Equations of state and anisotropy of Fe-Ni-Si alloys

Seismic observations provide constraints on the density, bulk sound speed, and bulk modulus of Earth's inner core, and x-ray diffraction (XRD) experiments can experimentally constrain such properties of iron alloys. The deviation of these seismically-inferred values from the properties of iron suggests the presence of light elements (e.g. Si, O, S, C, H) inside the core. While cosmochemical studies suggest Earth's core is composed primarily of iron alloyed with 5 wt% nickel, existing experimental XRD studies constraining pressure-density relations have predominantly focused on iron and iron alloyed with light elements, while neglecting the effect of nickel. In this study, we present high-precision equations of state for bcc- and hcp-structured Fe_0.91Ni_0.09 and Fe_0.80Ni_0.10Si_0.10 using powder XRD at room temperature up to 167 GPa and 175 GPa, respectively. By using tungsten powder as a pressure calibrant and helium as a pressure transmitting medium, we minimize error due to pressure calibration and non-hydrostatic stresses. The results are high fidelity equations of state (EOS). By systematically comparing our findings to an established EOS of hcp-Fe [Dewaele et al. 2006], we constrain the effect of nickel and silicon on the density, bulk sound speed, and bulk modulus of iron alloys, which is a critical step towards constraining the inner core's composition. We find that for iron alloys, high quality ambient temperature EOSs can dramatically improve the extrapolated high temperature equations of state to inner core conditions. By combining seismic observations and their associated uncertainties with our data and existing Fe light-element-alloy EOSs, we estimate their densities, bulk moduli, and bulk sound speeds at inner core conditions and propose an experimentally and seismologically consistent range of inner core compositions. Additionally, we obtain an unprecedented constraint on the effect of nickel and silicon on the axial ratio of iron alloys. Nickel has a measurably distinct effect on the c/a axial ratio of iron, as does alloying iron-nickel with silicon. We investigate the relationship between the c/a axial ratio and elastic anisotropy of iron alloys and discuss the implications for inner core seismic anisotropy.