Thermodynamic analysis of the Co–Al–C and Ni–Al–C systems by incorporating ab initio energetic calculations into the CALPHAD approach

The Co–Al–C ternary phase diagram has been constructed by combining ab initio energetic calculations with the CALPHAD approach, and the results have been compared with the Ni–Al–C ternary phase diagram obtained using the same procedure. In the thermodynamic analysis, special care was taken evaluating the expression of the free energy for the L12 and E21 structures. To treat these two structures as a continuous solution, the free energy was expressed using the (M,Al)3(Al,M)1(C,V a)1-type sublattice model. Because of the lack of experimental data, the thermodynamic properties of the E21 structure were evaluated using the Full Potential Linearized Augmented Plane Wave method. The calculated results show that the E21 phase in the Co–Al–C system is in equilibrium with fcc Co, the B2-type intermetallic compound, and the graphite phase. This finding is in good agreement with previous experimental results. On the other hand, the E21 phase does not exist in the Ni–Al–C ternary system. The phase equilibrium of the Co–Ni–Al–C quaternary system is discussed, taking into account the two-phase separation between the E21 phase and the L12 phase.