Thermodynamic assessment of Mg/Zr unary systems

Abstract

With consideration of the phase equilibrium dependency upon temperature (T) and pressure (P), the P-T type phase diagrams of Mg and Zr unary systems are constructed. The gaseous phase of the Mg system consists of the species Mg (g) and Mg2 (g), and the condensed phases are liquid, hexagonal close-packed (HCP_A3) and body centered cubic (BCC_A2). Similarly, the gaseous phase of the Zr system consists of the species Zr (g) and Zr2 (g), and the condensed phases are liquid, HCP_A3 (α), BCC_A2 (β) and a more open hexagonal structure (ω). The ω phase has a hexagonal lattice with three atoms per unit cell at (0, 0, 0), (1/3, 2/3, c/2a) and (2/3, 1/3, c/2a), where the c/a ratio is ∼0.62. The real solution model is applied to describe the molar Gibbs free energy of gaseous species by taking the fugacity coefficient into account to ensure the validity of the calculated phase diagrams under high temperature and high pressure. As for the description of the molar Gibbs free energy for condensed phases, the temperature and pressure dependent Murnaghan equation is employed, which is represented by Gpress and is correlated with the molar volume, the variations of voluminal thermal expansivity and compressibility with temperature, and the variation of bulk modulus with pressure. Based on the literature data available, the parameters of the pressure contribution part Gpress for the condensed phases are optimized by use of Pandat Software package. The calculated phase diagrams are well comparable with the experimental and theoretical reports. The favorable consistency between the calculated results for the optimized mechanical and thermophysical properties, such as the variations of the molar volume and the volume ratio with pressure and the molar heat capacity with temperature, and the experimental measurements from literatures further proves the reliability of the present thermodynamic assessment. According to the calculated results, it is indispensable for the contribution of Gpress to the global molar Gibbs free energy to be taken into consideration as the magnitude of pressure exceeds the order of 109 Pa. This CALPHAD method for developing the phase diagrams of Mg/Zr unary systems at high temperature and high pressure can be extended to study other unary systems.