Axial Compressibility and Thermal Equation of State of Hcp Fe–5wt% Ni–5wt% Si

Abstract

Knowledge of the elastic properties and equations of state of iron and iron alloys are of fundamental interest in Earth and planetary sciences as they are the main constituents of telluric planetary cores. Here, we present results of X-ray diffraction measurements on a ternary Fe–Ni–Si alloy with 5 wt% Ni and 5 wt% Si, quasi-hydrostatically compressed at ambient temperature up to 56 GPa, and under simultaneous high pressure and high temperature conditions, up to 74 GPa and 1750 K. The established pressure dependence of the c/a axial ratio at ambient temperature and the pressure–volume–temperature (P–V–T) equation of state are compared with previous work and literature studies. Our results show that Ni addition does not affect the compressibility and axial compressibility of Fe–Si alloys at ambient temperature, but we suggest that ternary Fe–Ni–Si alloys might have a reduced thermal expansion in respect to pure Fe and binary Fe–Si alloys. In particular, once the thermal equations of state are considered together with velocity measurements, we conclude that elements other than Si and Ni have to be present in the Earth’s inner core to account for both density and seismic velocities.

Sound Velocity Measurements of B2‐Fe‐Ni‐Si Alloy Under High Pressure by Inelastic X‐Ray Scattering: Implications for the Composition of Earth's Core

“…The equation of state (EOS) collected in run SD008 is consistent with previous studies on Fe‐Si based on observations of Edmund et al. (2020) that the addition of Ni does not affect compressibility (Figure S5 in Supporting Information ). Observed differences between EOS parameters of this study and previous work (Kamada et al., 2018; Edmund, Antonangeli, Decremps, Morard, et al., 2019; Edmund, Antonangeli, Decremps, Miozzi, et al., 2019) are related to differences in composition and employed fitting models (third order Birch‐Murnaghan (BM3) or Vinet).…”

“…(2019) (orange); hcp ‐Fe 0.86 Ni 0.05 Si 0.9 : Edmund et al. (2020) (yellow) (from case #1 to case #4, see Table S5 in Supporting Information ). Black diamonds and associated solid lines are Birch's law of B2‐Fe 0.67 Ni 0.06 Si 0.27 at 300 K. Triangles represent V P and V S ‐density relations from previous selected studies of hcp Fe 0.92 Ni 0.08 (white: Lin et al.…”

“…We applied the P th correction using the Mie‐Grüneisen Debye (MGD) model (e.g., Poirier, 2000). Thermoelastic parameters (i.e., Debye temperature θ , Grüneisen parameter γ and its logarithmic volume derivative q ) of hcp and hcp + B2‐Fe 0.84 Si 0.16 (R. A. Fischer et al., 2014), hcp ‐Fe 0.81 Ni 0.09 Si 0.1 (Morrison et al., 2018), hcp ‐Fe 0.91 Si 0.09 (Edmund, Antonangeli, Decremps, Miozzi, et al., 2019), and hcp ‐Fe 0.86 Ni 0.05 Si 0.9 (Edmund et al., 2020) from previous studies were used in the calculation. Table S5 in Supporting Information summarizes the thermodynamic parameters used to extrapolate density and sound velocities to ICB conditions.…”

Eutectic melting of Fe-3 at% Si-4 at% C up to 200 GPa and implications for the Earth's core

“…Finally, while the already mentioned recent calculation (Li et al, 2018) suggests Fe-C-Si alloys to have velocities compatible with PREM at inner core P-T conditions, experimental determinations support significant increase in the sound velocities of iron due Si alloying (Antonangeli et al, 2018;. This makes difficult to find solutions with large light element content simultaneously accounting for both velocities and density , in particular when allowing for the likely presence of nickel, which increases atomic mass and reduces the thermal expansion of the alloy (Edmund et al, 2020). Further experimental work is thus necessary to confirm the theoretical predictions.…”

High‐Pressure Deformation of Iron–Nickel–Silicon Alloys and Implications for Earth’s Inner Core

“…(1980): where subscript 0 indicates ambient conditions ( T = 300 K, P = 1 bar) and ρ is the molar density. Values of G 0 and are taken from the NRIXS fit in Figure 4, ρ 0 is from equation of state literature (Fe–5Si from Edmund et al., 2019; Fe–5Ni–5Si from Edmund et al., 2020; other alloys calculated from these and the pure Fe values of Dewaele et al., 2006), ρ is the preliminary reference Earth model (PREM) inner core density, and G ( P , T ) is calculated from ρ and the PREM inner core shear velocity (Dziewonski & Anderson, 1981). Selecting locations in the inner core, namely the inner core boundary (ICB) and inner core center (ICC), allows to be solved at the corresponding pressure and temperature conditions.…”