The elastic properties of hcp-Fe1 − xSix at Earth's inner-core conditions ☆

The density of the Earth's inner core is less than that of pure iron and the P-wave velocities and, particularly, the S-wave velocities in the inner core observed from seismology are lower than those generally obtained from mineral physics. On the basis of measurements of compressional sound velocities to ∼100 GPa in diamond-anvil cells, extrapolated to inner-core pressures, it has been suggested that both the inner-core density and P-wave velocity can be matched simultaneously by the properties of a hexagonal-close-packed (hcp) Fe–Si or Fe–Ni–Si alloy. In this paper we present the results of ab initio molecular dynamics simulations of hcp-Fe–Si alloys at 360 GPa and at temperatures up to melting. We find that although the inner-core density can be readily matched by an Fe–Si alloy, the same is not true for the wave velocities. At inner-core temperatures, the P-wave velocity in hcp-Fe–Si remains equal to, or slightly above, that of hcp-Fe and shows little change with silicon content. The S-wave velocity is reduced with respect to that of pure hcp-iron, except for temperatures immediately prior to melting, where the velocities are almost equal; this is a consequence of the fact that the strong temperature dependence of the shear modulus that was seen in similar simulations of hcp-Fe just prior to melting was not found in hcp-Fe–Si, and so in this temperature range the reduced S-wave velocity of pure iron closely matches that of the alloy. Our results show that for an hcp-Fe–Si alloy matching the inner-core density, both the P-wave and the S-wave velocities will be higher than those observed by seismology and we conclude, therefore, that our calculations indicate that inner core velocities cannot be explained by an hcp-Fe–Si alloy. The opposite conclusion, obtained previously from experimental data measured at lower pressures, is a consequence of: (i) the necessarily large extrapolation in pressure and temperature required to extend the experimental results to inner-core conditions and (ii) the use of a velocity–density relationship for pure hcp-iron that is now considered to be incorrect.