Thermodynamic modeling of the Te-X (X = Zr, Ce, Eu) systems

Abstract Thermodynamic descriptions of the tellurium-zirconium (Te-Zr), tellurium-cerium (Te-Ce) and tellurium-europium (Te-Eu) systems have been carried out using the CALPHAD (CALculation of PHAse Diagrams) method based on the experimental phase equilibria data available in the literature and the enthalpies of formation calculated by first-principles calculations in the present work. The liquid phase was described by the substitutional solution model for the Te-Zr and Te-Eu systems while the associated solution model for the Te-Ce system with CeTe as associate. The intermetallics Zr3Te, ZrTe, Zr5Te4, ZrTe3, ZrTe5, CeTe, Ce4Te7, CeTe2, Ce2Te5, CeTe3, Eu4Te7 and Eu3Te7 were treated as stoichiometric compounds while Zr1+xTe2, Ce3-xTe4 and Eu1-xTe were modeled by the sublattice model Te1/3(Zr, Va)1/3(Zr, Te)1/3, (Ce, Va)3/7Te4/7 and (Eu, Va)0.5Te0.5, respectively, on the basis of their homogeneity ranges and crystal structures. A set of self-consistent thermodynamic parameters for the Te-X (X = Zr, Ce, Eu) systems was obtained. Comparisons between the calculated results and experimental data available in the literature show that most reliable experimental information can be satisfactorily accounted for by the present modeling.