

Iron is one of the most plentiful components on the planet earth and plays a crucial role in our lives. The analysis of iron at high pressures and temperatures is of great geophysical importance because iron makes up the majority of the Earth’s liquid outer core and solid inner core. The technical utility of iron is due to the large phase space of iron-based alloys, which is the source of a wide range of steel microstructures that can be produced with minor compositional changes and proper thermal treatment. The iron phase structure at the extreme conditions under the inner core conditions of the earth is still not conclusive especially in the vicinity of temperature around 6000 K and pressures nearing 300 GPa. Time-dependent
density functional theory (TDDFT) enables calculating electronic transport properties in warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In TDDFT, the electrical conductivity is computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm’s law in WDM. We present TDDFT calculations of the electrical conductivity for iron within the pressure and temperature range found in Earth’s core. We discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood formalism and dielectric models.