A 3rd generation CALPHAD description for pure Mo is presented, with several approaches explored and the final optimized model parameters provided. The lattice stabilities of Mo are critically reviewed, and the inflectiondetection method is recommended for their estimation. Ab initio data are employed to train a machine learning potential, which is then used to support the determination of the instability temperature and the modelling of the liquid phase. The thermodynamic properties of the various phases are successfully described, demonstrating an overall good agreement with the experimental data, even at low temperatures. The unique characteristics of Mo, including significant electronic and anharmonic contributions, are addressed during the modelling. The Equal Entropy Criterion (EEC) is adopted to avoid solid phase stabilization above the melting point. Each modelling choice is thoughtfully discussed and analysed, providing a comprehensive overview of the current best practice for 3rd generation CALPHAD modelling of pure high-melting elements like Mo.

The development of advanced thermodynamic descriptions for pure elements is essential for accurate modelling of multicomponent systems. The third-generation Calphad descriptions incorporate physical effects such as electronic, vibrational and anharmonic contributions. In this study, we have developed a third-generation Calphad description for pure niobium (Nb). Thermodynamic properties of key phases — bcc, fcc, hcp and liquid — are presented for pure Nb. The vibrational contribution to the heat capacity of the solid phases has been modelled with the Einstein model, and the liquid phase has been modelled with the two-state model. In addition, the modelling of unstable phases has been extensively analysed. The traditional Calphad approach is evaluated and compared with the ab initio approach, which has a stronger theoretical basis. The 0 K energies of the unstable phases, fcc and hcp, have been selected from ab initio calculations using the inflection–detection method. Good agreement has been achieved with the selected experimental and ab initio data.