Co-base superalloys have garnered a lot of attention since the possibility to form an ordered L12- was demonstrated  because of their high-temperature strength, environmental resistance and Cobalt's slightly higher melting point compared to Nickel. However, the insufficient stability of the ' phase and their high density are still issues that need to be addressed. To achieve this  hardened Co-base superalloys with increasingly complex multi component alloy compositions are developed. Unfortunately, employing first-principles calculation to accompany such alloy developments by modeling is often hampered by the inability of such methods to tackle multi component systems efficiently.

In the present work, the exact muffin-tin orbitals method (EMTO) combined with the coherent potential approximation (CPA)  based on density functional theory (DFT), was used to investigate the effect of alloying on stabilizing the ' phase in a multi-component Co-based system. We compared the results of VASP-SQS (special quasi-random structure ) and EMTO-CPA calculations for the  phase in the Co3(Al, TM) and Ni3Al systems (TM being transition metals). The lattice parameter, elastic constants, and Debye temperature are consistent with experimental results and other calculations. The predicted thermodynamic properties, e.g. the Gibbs free energy, entropy, and linear thermal expansion coefficient, agree well with the CALPHAD data, experimental results, and other available calculations.

The EMTO-CPA method and Debye-Grüneisen modeling used in this work ensure the high accuracy for capturing the alloying effect on the stability of  phase in a multi-component complex Co-based system. It also demonstrates the good potential for designing novel multi-component Co-based alloys based on first-principles calculation. Our results show that Ni aids in the stabilization of the W-free (CoNi)3(Al, Mo, Nb)-type  phase. Furthermore, the findings indicate that it is critical to consider the various contributions to Gibbs free energy.