First-principles Anharmonic Free-Energy Calculation of Iron Up to Core Conditions: Implications for Earth Inner Core Crystal Structure

Study of crystalline iron at Earth’s inner-core (IC) conditions finds two main challenges: first, at such high temperatures (> 5000 K, near melting) anharmonic effects are significant; second, due to magnetic phenomena many-body effects (correlation) are important, such that standard ab initio methods (e.g., DFT) fail to reproduce experimental data. To tackle the first difficulty we utilized harmonically-mapped averaging (HMA) to measure anharmonic free energy with orders of magnitude speedup in computation compared to conventional methods. As for the second complication, we apply DMFT (dynamical mean-field theory) to explicitly capture the many-body effects and magnetism on the static lattice energy. Standard DFT is then used to capture quasiharmonic and anharmonic effects.
We apply this hybrid DFT+DMFT approach to the low pressure/temperature region of the phase diagram, where experimental data are available, and find excellent agreement in c/a-ratio, equation-of-state, and fcc-hcp phase coexistence line. Then, we turn to the high pressure/temperature region using the most likely Earth’s IC candidate structures (viz., hcp, bcc, and fcc). We report findings regarding the phase relation between these phases in the vicinity of the IC conditions.