Thermodynamic properties of liquid sodium under high pressure

Acquiring reliable thermodynamic properties in liquid metals at high pressure and temperature is still a challenge in both experiment and theory. Equation of state (EoS) offers an alternative approach free of many of the difficulties. Here using the EoS of a power law form we obtained the thermodynamic properties of liquid sodium under pressure along the isothermal lines, including isothermal buck modulus, thermal expansion coefficient, Grüneisen parameter, and Anderson-Grüneisen parameter. The results are in excellent agreement with available experimental data measured by a piezometer at high temperature and high pressure and sound velocity measurement with pulse-echo technique. We found that the pressure derivative of the isothermal bulk modulus at zero pressure is a monotonic function of temperature and has a value around 4. In addition, unexpected crossing points were found in the isobaric thermal expansion coefficient and Grüneisen parameter; and a minimum in the isobaric heat under isothermal compression was also observed. While some of these detailed predictions are yet to be confirmed by further experiment, our results suggest that the power law form may be a more suitable choice for the EoS of liquids metals.