Thermodynamic description of the Ge–Na and Ge–K systems using the CALPHAD approach supported by first-principles calculations

Abstract Thermodynamic optimization of the Ge–Na and Ge–K systems has been performed by means of the CALPHAD method combined with first-principles calculations. The enthalpies of formation of GeNa and GeK obtained via first-principles calculations are −16.88 and −20.90 kJ/mol atom, respectively. The liquid phase was modeled with the Redlich–Kister polynomial. The six intermetallic compounds (Ge 4 Na, GeNa, GeNa 3 , Ge 4 K, GeK and GeK 3 ) were described as stoichiometric compounds. The Gibbs energy functions for individual phases in the Ge–Na and Ge–K systems were evaluated by considering both the first-principles computed enthalpies of formation and the experimental phase equilibrium data. A set of self-consistent thermodynamic parameters for the Ge–Na and Ge–K systems has been obtained, and the calculated results show a good agreement with the corresponding experimental data.