Thermodynamic modeling of the Hf–Sn and Sn–Y systems

Based on experimental thermodynamic and phase equilibrium data, the Hf–Sn and Sn–Y systems have been modeled by computational thermodynamics using the CALPHAD method. The enthalpies of formation (ΔfH) for Hf5Sn3, Hf5Sn4 and HfSn2 (−36.95, −38.79 and −27.96 kJ/mol-atom, respectively) obtained via first-principles calculations were used in the thermodynamic modeling. The solution phases including Liquid, (αHf), (βHf), (αY), and (βY) were modeled with the Redlich–Kister polynomial. The nine intermetallic compounds, i.e., Hf5Sn3, Hf5Sn4, HfSn2, Sn3Y5, Sn4Y5, Sn10Y11, Sn2Y, Sn5Y2 and Sn3Y, were described as stoichiometric phases. A set of self-consistent thermodynamic parameters for both Hf–Sn and Sn–Y systems has been obtained. The calculated results show a good agreement with the available experimental data.