First-principles calculations and thermodynamic modeling of the ruthenium–terbium and ruthenium–lanthanum systems

Abstract

• DFT (Quantum ESPRESSO) and CALPHAD combined for Ru–La and Ru–Tb binaries. • Formation enthalpies integrated to build consistent, predictive phase diagrams. • First complete thermodynamic modelling proposed for the Ru–Tb system. • Results benchmarked against literature; parameters provided for liquid and solid solutions. . This work presents a thermodynamic assessment of the Ru–La and Ru–Tb binary systems by combining first-principles calculations and the CALPHAD approach. Because of the scarcity of available thermodynamic and phase-equilibrium data for these systems, ab initio calculations were performed to estimate the formation enthalpies of the intermetallic compounds and provide additional input for the optimization procedure. The liquid and solid solution phases were described using substitutional solution models, while the intermetallic compounds were treated as stoichiometric phases. A consistent set of thermodynamic parameters was obtained using the Parrot module of Thermo-Calc. The calculated phase diagrams show satisfactory agreement with the available experimental data, including invariant reactions and phase boundaries. In addition, the calculated Gibbs energy of mixing and thermodynamic properties provide further insight into the stability of the liquid phase and intermediate compounds. The present assessment contributes to improving the thermodynamic description of the Ru–La and Ru–Tb systems and provides a useful basis for future investigations of Ru-containing rare-earth alloys.