Thermodynamic modeling of the Nb-Ni system with uncertainty quantification using PyCalphad and ESPEI

The Nb–Ni system is remodeled with uncertainty quantification (UQ) using software tools of PyCalphad and ESPEI (the Extensible, Self-optimizing Phase Equilibria Infrastructure) with the presently implemented capability of modeling site fraction based on Wyckoff positions. The five- and three-sublattice models are used to model the topologically close pack (TCP) μ-Nb7Ni6 and δ-NbNi3 phases according to their Wyckoff positions. The inputs for CALPHAD-based thermodynamic modeling include the thermochemical data as a function of temperature predicted by first-principles and phonon calculations based on density functional theory (DFT), ab initio molecular dynamics (AIMD) simulations, together with phase equilibrium and site fraction data in the literature. In addition to phase diagram and thermodynamic properties, the CALPHAD-based predictions of site fractions of Nb in μ-Nb7Ni6 agree well with experimental data. Furthermore, the UQ estimation using the Markov Chain Monte Carlo (MCMC) method as implemented in ESPEI is applied to study the uncertainty of site fraction in μ-Nb7Ni6 and enthalpy of mixing (ΔHmix) in liquid.