Refining the chemical composition of the inner core with multicomponent alloys: from first-principles to thermodynamics and seismology

Abstract:

We compute the solubility limits of Si in the hexagonal-close packed (hcp) phase of iron using standard thermodynamical treatment of solid solutions with data obtained from first-principles calculations. For this, we consider the system with end-members hcp Fe and the B2 phase of FeSi. Si and Fe enter both structures in substitution of one another. The system is characterized by an immiscibility gap, which according to our results widens with pressure. At core conditions about 5 wt.% Si can be dissolved into the hcp phase of Fe. Comparatively there is much more Fe that can enter the FeSi B2 phase.

In a second step we start with the hcp Fe-Si alloys and add the most probable light elements found in the core: H, C, O, and S. The light elements can enter the hcp structure either as interstitial impurities, in case of H, C, O, or in substitution of Fe, in case of S. We consider several insertion patterns with the light elements both adjacent and far apart. For each of these new phases we compute the elastic constants tensors and the seismic properties. Based on our theoretical results and the comparisons with PREM we discuss in detail the possible composition of the Earth’s inner core, we rule out certain light elements, like H, and we show that the distribution pattern is not important.

This is also the first time the elastic constants tensor is computed from lattice dynamics using the response function in the Planar Augmented Wavefunction approach of the Density Functional Theory [1].

[1] A. Martin, M. Torrent, R. Caracas, submitted (2015); A. Martin, PhD thesis (2015).