Thermodynamic evaluation of the germanium-lutetium and dysprosium-germanium binary systems

The Ge-Lu and Dy-Ge binary systems have been optimized using the available experimental data on phase diagrams and thermodynamic functions by means of the CALPHAD approach. The Ge-Lu system contains seven phases based on six intermetallic compounds: Ge1.8Lu, Ge3Lu2, Ge5Lu4, Ge10Lu11, Ge4Lu5, and Ge3Lu5, which were all treated as stoichiometric compounds. For the Dy-Ge system seven intermetallic compounds were found: Dy5Ge3, Dy5Ge4, DyGe, Dy2Ge3, Dy3Ge5, DyGe2 and DyGe3. These phases were stoichiometric except Dy5Ge3 that has a homogeneity range, was treated by a two-sublattice model with substitution in each sublattice. A solution model has been used for the description of the excess term of the Gibbs energy for the liquid phase and the solid solution for the Dy-Ge system. The Ge-Lu system was examined using two different descriptions of the liquid phase: exponential dependence of temperature (Kaptay model) and linear dependence (Redlich-Kister model). The calculations based on the thermodynamic modeling are in good agreement with the phase diagram data and experimental thermodynamic values available in the literature. The process of modeling allows us to calculate the phase equilibria and thermodynamic properties of the liquid phase and intermetallic compounds for the first time. The results obtained are reported in a series of figures and tables in this manuscript.