The effects of ferromagnetism and interstitial hydrogen on the equation of states of hcp and dhcp FeHx: Implications for the Earth's inner core age

Abstract

Hydrogen has been considered as an important candidate of light elements in the Earth's core. Because iron hydrides are unquenchable, hydrogen content is usually estimated from in-situ X-ray diffraction measurements assuming the following linear relation: x = (V FeHx-V Fe) / V H , where x is the hydrogen content, V H is the volume expansion caused by unit concentration of hydrogen, V FeHx and V Fe are volumes of FeH x and pure iron, respectively. To verify the linear relationship, we computed the equation of states of hexagonal iron with interstitial hydrogen by using the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA). The results indicate a discontinuous volume change at the magnetic transition and almost no compositional (x) dependence in the ferromagnetic phase at 20 GPa, whereas the linearity is confirmed in the non-magnetic phase. In addition to their effects on density-composition relationship in the Fe-FeH x system, which is important for estimating the hydrogen incorporation in planetary cores, the magnetism and interstitial hydrogen also affect the electrical resistivity of FeH x. The thermal conductivity can be calculated from the electrical resistivity by using the Wiedemann-Franz law, which is a critical parameter for modeling the thermal evolution of the Earth. Assuming an Fe 1-y Si y H x ternary outer core model (0.0  x  0.7), we calculated the thermal conductivity and the age of the inner core. The resultant thermal conductivity is ~100 W/m/K and the maximum inner core age ranges from 0.49 to 0.86 Gyr.

Impurity Resistivity of fcc and hcp Fe-Based Alloys: Thermal Stratification at the Top of the Core of Super-Earths

“…But H is known to enter the interstitial sites (Antonov et al, 2002;Fukai, 2006). The partial density of states (PDOS) of interstitial H in hcp and double hexagonal close-packed (dhcp) Fe is located at far below the Fermi energy (e.g., Tsumuraya et al, 2012;Gomi et al, 2018). Therefore, Gomi et al (2018) argued that the impurity resistivity of interstitial hydrogen is negligibly small.…”

“…The partial density of states (PDOS) of interstitial H in hcp and double hexagonal close-packed (dhcp) Fe is located at far below the Fermi energy (e.g., Tsumuraya et al, 2012;Gomi et al, 2018). Therefore, Gomi et al (2018) argued that the impurity resistivity of interstitial hydrogen is negligibly small. This is consistent with recent DAC experiments on fcc FeH x alloys (Ohta et al, 2018).…”

“…Then, we estimated the thermal conductivity via the Wiedemann-Franz law (Equation 1) using the present resistivity and the Lorenz number. The total electrical resistivity was calculated from the Cote and Meisel (1978) model combined with the present impurity resistivity and the phonon-contributed resistivity modeled by Gomi et al (2013Gomi et al ( , 2016Gomi et al ( , 2018.…”

“…However, this argument is limited to pure Fe. As well as the impurity resistivity calculation, the KKR-CPA method can easily simulate the DOS of disordered alloys (Gomi et al, 2016(Gomi et al, , 2018. This paper is organized as follows.…”

Heat Flow in Earth's Core From Invariant Electrical Resistivity of Fe‐Si on the Melting Boundary to 9 GPa: Do Light Elements Matter?

“…Experiments and calculations show, in general, that the effect of alloying with Fe is an increase in electrical resistivity and concomitant decrease in thermal conductivity (Gomi et al, ; Gomi & Yoshino, ; Wagle et al, ; Wagle et al, ) although experiments show that stoichiometric FeH is more conductive than pure Fe (Ohta, Nishihara, et al, ; Ohta, Suehiro, et al, ). The values of ρ and κ estimated for pure Fe at the CMB range from ~60–130 μΩcm and ~67–145 W/mK, respectively, while the addition of 9 wt% Si reduces thermal conductivity to ~41–60 W/mK at the same pressure (Seagle et al, ).…”