Compression experiments to 126 GPa and 2500 K and thermal equation of state of Fe3S: Implications for sulphur in the Earth's core

Abstract

Pressure-volume-temperature (P-V-T) experiments on Fe 3 S were conducted to 126 GPa and 2500 K in laser-heated diamond anvil cells (DAC) with in-situ X-ray diffraction (XRD). Seventy nine high-T data as well as four 300-K data were collected, based on which new thermal equations of state (EoS) for Fe 3 S were established. The room-T data together with existing data were fitted to the third order Birch-Murnaghan EoS, which yielded, K 0 = 126 ± 2 GPa and K' = 5.1 ± 1 with V 0 fixed at 377.0 Å 3 . A constant αK T term in the thermal pressure equation, Pth = αK T (T-300K), fitted the high-T data well to the highest temperature, which implies that the contributions from the anharmonic and electronic terms should be minor in the thermal pressure term. The high-T data were also fitted to the Mie-Grüneisen-Debye model; γ 0 = 1.01 ± 0.03 with θ 0 and q fixed at 417 K and 1 respectively. Calculations from the EoS show that crystalline Fe 3 S at 4000-5500 K is denser than the Earth's outer core and less dense than the inner core. Assuming a density reduction due to melting, liquid Fe 3 S would meet the outer core density profile, which however suggests that no less than 16 wt%S is needed to reconcile the observed outer core density deficit. The S-rich B2 phase, which was suggested to be a potential liquidus phase of an Fe 3 S-outer core above 250 GPa, namely the main constituent of its solid inner core, would likely be less dense than the Earth's inner core. As such, while the outer core density requires as much sulphur as 16 wt%, the resulting liquidus phase cannot meet the density of the inner core. Any sulphur-rich composition should therefore be rejected for the Earth's core.

Phase Relations of Earth’s Core-Forming Materials

“…The most recent high-T data were reported by Thompson et al [138] who proposed a thermal EoS from laser-heated DAC experiments with in situ XRD to 126 GPa and 2500 K. Figure 23b shows compression curves of Fe 3 S calculated with the EoS by Thompson et al [138] and Kamada et al [136]. The EoS by [138] calculates the density of solid Fe 3 S greater than by [136] since Kamada et al [136] adopted the large αK T value (0.011 GPa/K) proposed by Seagle et al [135]. [122,124,129,130,134].…”

“…The 300-K EoS was well constrained thanks to the wide pressure range covered up to 200 GPa [135][136][137][138] (Figure 23a). In contrast, the thermal parameters were less studied [135,137,138]. The most recent high-T data were reported by Thompson et al [138] who proposed a thermal EoS from laser-heated DAC experiments with in situ XRD to 126 GPa and 2500 K. Figure 23b shows compression curves of Fe 3 S calculated with the EoS by Thompson et al [138] and Kamada et al [136].…”

“…The Properties of Fe 3 S Since the Fe 3 S phase is stable over 200 GPa as an end-member of the subsystem Fe-Fe 3 S (Figure 20), constraining its physical properties provides vital information about a hypothetical sulphur-bearing core. The EoS of Fe 3 S has been experimentally examined with in situ XRD [128,[135][136][137][138]. The 300-K EoS was well constrained thanks to the wide pressure range covered up to 200 GPa [135][136][137][138] (Figure 23a).…”

“…The EoS of Fe 3 S has been experimentally examined with in situ XRD [128,[135][136][137][138]. The 300-K EoS was well constrained thanks to the wide pressure range covered up to 200 GPa [135][136][137][138] (Figure 23a). In contrast, the thermal parameters were less studied [135,137,138].…”

“…(b) Unit-cell volumes for Fe 3 S under high temperatures [138]. Compression curves based on the thermal EoS constructed by [138] are shown together with those by [136]. The figures are from [138].…”