Equation of state of liquid bismuth and its melting curve from ultrasonic investigation at high pressure

To obtain the equation of state of liquid bismuth and its melting curve, ultrasonic velocity meapelisurements were performed in a multi-anvil apparatus. Using a series of thermodynamic relationships, we extract the volume of liquid bismuth as functions of pressure and temperature up to 973 K and 4.3 GPa. We also introduce a calculation process to build the thermal equations of state of each phase of solid bismuth based on their phase transition boundaries. Combining the thermodynamic parameters of liquid and solid bismuth, we employ the Gibbs equation and the Clausius-Clapeyron equation and finally derive the melting curve up to 8 GPa, which shows excellent consistency with most previous theoretical and experimental results. These results not only demonstrate the accuracy of our experimental and theoretical methods, but also demonstrate the feasibility of the thermodynamic method for obtaining unknown melting curves.