Ab initio calculations of the elasticity of hcp-Fe as a function of temperature at inner-core pressure

Ab initio finite temperature molecular dynamics simulations have been used to calculate the elastic constants of hexagonal-close-packed (hcp) Fe as a function of temperature at ~ 300 GPa. The longitudinal modulus c11 decreases with temperature, in stark contrast to previous calculations, but in agreement with experimental observations on other transition metals at ambient pressures. c33 and c44 also decrease with temperature, while c12 and c23 slightly increase. When these moduli are used to calculate P-wave velocities through the crystal, the sense of the anisotropy is such that VP is fastest along the c-axis up to 5000 K; however, by 5500 K the anisotropy reverses with VP becoming faster in the a–b plane. This suggests that, for an inner core dominated by crystals of hcp-Fe aligned with the c-axis in the polar direction, the observed isotropic outer–inner core could result from the hcp-Fe being at a temperature close to melting where the axial wave velocities parallel and perpendicular to the c-axis become similar, while at greater depths in the inner–inner core, where iron is further from melting, stronger anisotropy is achieved with the faster P-wave velocities parallel to the polar axis. No other mechanisms, such as changes in composition or crystal alignment, are therefore required to account for the observed change in seismic anisotropy of the Earthʹs inner core with depth.