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

Abstract

We present powder X‐ray diffraction data on body centered cubic (bcc)‐ and hexagonal close packed (hcp)‐structured Fe_(0.91)Ni_(0.09) and Fe_(0.8)Ni_(0.1)Si_(0.1) at 300 K up to 167 and 175 GPa, respectively. The alloys were loaded with tungsten powder as a pressure calibrant and helium as a pressure transmitting medium into diamond anvil cells, and their equations of state and axial ratios were measured with high statistical quality. These equations of state are combined with thermal parameters from previous reports to improve the extrapolation of the density, adiabatic bulk modulus, and bulk sound speed to the pressures and temperatures of Earth's inner core. We propagate uncertainties and place constraints on the composition of Earth's inner core by combining these results with available data on light‐element alloys of iron and seismic observations. For example, the addition of 4.3 to 5.3 wt% silicon to Fe_(0.95)Ni_(0.05) alone can explain geophysical observations of the inner core boundary, as can up to 7.5 wt% sulfur with negligible amounts of silicon and oxygen. Our findings favor an inner core with less than ∼2 wt% oxygen and less than 1 wt% carbon, although uncertainties in electronic and anharmonic contributions to the equations of state may shift these values. The compositional space widens toward the center of the Earth, considering inner core seismic gradients. We demonstrate that hcp‐Fe_(0.91)Ni_(0.09) and hcp‐Fe_(0.8)Ni_(0.1)Si_(0.1) have measurably greater c/aaxial ratios than those of hcp‐Fe over the measured pressure range. We further investigate the relationship between the axial ratios, their pressure derivatives, and elastic anisotropy of hcp‐structured materials.