Abstract
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.
Highlights
Direct observations of the Earth’s core are made through seismic waves, whose velocities are dependent on the elastic properties of the material present
To determine whether similar premelting effects might occur in Fe– X alloys as opposed to pure hcp-Fe, in this paper we report, a study of the density and elastic properties of hcp-Fe–Si alloys at Earth’s inner-core conditions using first-principles calculations
For hcp-Fe0.9375Si0.0625, the reduction in density, with respect to that of pure iron, is almost constant over the entire temperature range, being ∼390–460 kg m−3 (∼2.9–3.4%) throughout, and that the density of hcp-Fe0.9375Si0.0625 is in good agreement with PREM for simulation temperatures above ∼6900 K
Summary
Direct observations of the Earth’s core are made through seismic waves, whose velocities are dependent on the elastic properties of the material present. Interpretation of the increasingly detailed seismic data for the inner core must depend on accurate knowledge of the elastic properties of the constituent materials, but the exact composition of the inner core remains unknown and so a number of candidates must be considered. It has been supposed for many years that the inner-core density is less than that of pure iron and, that one or more light alloying elements must be present (Birch, 1952; Alfè et al, 2007; Hirose et al, 2013; Deng et al, 2013). One of the more likely candidate elements is silicon – geochemical models based on cosmochemical arguments suggest that Earth’s core could contain up to 20 wt.% Si (see e.g. Fischer et al, 2012)
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