Molecular dynamics estimates for the thermodynamic properties of the Fe–S liquid cores of the Moon, Io, Europa, and Ganymede

A molecular dynamics (MD) simulation is performed for the physical and chemical properties of solid and liquid Fe–S solutions using the embedded atom model (EAM) potential as applied to the internal structure of the Moon, Io, Europa, and Ganymede under the assumption that the satellites' cores can be described by a two-component iron–sulfur system. Calculated results are presented for the thermodynamic parameters including the caloric, thermal, and elastic properties (specific heat, thermal expansion, Grüneisen parameter, density, compression module, velocity of sound, and adiabatic gradient) of the Fe–S solutions at sulfur concentrations of 0–18 at %, temperatures of up to 2500 K, and pressures of up to 14 GPa. The velocity of sound, which increases as pressure rises, is weakly dependent on sulfur concentration and temperature. For the Moon’s outer Fe–S core (~5 GPa/2000 K), which contains 6–16 at % (3.5–10 wt %) sulfur, the density and the velocity of sound are estimated at 6.3–7.0 g/cm³ and 4000 ± 50 m/s, respectively. The MD calculations are compared with the interpretation of the Apollo observations (Weber et al., 2011) to show a good consistency of the velocity of P-waves in the Moon’s liquid core whereas the thermodynamic density of the Fe–S core is not consistent with the seismic models with ρ = 5.1–5.2 g/cm³ (Garcia et al., 2011; Weber et al., 2011). The revision the density values for the core leads to the revision of its size and mass. At sulfur concentrations of 3.5–10 wt %, the density of the Fe–S melt is 20–30% higher that the seismic density of the core. Therefore, the most likely radius of the Moon’s outer core must be less than 330 km (Weber et al., 2011) because, provided that the constraint on the Moon’s mass and moment of inertia is satisfied, an increase in the density of the core must lead to a reduction of its radius. For Jupiter’s Galilean moons Io, Europa, and Ganymede, constraints are obtained on the size, density, and sound velocity of the Fe–S liquid cores. The geophysical and geochemical characteristics of the internal structure of the Moon and Jupiter’s moons are compared. The calculations of the adiabatic gradient at the P–T conditions for the Fe–S cores of the Moon, Io, Europa, and Ganymede suggest the top-down crystallization of the core (Fe-snow scenario).