<i>Ab initio</i> prediction of phase stability of quaternary Mo1−<i>x</i>M<i>x</i>AlB (M = Cr, Fe, Mn, Nb, Sc, Ta, Ti, V, and W) MAB solid solutions

In this study, we explored the phase stability of quaternary Mo1−xMxAlB (M = Cr, Fe, Mn, Nb, Sc, Ta, Ti, V, and W) solid solutions by employing a cluster expansion method to generate structures with different concentrations of M atoms. Using the first-principles calculations based on density functional theory, we predicted that these compounds exhibit a preference for either fully random structures or phase-segregated (M-rich regions) phases against the competing phases. To evaluate the Gibbs free energy of Mo1−xMxAlB alloys, we investigated the impact of various entropy contributions, including configurational, electronic, and vibrational entropy. Our study revealed that configurational entropy plays an important role in stabilizing the random phases observed in Mo1−xMxAlB compounds, highlighting its importance in understanding the thermodynamic behavior of these alloys. However, the vibrational and electronic entropy changes with respect to competing phases can stabilize or destabilize Mo1−xMxAlB depending on their sign. Our results indicate that, while W is soluble across the entire range of mixing ratios, Sc and Ti are completely insoluble in any ratio. On the other hand, Cr, Ta, Nb, and V can be successfully incorporated into the MoAlB lattice at varying fractions at elevated temperatures. The size, valence electron concentration, and electronegativity differences between Mo and M can be utilized as descriptors to identify stable Mo1−xMxAlB compounds. We extensively examined the structural, dynamical stability, thermal conductivity, and mechanical properties of Mo1−xMxAlB compounds. We analyze their dependence on the choice of the M element incorporated in the alloy. Our findings can guide the design and engineering of these materials to tailor their properties to specific applications based on the choice of the M element.