First-principles aided thermodynamic modeling of the Nb–Re system

A thermodynamic description of the Nb–Re binary system is developed by means of the CALPHAD method using present first-principles calculations based on density functional theory and experimental data in the literature. In addition to terminal solution phases, there are two intermetallic phases in the system, sigma (σ) and chi (χ), all modeled with sublattice models. Special quasirandom structures (SQS) are employed to mimic the random mixing of the bcc, hcp, and fcc solid solution phases. It is found that the enthalpy of mixing predicted from first-principles calculations is positive for the hcp and fcc solid solution phases, while negative for the bcc solid solution phase. Finite temperature thermodynamic properties of end-members and dilute mixing in each sublattice of the complex σ and χ phases are predicted from first-principles calculations and the Debye–Grüneisen model. The calculated phase diagram agrees well with selected experimental phase equilibrium data in the literature.