Thermodynamic reassessment of Nb-Ni-Ti system with order–disorder model

•Thermodynamic re-assessment of Ni-Ti and Nb-Ni-Ti systems using CALPHAD with DFT.•Incorporation of order-disorder model in ternary and binaries.•Ternary solubility in the binary phases Ni3Ti, NiTi, and NbNi3 are obtained by DFT.•Solubility of Ni3Ti, NiTi, and NbNi3 in ternary are incorporated in modelling.•The calculated ternary Nb-Ni-Ti system compared with experimental data. A thermodynamic description of the Nb-Ni-Ti system is refined by combining results of first-principle total energy calculations with the CALPHAD approach. The lower order binary system Ni-Ti is reassessed with all available thermochemical and phase diagram data. Single Gibbs energy description is used for ordered and disordered bcc phase in this system. To make consistent extrapolation to ternary system, metastable B2 phase is introduced in both Nb-Ni and Nb-Ti systems. The enthalpy of formation of binary intermediate phases are calculated by first-principle method, which are compared with the experimental data. The energy of formation of hypothetical end-members in Ni-Ti binary system and the ternary solubility in the binary phases Ni3Ti, NiTi, and NbNi3 are also calculated by first-principle method and incorporated in the modelling of those phases. Calculated phase diagram and thermochemical properties of Ni-Ti system is show good agreement with experimental data. The calculated ternary Nb-Ni-Ti system is summarily presented in the form of isothermal and isopleth sections, liquids projection and reaction scheme, with appropriate comparisons with available experimental data.