Shock temperature and melting in iron sulfides at core pressures

Abstract

The temperatures of shock-compressed FeS and FeS_2 in the pressure ranges 125–170 GPa and 100–244 GPa, respectively, are reported and used to constrain the melting curves and thermodynamic properties to core pressures. A fit of the Lindemann law parameters corresponding to the usual functional form for the lattice Grüneisen parameter gives γ_L = 1.17 ± 0.13 and n_L = 0.5 ± 0.5 for the high-pressure phase of FeS at ρ = 5340 kg/m^3 and γ_L = 2.18 ± 0.32 and n_L = 1.6 ± 0.7 for FeS_2 at ρ = 5011 kg/m^3. The entropies of fusion are ∼203 J kg−1 K−1 for FeS at 120 GPa and ∼180 J kg^−1 K^−1 for FeS_2 at 220 GPa. We find that the melting temperature of FeS is 3240±200 K, 4210 ± 700 K, and 4310 ± 750 K at 136 GPa, 330 GPa, and 360 GPa, respectively. For FeS_2, the melting temperatures are 3990 ± 300 K, 5310 ± 700 K, and 5440 ± 750 K, respectively, for the same pressures. The electronic specific heat for FeS is given by C_e = β_0 (ρ_0/ρ)γe with β0 = 0.25 ± 0.10 J kg^−1 K^−2 and γ_e = 1.34 for ρ0 = 5340 kg/m3 for the high-pressure solid phase and β_0 ≈ 0.05 J kg−1 K^−2 and γe = 1.34 for ρ_0 = 5150 kg/m^3 for the liquid phase. For FeS_2, there is no detectable electronic contribution, and the lattice specific heat is only 67% of the Dulong-Petit limit, possibly implying tight S-S binding in S_2 units. A reexamination of all shock wave melting data for Fe indicates these approximately agree, but they do not resolve the disagreement between the extrapolated static diamond anvil cell data sets. Fe should melt at ∼6600 K at 243 GPa and 6900 ± 750 K at 330 GPa (the pressure of the inner core-outer core boundary). Because the FeS melting curve falls well below that of FeS_2, FeS may eventually undergo peritectic melting at high pressures, while FeS_2 melts congruently.