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

The Nb-Ni system has been remodeled with uncertainty quantification (UQ) by using the presently upgraded software tools of PyCalphad and ESPEI that contain the new capability to model site occupancy of Wyckoff position for the phases of interest. Specifically, the five- and three-sublattice models are used to model the topologically close pack (TCP) phases of μ-Nb7Ni6 and δ-NbNi3, respectively, according to exactly their Wyckoff positions; where the inputs for CALPHAD-based modeling include the presently predicted thermochemical data as a function of temperature by density functional theory (DFT) based first-principles and phonon calculations together with both phase equilibrium and site occupancy data in the literature. Besides phase diagram and thermodynamic properties, the present CALPHAD predictions of site occupancies are also agreed well with experimental data such as the measured Nb sites in μ-Nb7Ni6. In addition, the predicted UQ values using the Markov Chain Monte Carlo (MCMC) method as implemented in ESPEI make it possible to quantify uncertainties in the Nb-Ni system, such as site occupancies in μ-Nb7Ni6 and enthalpy of mixing in liquid.