First-principles prediction of the Co–Al phase diagram including configurational, vibrational and magnetic contributions

Co-based superalloys have attracted attention to replace Ni-based superalloys in high temperature structural applications because of their higher melting temperature and corrosion resistance. Strengthening is provided by Co3(Al, X) (X = W, Cr, Mo, Ni) phases and optimization of their properties requires detailed information about the free energies of the different phases and of the phase diagram of the Co–Al system. This is achieved in this paper through first principles calculations in combination with statistical mechanics. Configurational entropic contributions to the free energy were included through Monte Carlo simulations using the cluster expansion formalism. The vibrational entropy of each phase was determined through the length-stiffness relationship while the magnetic entropy was also included through the Heisenberg Hamiltonian. The computed phase diagram is compared with the currently accepted experimental phase diagram and the different contributions to the stability of each phase are analyzed independently. The potential of this strategy to predict phase diagrams of magnetic systems is clearly established.