Thermodynamic modeling of the Ge–Sc system supported by key experiments and first-principles calculation

The Ge–Sc system is assessed by means of CALPHAD (CALculation of PHAse Diagram) approach, supplemented with decisive experiments and enthalpies of formation computed via first-principles calculations. Ten Ge–Sc alloys are prepared by arc melting the pure elements. The annealed samples are analyzed by means of X-ray diffraction, scanning electron microscopy with energy-dispersive X-ray spectrometry, electronic probe microanalysis and differential thermal analysis. Five compounds (ScGe2, ScGe, Sc11Ge10, Sc5Ge4 and Sc5Ge3) are observed in the equilibrium condition, and their enthalpies of formation at 0 K are computed via first-principles calculations to supply the necessary thermodynamic data for the modeling. A set of self-consistent thermodynamic parameters for the Ge–Sc system is finally obtained. The calculated results show a good agreement with the experimental data.

► The phase diagram of the Ge–Sc system was determined via key experiments by means of XRD, SEM/EDX, EPMA and DTA. ► The enthalpy of formation for all compounds in the Ge–Sc system was computed via the first-principles calculations. ► An optimal set of thermodynamic parameters was obtained.