Thermodynamic modeling of the Ge-La binary system

The Ge-La binary system was critically assessed by means of the calculation of phase diagram (CALPHAD) technique. The associate model was used for the liquid phase containing the constituent species Ge, La, Ge₃La₅, and Ge_1.7La. The terminal solid solution diamond-(Ge) with a small solubility of La was described using the substitutional model, in which the excess Gibbs energy was formulated with the Redlich-Kister equation. The compounds with homogeneity ranges, α(Ge_1.7La), β(Ge_1.7La), and (GeLa), were modeled using two sublattices as α(Ge,La)_1.7La, β(Ge,La)_1.7La, and (Ge,La)(Ge,La), respectively. The intermediate phases with no solubility ranges, Ge₄La₅, Ge₃La₄, Ge₃La₅, and GeLa₃, were treated as stoichiometric compounds. The three allotropic modifications of La, dhcp-La, fcc-La, and bcc-La, were kept as pure element phases since no solubility of Ge in La was reported. A set of self-consistent thermodynamic parameters of the Ge-La binary system was obtained. The calculation results agree well with the available experimental data from literatures.