Rebecca A. Fischer

Equations of state in the Fe‐FeSi system at high pressures and temperatures

Earths core is an iron-rich alloy containing several weight percent of light element(s), possibly including silicon. Therefore, the high pressure-temperature equations of state of iron-silicon alloys can provide understanding of the properties of Earths core. We performed X-ray diffraction experiments using laser-heated diamond anvil cells to achieve simultaneous high pressures and temperatures, up to ~200 GPa for Fe–9 wt % Si alloy and ~145 GPa for stoichiometric FeSi. We determined equations of state of the D03, hcp + B2, and hcp phases of Fe–9Si, and the B20 and B2 phases of FeSi. We also calculated equations of state of Fe, Fe11Si, Fe5Si, Fe3Si, and FeSi using ab initio methods, finding that iron and silicon atoms have similar volumes at high pressures. By comparing our experimentally determined equations of state to the observed core density deficit, we find that the maximum amount of silicon in the outer core is ~11 wt %, while the maximum amount in the inner core is 6–8 wt %, for a purely Fe-Si-Ni core. Bulk sound speeds predicted from our equations of state also match those of the inner and outer core for similar ranges of compositions. We find a compositional contrast between the inner and outer core of 3.5–5.6 wt % silicon, depending on the seismological model used. Theoretical and experimental equations of state agree at high pressures. We find a good match to the observed density, density profile, and sound speed of the Earths core, suggesting that silicon is a viable candidate for the dominant light element.

Radial mixing and Ru–Mo isotope systematics under different accretion scenarios

The Ru-Mo isotopic compositions of inner Solar System bodies may reflect the provenance of accreted material and how it evolved with time, both of which are controlled by the accretion scenario these bodies experienced. Here we use a total of 116 N-body simulations of terrestrial planet accretion, run in the Eccentric Jupiter and Saturn (EJS), Circular Jupiter and Saturn (CJS), and Grand Tack scenarios, to model the Ru-Mo anomalies of Earth, Mars, and Theia analogues. This model starts by applying an initial step function in Ru-Mo isotopic composition, with compositions reflecting those in meteorites, and traces compositional evolution as planets accrete. The mass-weighted provenance of the resulting planets reveals more radial mixing in Grand Tack simulations than in EJS/CJS simulations, and more efficient mixing among late-accreted material than during the main phase of accretion in EJS/CJS simulations. We find that an extensive homogenous inner disk region is required to reproduce Earths observed Ru-Mo composition. EJS/CJS simulations require a homogeneous reservoir in the inner disk extending to ≥3-4 AU (≥74-98% of initial mass) to reproduce Earths composition, while Grand Tack simulations require a homogeneous reservoir extending to ≥3-10 AU (≥97-99% of initial mass), and likely to ≥6-10 AU. In the Grand Tack model, Jupiters initial location (the most likely location for a discontinuity in isotopic composition) is ~3.5 AU; however, this step location has only a 33% likelihood of producing an Earth with the correct Ru-Mo isotopic signature for the most plausible model conditions. Our results give the testable predictions that Mars has zero Ru anomaly and small or zero Mo anomaly, and the Moon has zero Mo anomaly. These predictions are insensitive to wide variations in parameter choices.

Equation of state of pyrite to 80 GPa and 2400 K

Abstract The high-cosmic abundance of sulfur is not reflected in the terrestrial crust, implying it is either sequestered in the Earth’s interior or was volatilized during accretion. As it has widely been suggested that sulfur could be one of the contributing light elements leading to the density deficit of Earth’s core, a robust thermal equation of state of iron sulfide is useful for understanding the evolution and properties of Earth’s interior. We performed X-ray diffraction measurements on FeS2 achieving pressures from 15 to 80 GPa and temperatures up to 2400 K using laser-heated diamond-anvil cells. No phase transitions were observed in the pyrite structure over the pressure and temperature ranges investigated. Combining our new P-V-T data with previously published room-temperature compression and thermochemical data, we fit a Debye temperature of 624(14) K and determined a Mie-Grüneisen equation of state for pyrite having bulk modulus KT = 141.2(18) GPa, pressure derivative KT′=5.56(24)

The axial ratio of hcp Fe and Fe–Ni–Si alloys to the conditions of Earth’s inner core

K_{\rm{T}}^\prime = 5.56\left( {24} \right)

The W-WO2 oxygen fugacity buffer (WWO) at high pressure and temperature: Implications for fO2 buffering and metal-silicate partitioning

, Grüneisen parameter γ0 = 1.41, anharmonic coefficient A2 = 2.53(27) × 10−3 J/(K2·mol), and q = 2.06(27). These findings are compared to previously published equation of state parameters for pyrite from static compression, shock compression, and ab initio studies. This revised equation of state for pyrite is consistent with an outer core density deficit satisfied by 11.4(10) wt% sulfur, yet matching the bulk sound speed of PREM requires an outer core composition of 4.8(19) wt% S. This discrepancy suggests that sulfur alone cannot satisfy both seismological constraints simultaneously and cannot be the only light element within Earth’s core, and so the sulfur content needed to satisfy density constraints using our FeS2 equation of state should be considered an upper bound for sulfur in the Earth’s core.

High-pressure, high-temperature equations of state using nanofabricated controlled-geometry Ni/SiO2/Ni double hot-plate samples

Abstract The Earth’s iron-rich inner core is seismically anisotropic, which may be due to the preferred orientation of Fe-rich hexagonal close packed (hcp) alloy crystals. Elastic anisotropy in a hexagonal crystal is related to its c/a axial ratio; therefore, it is important to know how this ratio depends on volume (or pressure), temperature, and composition. Experimental data on the axial ratio of iron and alloys in the Fe-Ni-Si system from 15 previous studies are combined here to parameterize the effects of these variables. The axial ratio increases with increasing volume, temperature, silicon content, and nickel content. When an hcp phase coexists with another structure, sample recovery and chemical analysis from each pressure-temperature point is one method for determining the phase’s composition and thus the position of the phase boundary. An alternate method is demonstrated here, using this parameterization to calculate the composition of an hcp phase whose volume, temperature, and axial ratio are measured. The hcp to hcp+B2 phase boundary in the Fe-FeSi system is parameterized as a function of pressure, temperature, and composition, showing that a silicon-rich inner core may be an hcp+B2 mixture. These findings could help explain observations of a layered seismic anisotropy structure in the Earth’s inner core.

High pressure metal–silicate partitioning of Ni, Co, V, Cr, Si, and O

Abstract Synchrotron X-ray diffraction data were obtained to simultaneously measure unit-cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. Both W and WO2 unit-cell volume data were fit to Mie-Grüneisen equations of state; parameters for W are KT = 307 (±0.4) GPa, KT′ = 4.05(±0.04)

Equation of state and phase diagram of FeO

K_{\rm{T}}^{_\prime }\, = \,4.05\left( { \pm 0.04} \right)

Phase relations in the Fe-FeSi system at high pressures and temperatures

, γ0 = 1.61 (±0.03), and q = 1.54 (±0.13). Three phases were observed in WO2 with structures in the P21/c, Pnma, and C2/c space groups. The transition pressures are 4 and 32 GPa for the P21/c-Pnma and Pnma-C2/c phase changes, respectively. The P21/c and Pnma phases have previously been described, whereas the C2/c phase is newly described here. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 238 (±7), 230 (±5), 304 (±3) GPa, KT′ = 4

Phase transition and metallization of FeO at high pressures and temperatures

K_{\rm{T}}^{_\prime }\, = \,4