Thermoelastic properties of liquid Fe-C revealed by sound velocity and density measurements at high pressure

Carbon is one of the possible light elements in the cores of the terrestrial planets. The P wave velocity (V_P) and density (ρ) are important factors for estimating the chemical composition and physical properties of the core. We simultaneously measured the V_P and ρ of Fe-3.5 wt % C up to 3.4 GPa and 1850 K by using ultrasonic pulse-echo method and X-ray absorption methods. The V_P of liquid Fe-3.5 wt % C decreased linearly with increasing temperature at constant pressure. The addition of carbon decreased the V_P of liquid Fe by about 2% at 3 GPa and 1700 K and decreased the Fe density by about 2% at 2 GPa and 1700 K. The bulk modulus of liquid Fe-C and its pressure (P) and temperature (T) effects were precisely determined from directly measured ρ and V_P data to be K_{0,1700 K} = 83.9 GPa, dK_T/dP = 5.9(2), and dK_T/dT = −0.063 GPa/K. The addition of carbon did not affect the isothermal bulk modulus (K_T) of liquid Fe, but it decreased the dK/dT of liquid Fe. In the ρ-V_P relationship, V_P increases linearly with ρ and can be approximated as V_P (m/s) = −6786(506) + 1537(71) × ρ (g/cm³), suggesting that Birch's law is valid for liquid Fe-C at the present P-T conditions. Our results imply that at the conditions of the lunar core, the elastic properties of an Fe-C core are more affected by temperature than those of Fe-S core.