Thermodynamic reassessment of the Mo–Hf and Mo–Zr systems supported by first-principles calculations

Based on the experimental phase equilibria and thermodynamic data available in the literature and enthalpies of formation computed from first-principles calculations, the thermodynamic reassessment of the Mo–Hf and Mo–Zr systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method. The enthalpies of formation for stable and metastable Laves (C15, C36, C14) phases and enthalpy of mixing for the β(bcc) solid solution phase in dilute solution were predicted via first-principles calculations to supply the necessary thermodynamic data for the modeling in order to obtain the thermodynamic parameters with physical sound meaning. The relative stability of Laves C14, C15 and C36 in the systems was discussed. The solution phases, i.e. liquid, β(bcc) and α(hcp) were described by the substitutional solution model, and all the Laves phases in the systems were described using two sublattice model. A set of self-consistent thermodynamic parameters were obtained for these binary systems, which agrees well with the experimental data in the literature. Based on these results, the trend of the site occupancy fraction of Laves phase changing with temperature was predicted. The isothermal section and the liquidus projection of Mo-Hf-Zr system were also predicted by combing with the Zr–Hf system reported in the literature.