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

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 (Ge4Na, GeNa, GeNa3, Ge4K, GeK and GeK3) 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.