Thermodynamic descriptions of the Sb/Ge unary systems

This paper focuses on the theoretical descriptions of the Gibbs energies concerning the unary systems of Antimony and Germanium. The Gibbs energy expressions of the vapor phase and the condensed phases are included in order to study the influences of temperature and pressure on the phase equilibrium status. The vapor phase is treated as a real solution of the constituent species by considering the fugacity coefficients of gas species in order to assure the reasonability of the P-T (Pressure-Temperature) diagrams at high pressure. The condensed phases are described in the light of the pressure dependent Murnaghan equation which is presented as a pressure dependent contribution Gpres in the present work. The pressure correction factors for the condensed phases include the molar volume, the parameters of the variations of the thermal expansivity and the compressibility with temperature, and the variation of the bulk modulus with pressure. The related parameters of the vapor phase and all the condensed phases are thermodynamically optimized for Sb and Ge unary systems, on the basis of experimental measurements in literature. The calculated results of the P-T relations and the P-V (Pressure-Volume) curves agree well with the experimental data. The calculated slope of liquid-solid coexistence curve at the low pressure of the P-T phase diagram of Sb unary system follows Clausius-Clapeyron equation. The calculated heat capacity curves of condensed phases of Sb and Ge are analyzed and discussed to assure the reasonability of the thermodynamic models described in the paper. The present thermodynamic descriptions of both unary systems are of great benefit to the preparation process of the CoSb3-based thermoelectric materials, especially for the prevention of the volatilization of Sb containing vapor species and the determination of the sintering temperature under certain pressure.