Resolving the Iron Phase Stability Debate in Earth's Inner Core: A Consistent Thermodynamic Benchmark

Understanding the stable phase of iron under Earth's inner core conditions is fundamental to interpreting its composition, evolution, and dynamics. Despite its importance, the stability of candidate phases (e.g., bcc, fcc, hcp) remains contentious due to the extreme pressure-temperature conditions and the meagre free energy differences (~10 meV/atom) between them. This has resulted in conflicting predictions from ab initio, force field, and machine learning approaches. To resolve this discrepancy, we introduce a Bain-path thermodynamic integration (BP-TI) method that directly computes free energy differences from the work performed by internal stress along a transformation path. This approach eliminates the need for an external reference system and avoids the uncertainties associated with conventional entropy calculations. Applying this rigorous benchmark with strict convergence criteria, we find that hcp Fe is the thermodynamically stable phase with the highest melting temperature under inner core conditions. In contrast, bcc Fe is consistently shown to be metastable across all tested interatomic potentials and computational methods. This metastability is intrinsic, persisting independent of simulation cell size and thus is not a finite-size artifact. Our findings reconcile previous disparities and provide a robust thermodynamic foundation for future studies of inner-core properties and dynamics.