A New Reference for the Thermal Equation of State of Iron

Abstract

The high-pressure, high-temperature behavior of iron was investigated to 140 GPa and 3500 K with in situ synchrotron X-ray diffraction. Iron samples were compressed in diamond-anvil cells and heated up with the double-sided laser-heating system installed at the high-pressure ID27 of the European Synchrotron Radiation Facility (ESRF). Three different structures, namely α-bcc, γ-fcc or ε-hcp Fe were identified as a function of pressure and temperature in the domain we explored. At pressures above 90 GPa, it is clearly shown that ε-iron is the single stable solid phase up to 160 GPa at high temperatures. The analysis of the P-V-T relationship allows us to propose a reliable experimental thermal equation of state (EoS) for iron. We also show that the addition of low pressure points to our EoS refinement yields more robust constrain on the determination of the reference volume V0 of the ε-hcp structure, which has important implications on the final parametrization of the equation of state. The extrapolation of the proposed EoS to core pressure conditions indicates that a pure iron core would have an excess of density of 3% compared to the PREM density profile.

Equation of State of hcp Fe‐C‐Si Alloys and the Effect of C Incorporation Mechanism on the Density of hcp Fe Alloys at 300 K

“…A comprehensive comparison of the equations of state parameters K 0 and K 0 ′ of the different alloys considered here is illustrated in the inset in Figure 2a. The data published by Dewaele et al (2006), Sakai et al (2014), Yang et al (2019), and Miozzi, Matas, et al (2020) for pure Fe and by Edmund et al (2019) and Yang et al (2019) for Fe-Si and Fe-C alloys, respectively, were reevaluated in order to obtain the variance-covariance matrixes (Angel, 2000) and to construct the confidence ellipses (Table 1; inset Figure 2a). The confidence ellipses of our data set are larger than those reported in the literature.…”

“…This might be due to the different pressure and volume uncertainties, how these are taken into account in the analysis, and to the number and range of measured pressure points in the different studies. Here, both pressure and volume uncertainties were weighted, whereas most of the (Edmund et al, 2019;Yang et al, 2019) and reference EoS for pure Fe (Dewaele et al, 2006;Miozzi, Matas, et al, 2020;Sakai et al, 2014;Yang et al, 2019) are shown for comparison. Inset: confidence ellipses centered on each data point, representing the 68.3% confidence level.…”

“…When performing an equally weighted fit, errors are smaller, and thus, also, the correlation between K 0 and K 0 ′ is smaller. In addition, given the trade-off between V 0 , K 0 , and K 0 ′, it is important to measure the volume of the hcp structure at the lowest pressure in order to constrain the refinement of the room temperature EoS (see, e.g., Miozzi, Matas, et al, 2020). In our study, due to the lack of low-pressure points (we report P-V data from 48 GPa; see Table S1), the EoS refinement provides a less robust constraint of the reference volume at P = 0 (i.e., V 0 ).…”

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

“…Measured volumes of quenched hcp Fe collected in this study are presented in Figure 2 and are systematically larger, over the whole pressure range, than those of pure hcp Fe from literature (e.g. Dewaele et al, 2006;Miozzi et al, 2020). Although Si shows a large solubility in hcp Fe under high pressure, up to ~18 at % Si (e.g.…”

“…Green triangles represent the experimental data from this study, purple line the EoS fitted with the elastic parameter of pure Fe, black squares the experimental data on Fe-9.5 at % Si from . Blue dashed line the EoS of pure Fe (hcp) from (Miozzi et al 2020). Inset: Ternary Fe-Si-C diagram showing the phase relations in the iron rich side.…”