Density and sound velocity of liquid Fe-S alloys at Earth's outer core P-T conditions

Abstract

Pressure-temperature-volume (P-T-V) data on liquid iron-sulfur (Fe-S) alloys at the Earth's outer core conditions (~136 to 330 GPa, ~4000 to 7000 K) have been obtained by first-principles molecular dynamics simulations. We developed a thermal equation of state (EoS) composed of Murnaghan and Mie-Grüneisen-Debye expressions for liquid Fe-S alloys. The density and sound velocity are calculated and compared with Preliminary Reference Earth Model (PREM) to constrain the S concentration in the outer core. Since the temperature at the inner core boundary (TICB) has not been measured precisely (4850~7100 K), we deduce that the S concentration ranges from 10~14 wt% assuming S is the only light element. Our results also show that Fe-S alloys cannot satisfy the seismological density and sound velocity simultaneously and thus S element is not the only light element. Considering the geophysical and geochemical constraints, we propose that the outer core contains no more than 3.5 wt% S, 2.5 wt% O, or 3.8 wt% Si. In addition, the developed thermal EoS can be utilized to calculate the thermal properties of liquid Fe-S alloys, which may serve as the fundamental parameters to model the Earth's outer core.

Phase Relations of Earth’s Core-Forming Materials

“…The density of liquid Fe 3 S (Fe-16S) estimated from that of solid Fe 3 S is from Thompson et al [138]. Results from the first-principles calculations are also shown (Badro et al [88]; Umemoto et al [144]; Ichikawa and Tsuchiya [89]; Fu et al [145]). The green open stars denote the pure Fe properties by [88].…”

“…Data of Fe-S liquids are summarized in Figure 25b including estimates based on solid compression data [138], first-principles calculations [88,89,144,145], and shock compression experiments [146]. Thompson et al [138] estimated the density profile of liquid Fe3S by assuming a ΔV upon melting (ΔVm) for Fe3S to be the same as for pure iron at core pressures, and assuming a temperature gradient by 1500 K through the outer core, which [138] at 300 (black dashed), 4000 (black solid), and 5500 K (green solid), compared with a compression profile of hcp Fe [4] along a 5500 K isotherm and the PREM profiles [51].…”

High-pressure melting experiments of Fe3S and a thermodynamic model of the Fe–S liquids for the Earth’s core

“…The profiles are along each isentrope starting at a temperature of the inner core boundary (T ICB ) (figure 8). Results from the first principles calculations are shown (lines: [17][18][19]; stars: [16]). Results from the density measurements of a shock wave compression study [69] are also plotted.…”

“…We then calculated the density and Vp profiles for Fe-16 wt%S (Fe 3 S) and Fe-6 wt%S liquids core along their isentropes, compared with existing data by first-principles calculation [16][17][18][19], shock wave compression experiment [69], and a seismologically constrained model (PREM, [70]) (figure 9). Considering the two competing factors, which are temperature and concentration of sulphur, our density profiles are qualitatively consistent with those of the first-principles calculations [16][17][18][19]. Our calculated density profile for Fe-16 wt%S matches the PREM values at 5710 K at the ICB.…”

“…As the large part of the core is molten, the compositional model for the liquid outer core is primarily important. First-principles calculations predicted the density and velocity for Fe-S liquids under core pressures [16][17][18][19]. On the other hand, direct experimental examination of the physical properties of a liquid under core pressures such as in diamond anvil cells (DACs) is currently very challenging due to the extreme conditions [20,21].…”