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.

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Compression and decompression experiments on face-centered cubic (fcc) γ′-Fe4N to 77 GPa at room temperature were conducted in a diamond-anvil cell with in situ X-ray diffraction (XRD) to examine its stability under high pressure. In the investigated pressure range, γ′-Fe4N did not show any structural transitions. However, a peak broadening was observed in the XRD patterns above 60 GPa. The obtained pressure-volume data to 60 GPa were fitted to the third-order Birch-Murnaghan equation of state (EoS), which yielded the following elastic parameters: K0 = 169 (6) GPa, K′ = 4.1 (4), with a fixed V0 = 54.95 Å at 1 bar. A quantitative Schreinemakers' web was obtained at 15–60 GPa and 300–1600 K by combining the EoS for γ′-Fe4N with reported phase stability data at low pressures. The web indicates the existence of an invariant point at 41 GPa and 1000 K where γ′-Fe4N, hexagonal closed-packed (hcp) ε-Fe7N3, double hexagonal closed-packed β-Fe7N3, and hcp Fe phases are stable. From the invariant point, a reaction γ′-Fe4N = β-Fe7N3 + hcp Fe originates toward the high-pressure side, which determines the high-pressure stability of γ′-Fe4N at 56 GPa and 300 K. Therefore, the γ′-Fe4N phase observed in the experiments beyond this pressure must be metastable. The obtained results support the existing idea that β-Fe7N3 would be the most nitrogen-rich iron compound under core conditions. An iron carbonitride Fe7(C,N)3 found as a mantle-derived diamond inclusion implies that β-Fe7N3 and Fe7C3 may form a continuous solid solution in the mantle deeper than 1000 km depth. Diamond formation may be related to the presence of fluids in the mantle, and dehydration reactions of high-pressure hydrous phase D might have supplied free fluids in the mantle at depths greater than 1000 km. As such, the existence of Fe7(C,N)3 in diamond can be an indicator of water transportation to the deep mantle.

Melting experiments on Fe3S were conducted to 75 GPa and 2800 K in laser-heated and internally resistive-heated diamond anvil cells with in-situ x-ray diffraction and/or post-mortem textural observation. From the constrained melting curve, we assessed the thermal equation of state for Fe3S liquid. Then we constructed a thermodynamic model of melting of the system Fe–Fe3S including the eutectic relation under high pressures based on our new experimental data. The mixing properties of Fe–S liquids under high pressures were evaluated in order to account for existing experimental data on eutectic temperature. The results demonstrate that the mixing of Fe and S liquids are nonideal at any core pressure. The calculated sulphur content in eutectic point decreases with increasing pressure to 120 GPa and is fairly constant of 8 wt% at greater pressures. From the Gibbs free energy, we derived the parameters to calculate the crystallising point of an Fe–S core and its isentrope, and then we calculated the density and the longitudinal seismic wave velocity (Vp) of these liquids along each isentrope. While Fe3S liquid can account for the seismologically constrained density and Vp profiles over the outer core, the density of the precipitating phase is too low for the inner core. On the other hand, a hypothetical Fe–S liquid core with a bulk composition on the Fe-rich side of the eutectic point cannot represent the density and Vp profiles of the Earth’s outer core. Therefore, Earth’s core cannot be approximated by the system Fe–S and it should include another light element.