Reconstructing the phase diagram of iron in the terapascal region via the statistical moment method

TD Cuong and AD Phan, PHYSICAL REVIEW B, 108, 134111 (2023).

DOI: 10.1103/PhysRevB.108.134111

Recently, astronomers have reached a significant milestone on a journey of Universe exploration with more than 5400 confirmed exoplanets. Therefore determining the physical properties of minerals in the terapascal area has become an urgent mission to gain insights into exoplanetary dynamics and evolution. Herein, we develop a theoretical model to obtain a more reliable picture of the ultrahigh-pressure structural transformation in iron, which is the most prominent metal in the core of super-Earths, gas giants, and ice giants. First, we revisit the previously computed hcp-fcc boundary under extreme conditions between 3 and 7 TPa. Available ab initio data for the ground-state energy are utilized to construct the Rydberg pairwise potential for iron. On that basis, the statistical moment method is improved to calculate the total vibrational free energy without enormous computational workloads. Our analyses reveal that the widely employed quasiharmonic approximation is insufficient to capture the hcp-fcc phase-transition behaviors of iron. The primary reason is that the lack of inversion symmetry creates strong odd-order anharmonic effects, thereby enhancing the thermodynamic stability of the hcp structure. Second, we extend the modified work-heat equivalence principle to deduce the melting quantities from the Holzapfel equation-of-state parameters up to 10 TPa. Our steep melting lines accord fully with the state-of- the-art static measurements, dynamic experiments, and ab initio simulations. In particular, we observe that the melting gradient of hcp iron is always higher than the adiabatic slope of liquid iron. This difference has a profound geophysical implication for the core solidification and the magnetic-field generation of super-Earths. Finally, we perform numerical calculations for the Hugoniot and isentropic profiles. Our theoretical predictions would facilitate designing future multishock and ramp-wave studies to uncover the mystery of extrasolar worlds.

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