Thermal equation of state of hcp‐iron: Constraint on the density deficit of Earth's solid inner core

Abstract

We conducted high‐pressure experiments on hexagonal close packed iron (hcp‐Fe) in MgO, NaCl, and Ne pressure‐transmitting media and found general agreement among the experimental data at 300 K that yield the best fitted values of the bulk modulus K0 = 172.7(±1.4) GPa and its pressure derivative K0′ = 4.79(±0.05) for hcp‐Fe, using the third‐order Birch‐Murnaghan equation of state. Using the derived thermal pressures for hcp‐Fe up to 100 GPa and 1800 K and previous shockwave Hugoniot data, we developed a thermal equation of state of hcp‐Fe. The thermal equation of state of hcp‐Fe is further used to calculate the densities of iron along adiabatic geotherms to define the density deficit of the inner core, which serves as the basis for developing quantitative composition models of the Earth's inner core. We determine the density deficit at the inner core boundary to be 3.6%, assuming an inner core boundary temperature of 6000 K.

Phase Stability and Thermal Equation of State of Iron Carbide Fe3C to 245 GPa

“…The solid circles represent the Hugoniot data of Fe 3 C (this work). The open symbols (circle, Sata et al, ; square, Li et al, ; up triangle, Litasov et al, ; down triangle, Ono & Mibe, ) represent the 300‐K isothermal compression data of Fe 3 C. The Hugoniot data (solid diamond; Brown et al, ) and 300‐K isothermal compression data (open diamond; Fei et al, ) of pure iron are also plotted for comparison. The solid and dot lines represent the fitted Hugoniot curve and three‐order Birch‐Murnaghan equation of state curve, respectively.…”

Phase relations of Fe3C and Fe7C3 up to 185 GPa and 5200 K: Implication for the stability of iron carbide in the Earth's core

“…The uncertainty in temperature is about 50-200 K estimated from both heating sides. [Fei et al, 2016], which were found to be comparable to pressures within AE2-4 GPa obtained from the measured lattice parameters of B2-KCl using its EoS at 300 K. Because the transparent pressure medium and thermal insulator do not act as a laser absorber, the 300 K EoS has been found to give similar pressures to that of the hot sample in cases where the thermal equation of state of the sample was known [Campbell et al, 2007]. The reported pressures from KCl thus represent a minimum estimate without correction for thermal pressure and may underestimate the pressure by a few GPa [Anzellini et al, 2013].…”

Equations of State and Anisotropy of Fe‐Ni‐Si Alloys

“…The uncertainty contributions due to the isothermal EOS parameters V 0 , K T 0 , and for hcp‐Fe, hcp‐Fe 0.91 Ni 0.09 , and hcp‐Fe 0.8 Ni 0.1 Si 0.1 are found to be of similar magnitude to the uncertainty due to γ 0 and q , which highlights the importance of accurately constraining the parameters V 0 , K T 0 , and to obtain reliable thermal equations of state. One of the greatest sources of uncertainty is due to the electronic and anharmonic contributions to the thermal pressure, which are not well constrained (e.g., Alfè et al, ; Fei et al, ; Martorell, Vočadlo, et al, ; Martorell, Brodholt, et al, , Martorell et al, ; Moustafa et al, ). To account for this, we enlarge our error bars on density, adiabatic bulk modulus, and bulk sound speed.…”

“…Several general conclusions can be drawn about the c / a axial ratios of pure iron. At 300 K, there is a weak decrease in the axial ratio of iron with pressure (e.g., Boehler et al, ; Dewaele et al, ; Fei et al, ; Steinle‐Neumann et al, ). However, ab initio calculations at 0 K instead show a weak increase in the axial ratio of iron with pressure (Cohen et al, ; Gannarelli et al, ; Steinle‐Neumann et al, , ).…”