An ab initio study on the effect of silicon and nickel iron alloys in the Earth’s inner core

The hexagonal close-packed structure (hcp) is the accepted stable form of pure iron (Fe) under Earth’s core conditions. It has been proposed, however, that especially when alloyed with lighter elements, the body-centred (bcc) and face-centred (fcc) cubic structures cannot be excluded from the inner core [1]. At relatively modest conditions, experiments have shown that small amounts of silicon can stabilise the bcc phase with respect to the hcp phase [2]. This has been confirmed by zero temperature density functional theory calculations extended to the pressure of the inner core [3]. Furthermore, an experimental study [4] at high pressures and temperatures showed that ~10% nickel would stabilise the bcc structure in the inner core. In this study we use ab initio lattice dynamics to investigate the relative thermodynamical and vibrational stability of all three candidate phases and evaluate the effect of temperature, using Si and Ni as the alloying elements. We note that at the temperature of interest (5500K), anharmonic effects neglected in this study may play an important role, and they will be investigated at a later stage. Our results confirm that increasing concentration of Si vibrationally stabilises bcc Fe at core pressures, but the addition of Ni does not. Within the quasi-harmonic approximation, high temperature acts towards minimising the free energy differences between the different phases, and we find that for a Si concentration of ~7 wt.%, fcc becomes thermodynamically the most stable phase at Earth’s core conditions. Nickel has a less pronounced effect, although above ~26 wt.% Ni, fcc again becomes the most stable phase thermodynamically; our results indicate that Fe-Ni alloys can not be found in the bcc phase in the Earth’s inner core. This is in agreement with a recent experimental study [5]. Finally, based on the derived temperature-composition phase diagrams for both the Si and Ni alloys, we suggest that the inner core may exist in the two-phase region, with fcc and hcp coexisting throughout the core. References: [1] Vočadlo, L. et al., Earth Planet. Sci. Lett., 268 (2008) 444-449. [2] Lin, J.-F. et al., Science, 295 (2002) 313-315. [3] Côté, A.S. et al., J. Phys. Chem. Solid, 69 (2008) 2177-2181. [4] Dubrovinsky, L. et al., Science, 316 (2007) 1880- 1883. [5] Kuwayama Y. et al., Earth Planet. Sci. Lett., 273 (2008) 379-385.