Equations of State, Sound Velocities, and Thermoelasticity of Iron-Nickel-Silicon Alloys in the Earth’s Inner Core

Abstract

The core of the Earth is predominately iron alloyed with approximately 5 wt% nickel along with some amount of light elements, e.g., Si, O, S, C, H, Mg. Mineral physics studies, in conjunction with seismological and cosmochemical observations, provide an opportunity to improve constraints on the composition of the core. In this thesis, we investigate the thermoelastic and vibrational properties of bcc- and hcp-structured Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 (atomic percent) at high pressures. We present powder x-ray diffraction data on bcc- and hcp-structured Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 at 300 K up to 167 GPa and 175 GPa, respectively. The alloys were compressed in 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 place constraints on the composition of Earth’s inner core by combining these results with seismic observations and available data on other light-element alloys of iron. We find the addition of 4.3 to 5.3 wt% silicon to Fe0.95Ni0.05 alone can explain geophysical observations of density, adiabatic bulk modulus, and bulk sound speed at 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. Seismic studies provide evidence for an anisotropic inner core, which is suggested to be related to the ratio of the c- to a-unit cell parameters of hcp-structured materials. We demonstrate hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 have measurably greater c/a axial 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. Next, we present high pressure NRIXS data on bcc- and hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 at 300 K with in situ x-ray diffraction. From these data, we determine the partial phonon density of states for each composition, and we systematically compare our results to iron. We constrain the Debye sound velocity from the low energy region of the phonon density of states. Using our previously determined equations of state for the same compositions, we constrain the compressional and shear sound velocities and shear moduli. At 300 K, we find that 9 at% nickel decreases the shear velocity of hcp-iron by ∼6% and that silicon has a minimal effect on the shear velocity of hcp-Fe0.91Ni0.09. Thermal effects likely play a large role in the sound velocities of iron alloys at core conditions, so constraining these effects is critical to further constrain the composition of the core. From the volume scaling of the phonon DOS, we find the 300 K vibrational components of the Gruneisen parameter for hcp-Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 are very similar to that of hcp-Fe within uncertainties. We also constrain vibrational thermal pressure from the volume dependence of vibrational free energy, and we find negligible differences within uncertainty between the vibrational thermal pressures of hcp-Fe, Fe0.91Ni0.09, and Fe0.8Ni0.1Si0.1. By combining the vibrational component of thermal pressure with theoretical estimates of the anharmonic and electronic contributions, we provide an estimate for the total thermal pressure. We constrain a variety of additional parameters from the NRIXS data and phonon density of states, including the vibrational component of entropy, the vibrational thermal expansion, the vibrational kinetic energy, the Lamb-Mossbauer factor, and the vibrational specific heat.