Structure of Iron at Giant-Planet and Exoplanet Interior Conditions

Abstract:

Ab-initio molecular-dynamics (AIMD) and electronic-structure calculations using the density-functional approach show that the body-centered cubic (bcc) phase of Fe is mechanically unstable at conditions ranging from Earth’s inner-core conditions (P ~ 360 GPa and T ~ 5500 K) up to pressures and temperatures of at least 1.5 TPa and 7000 K, conditions relevant to giant- and to many extrasolar-planet interiors. AIMD calculations for tetragonal distortions of Fe along the isochoric Bain path for densities of 18 and 20 g/cc at temperatures of 6000 and 7000 K indicate stresses becoming anisotropic for tetragonal distortions on either side of the lattice-parameter ratio c/a = 1, resulting in anisotropy in longitudinal stress, S_L: S_L > 0 for c/a < 1 and S_L < 0 for c/a > 1, with S_L ~ 0 within uncertainties for c/a = 1. The shear modulus B_S becomes negative, violating the Born stability criterion. Variation of the longitudinal stress S_L with free energy for the static lattice shows the same mechanical instability seen in the AIMD calculations, revealing the role of mechanical instability in causing the anomalies in S_L. Also, based on free-energy calculations with temperature-dependent phonon and electron contributions, the hexagonal close-packed (hcp) phase of Fe is found to be the most stable for pressure-temperature conditions extending beyond those of Earth’s inner core to the 1.5 TPa range.