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A new experimental setup for simultaneous P-wave velocity (VP) and density (ρ) measurements for liquid alloys is developed using ultrasonic and X-ray absorption methods combined with X-ray tomography at high pressures and high temperatures. The new setup allows us to directly determine adiabatic bulk moduli (KS) and to discuss the correlation between the VP and ρ of the liquid sample. We measured VP and ρ of liquid Ni68S32 up to 5.6 GPa and 1045 K using this technique. The effect of pressure on the VP and ρ values of liquid Ni68S32 is similar to that of liquid Fe57S43. (Both compositions correspond to near-eutectic ones.) The obtained KS values are well fitted to the finite strain equation with a K S 0 value (KS at ambient pressure) of 31.1 GPa and a dKS/dP value of 8.44. The measured VP was found to increase linearly with increasing ρ, as approximated by the relationship: VP [m/s] = 1.29 ρ [kg/m3] – 5726, suggesting that liquid Ni–S follows an empirical linear relationship, Birch's law. The dVP/dρ slope is similar between Ni68S32 and Fe57S43 liquids, while the VP–ρ plot of liquid Ni–S is markedly different from that of liquid Fe–S, which indicates that the effect of Ni on Birch's law is important for understanding the VP–ρ relation of planetary and Moon's molten cores.

A technique for density measurement under high pressure and high temperature was developed using the X-ray absorption imaging method combined with an externally heated diamond anvil cell. The densities of solid and liquid In were measured in the pressure and temperature ranges of 3.2–18.6 GPa and 294–719 K. The densities obtained through the X-ray absorption imaging method were in good agreement (less than 2.0% difference) with those obtained through X-ray diffraction. Based on the measured density, the isothermal bulk modulus of solid In is determined as 48.0 ± 1.1−40.9 ± 0.8 GPa at 500 K, assuming K ′ = 4 to 6. The compression curve of liquid In approaches that of solid In at higher pressures and does not cross over the solid compression curve in the measurement range. The present technique enables us to determine the densities of both solids and liquids precisely in a wide pressure and temperature range.

The effects of pressure and temperature on the lattice constants and thermal expansion coefficients of Indium were studied up to 18.6 GPa and 506 K by using in situ X-ray diffraction method with an externally heated diamond anvil cell. Indium exhibits a tetragonal structure. The measured c/a ratio of tetragonal structure decreases with increasing temperature and its temperature dependence decreases with increasing pressure. The thermal expansion coefficient of the a-axis also decreases with increasing pressure up to 7 GPa and remains almost constant above 7 GPa, whereas that of the c-axis increases monotonously with pressure and changes from negative to positive at around 7 GPa. The observed behavior suggests that temperature reduces the tetragonal distortion of indium, and its effect is dominant below 7 GPa; in contrast, pressure enhances lattice distortion, and tends to have a stronger effect above 7 GPa.

Carbon is one of the possible light elements in the cores of the terrestrial planets. The P-wave velocity (VP) and density (ρ) are important factors for estimating the chemical composition and physical properties of the core. We simultaneously measured the VP and ρ of Fe-3.5 wt% C up to 3.4 GPa and 1850 K using ultrasonic pulse-echo method and X-ray absorption methods. The VP of liquid Fe-3.5 wt% C decreased linearly with increasing temperature at constant pressure. The addition of carbon decreased the VP 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 VP data to be K0,1700K = 83.9 GPa, dKT/dP = 5.9(2), and dKT/dT = −0.063(8) GPa/K. The addition of carbon did not affect the isothermal bulk modulus (KT) of liquid Fe but it decreased the dK/dT of liquid Fe. In the ρ–VP relationship, VP increases linearly with ρ and can be approximated as VP (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.

The cores of the Earth and other differentiated bodies are believed to be comprised of iron and various amounts of light elements. Measuring the densities and sound velocities of iron and its alloys at high pressures and high temperatures is crucial for understanding the structure and composition of these cores. In this study, the sound velocities ( v P and v S ) and density measurements of body-centered cubic ( bcc )-Fe were determined experimentally up to 6.3 GPa and 800 K using ultrasonic and X-ray diffraction methods. Based on the measured v P , v S , and density, we obtained the following parameters regarding the adiabatic bulk K S and shear G moduli of bcc -Fe: K S0 = 163.2(15) GPa, ∂ K S /∂ P = 6.75(33), ∂ K S /∂ T = −0.038(3) GPa/K, G 0 = 81.4(6) GPa, ∂ G /∂ P = 1.66(14), and ∂ G /∂ T = −0.029(1) GPa/K. Moreover, we observed that the sound velocity–density relationship for bcc -Fe depended on temperature in the pressure and temperature ranges analyzed in this study and the effect of temperature on v S was stronger than that on v P at a constant density, e.g., 6.0% and 2.7% depression for v S and v P , respectively, from 300 to 800 K at 8000 kg/m 3 . Furthermore, the effects of temperature on both v P and v S at a constant density were much greater for bcc -Fe than for ɛ-FeSi (cubic B20 structure), according to previously obtained measurements, which may be attributable to differences in the degree of thermal pressure. These results suggest that the effects of temperature on the sound velocity–density relationship for Fe alloys strongly depend on their crystal structures and light element contents in the range of pressure and temperature studied.

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.

Carbon is a plausible light element candidate in the Earth’s outer core. We measured the density of liquid Fe-3.5 wt% C up to 6.8 GPa and 2200 K using an X-ray absorption method. The compression curve of liquid Fe–C was fitted using the third-order Birch–Murnaghan equation of state. The bulk modulus and its pressure derivative are K0,1500K = 55.3 ± 2.5 GPa and (dK0/dP)T = 5.2 ± 1.5, and the thermal expansion coefficient is α = 0.86 ± 0.04 × 10−4 K−1. The Fe–C density abruptly increases at pressures between 4.3 and 5.5 GPa in the range of present temperatures. Compared with the results of previous density measurements of liquid Fe–C, the effect of carbon on the density of liquid Fe shows a nonideal mixing behavior. The abrupt density increase and nonideal mixing behavior are important factors in determining the light element content in the Earth’s core.