Thermodynamic assessment of the Eu-Rh system by the combination of ab-initio calculations and CALPHAD approach

Abstract

In this work, a standard enthalpies of formation for metal compounds within the Eu-Rh system were determined using first-principles calculations within the framework of density functional theory (DFT). The system analysis was carried out by employing thermodynamic data and phase diagram information sourced from literature, and a CALPHAD-type optimization and Thermo-Calc software.

The Eu-Rh phase diagram includes four intermetallic compounds: ${\text{Eu}}_9\text{Rh},{\text{Eu}}_3\text{Rh},{\text{Eu}}_5\text{Rh}\text{and}\text{Eu}{\text{Rh}}_{2.}$ All phases present a stoichiometry, except the $\text{Eu}{\text{Rh}}_2\text{,}$ which has a homogeneity range and was modeled using a two-sublattice model with substitution in each sublattice.

To describe the additional term of the Gibbs energy (${}^{\text{ex}}G)$ for the liquid phase and the solid solution within the Eu-Rh system, a solution model has been used. The liquid phase was characterized using the linear dependence of the Redlich-Kister model. The individual Gibbs energies include temperature-dependent contributions for all compounds. A comparative analysis shows a good agreement between the enthalpies of formation calculated in this study using the VASP method and current literature data. Finally, a set of self-consistent thermodynamic parameters for the Eu-Rh system was derived.