A hybrid methodology based on first-principles calculations and Calphad to predict the Ni-Co phase diagram incorporating configurational, vibrational and magnetic contributions

A hybrid strategy is presented to determine the phase diagram of the Ni-Co system without experimental input through the combination of first-principles calculations, cluster expansion and Monte Carlo simulations with the Calphad methodology. To this end, the Gibbs free energies of the different phases in the convex hull were calculated from semi-grand canonical and canonical Monte Carlo simulations including the effect of the configurational, vibrational and magnetic entropic contributions. They were used to create the corresponding thermodynamic database (TDB) following the Calphad formalism to predict the phase diagram. The simulation results are in reasonable agreement with the accepted ferromagnetic-paramagnetic transition temperature but show significant differences with the accepted hcp/fcc two phase boundaries, particularly at low temperatures, providing more accurate information of the Ni-Co phase diagram. Moreover, they indicate that vibrational entropic play a key role in the Ni-Co phase diagram, while magnetic entropic only affects the Gibbs free energies at high temperatures. The efficiency and accuracy of this strategy to predict the Ni-Co phase diagram is anticipated to be further applied to NiCoCr-based Multi-Principal Element Alloys.