Sound velocity and elastic properties of Fe–Ni and Fe–Ni–C liquids at high pressure

The sound velocity (V P) of liquid Fe–10 wt% Ni and Fe–10 wt% Ni–4 wt% C up to 6.6 GPa was studied using the ultrasonic pulse-echo method combined with synchrotron X-ray techniques. The obtained V P of liquid Fe–Ni is insensitive to temperature, whereas that of liquid Fe–Ni–C tends to decrease with increasing temperature. The V P values of both liquid Fe–Ni and Fe–Ni–C increase with pressure. Alloying with 10 wt% of Ni slightly reduces the V P of liquid Fe, whereas alloying with C is likely to increase the V P. However, a difference in V P between liquid Fe–Ni and Fe–Ni–C becomes to be smaller at higher temperature. By fitting the measured V P data with the Murnaghan equation of state, the adiabatic bulk modulus (K S0) and its pressure derivative (K S ′ ) were obtained to be K S0 = 103 GPa and K S ′ = 5.7 for liquid Fe–Ni and K S0 = 110 GPa and K S ′ = 7.6 for liquid Fe–Ni–C. The calculated density of liquid Fe–Ni–C using the obtained elastic parameters was consistent with the density values measured directly using the X-ray computed tomography technique. In the relation between the density (ρ) and sound velocity (V P) at 5 GPa (the lunar core condition), it was found that the effect of alloying Fe with Ni was that ρ increased mildly and V P decreased, whereas the effect of C dissolution was to decrease ρ but increase V P. In contrast, alloying with S significantly reduces both ρ and V P. Therefore, the effects of light elements (C and S) and Ni on the ρ and V P of liquid Fe are quite different under the lunar core conditions, providing a clue to constrain the light element in the lunar core by comparing with lunar seismic data.