Thermodynamic assessment of the Ga–Lu system by the combination of ab-initio calculations and the CALPHAD approach

First-principles calculations within DFT (density functional theory) were employed to calculate the enthalpies of formation of the metal compounds in the Ga–Lu system. The phase diagram and thermodynamic data of this system were critically optimized using the CALPHAD method and Thermo-Calc software. The Ga–Lu phase diagram contains five intermetallic compounds : G a 3 L u , G a 2 L u , G a 5 L u 3 , G a L u and G a 3 L u 5 . These phases were stoichiometric except G a 3 L u 5 that has a homogeneity range, was modeled by a two-sublattice model with substitution in each sublattice. The Ga–Lu system was evaluated using the substitutional solution model and the associate model to the description of the liquid phase, in which the excess Gibbs free energy ( G e x ) was formulated with Redlich–Kister polynomial. The values of the enthalpies of formation that we obtained using two models are in good agreement with those calculated in this work using the VASP code and with experimental data from the literature. The optimization procedure allows us to optimize for the first time all invariant equilibria, thermodynamic properties of the liquid phase and intermetallic compounds of the Ga–Lu system.