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 Fe0.91Ni0.09 and Fe0.8Ni0.1Si0.1 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 Fe0.95Ni0.05 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‐Fe0.91Ni0.09 and hcp‐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.

Velocity‐Density Systematics of Fe‐5wt%Si: Constraints on Si Content in the Earth's Inner Core

“…Shown in Figure as raw datapoints, the presented alloy exhibits a slightly higher volume than hcp‐Fe, consistent with literature on Fe‐Si alloys (Fischer et al, ; Lin, Campbell, et al,; Tateno et al, ). While the Earth's core is likely to be composed of an Fe‐Ni alloy, the addition of Ni likely does not significantly change the presented results and conclusions, due to the weak effect that Ni has on Vp relative to Fe and Si (Antonangeli et al,; Liu et al, ; Martorell et al, ; Wakamatsu et al, ) and its weak effect on density (Morrison et al, ). However, it is stressed that at present there are few constraints on the thermoelastic behavior of Fe‐Ni or Fe‐Ni‐Si alloys at simultaneous high P‐T conditions.…”

Chemical diversity of super-Earths as a consequence of formation

“…We then investigated how planets with primordial compositions, or those that have the same Fe/Mg ratios as their host stars, compare to these mass-radius relationships and the super-Earth data. We use the Fe/Mg ratio instead of 1 We have updated the equations of state to reflect better data obtained by Stixrude & Lithgow-Bertelloni (2011) for the mantle and that of the core by Morrison et al (2018). We chose the Fe 0.95 Ni 0.5 equation of state for the core, but to calculate the chemical budget we include an unspecified light alloy in the core that makes up 10% by mol and does not include magnesium, in line with the Earth (McDonough & Sun 1995), nor silicon, for simplification the Fe/Si ratio, as silicon is somewhat volatile (McDonough & Sun 1995), and thus may not be incorporated as readily into planets as magnesium.…”

High pressure thermoelasticity and sound velocities of Fe-Ni-Si alloys

“…However, there was considerable scatter in the data of iron (Mao et al, 2001) and iron-nickel, such that no effect could also be concluded from these measurements. A variety of experimental studies investigated the equations of state of hcp-iron-nickel at 300 K (Takahashi et al, 1968;Mao et al, 1990;Morrison et al, 2018) as well as at high temperatures (McQueen and Marsh, 1966;Asanuma et al, 2011;Sakai et al, 2014). However, constraints on the thermal equations of state of hcp-iron-nickel are limited and indicate a considerable range of thermal parameters associated with the effects of nickel (Ekholm et al, 2011;Côté et al, 2012;Martorell et al, 2013a).…”

“…Most constraints on iron-silicon sound velocities at inner core conditions come from ab initio studies (Vočadlo, 2007;Tsuchiya and Fujibuchi, 2009;Ono, 2013;Martorell et al, 2016). Isothermal equations of state of these alloys include Lin (2003); Hirao et al (2004); Ono et al (2007); Sata et al (2010); Asanuma et al (2011); Tateno et al (2015); Morrison et al (2018), and experimental thermal equations of state studies include Zhang and Guyot (1999); Fischer et al (2012Fischer et al ( , 2014; Tateno et al (2015), all utilizing x-ray diffraction techniques. However, to date, the thermal properties of ironnickel-silicon alloys, including constraints on the Grüneisen parameter, have not been investigated with techniques sensitive to the vibrational properties of the material.…”

“…Second, we estimate vibrational thermal pressure from the vibrational free energy derived from the phonon DOS. The thermal expansion is determined using constraints on the bulk modulus from the same alloys (Morrison et al, 2018). Additional parameters are derived from the phonon DOS including the vibrational kinetic energy, vibrational heat capacity and Lamb-Mössbauer factor.…”