Thermodynamic properties and phase stability of the Ba-Bi system: A combined computational and experimental study

The thermodynamic properties and phase stability of the Ba-Bi system are investigated computationally and experimentally in the present work. The enthalpies of formation and the finite temperature thermodynamic properties of seven compounds are predicted by first-principles calculations based on density functional theory (DFT), indicating five compounds (BaBi₃, Ba₁₁Bi₁₀, Ba₄Bi₃, Ba₅Bi₃, and Ba₂Bi) to be stable. Phase relations at 773 K and 858 K with composition x_Ba = 0.90 are established by isothermal annealing and powder X-ray diffraction (XRD) to clarify the previously observed phase transition at 796 K. The extremely low chemical activity of Ba in liquid for a wide range of temperatures and compositions indicates very strong short-range ordering in the liquid phase which is modeled in the present work by introducing the Ba₄Bi₃ and BaBi₃ associates in the liquid phase. Both thermodynamic and phase equilibrium data are then used to evaluate the model parameters in Gibbs energy functions of the five stable compounds and three solution phases of liquid, bcc, and rhombohedral phases by the CALPHAD (CALculation of PHAse Diagram) technique. The present work shows that the Ba-Bi system consists of three eutectic reactions, two peritectic reactions, one peritectoid reaction, and two congruent reactions, as well as that the concentrations of associates are very high in the liquid phase with very low concentration of atomic Ba, which provides the fundamental understanding as to why Bi can be used to remove Ba ions from molten salt solutions.