Thermodynamic Modeling of the Al-Ba and Ba-Ge Systems Supported by First-Principles Calculations

The phase diagrams of Al-Ba and Ba-Ge systems are optimized by coupling the CALPHAD approach and first-principles calculations. The binary intermetallic compounds were treated as stoichiometric phases. The total energies of nine intermetallic compounds: Al4Ba, Al13Ba7, Al5Ba3, Al5Ba4, Ba2Ge, Ba5Ge3, BaGe, β-Ba3Ge4 and BaGe2 were calculated by first-principles calculation using density functional theory approximation as implemented in the VASP (Vienna Ab-initio Simulation Package) code and used in the CALPHAD approach to assess the two systems. The liquid solutions are described by the Redlich–Kister polynomial model. A set of thermodynamic parameters were obtained for the Al-Ba and Ba-Ge systems. The calculated phase diagrams and thermodynamic properties are in good agreement with most of the accuracy available data.