Predictive theoretical screening of phase stability for chemical order and disorder in quaternary 312 and 413 MAX phases

In this work we systematically explore a class of atomically laminated materials, M(n+1)AX(n) (MAX) phases upon alloying between two transition metals, M ' and M '', from groups III to VI (Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W). The materials investigated focus on so called o-MAX phases with out-of-plane chemical ordering of M ' and M '', and their disordered counterparts, for A = Al and X = C. Through use of predictive phase stability calculations, we confirm all experimentally known phases to date, and also suggest a range of stable ordered and disordered hypothetical elemental combinations. Ordered o-MAX is favoured when (i) M ' next to the Al-layer does not form a corresponding binary rock-salt MC structure, (ii) the size difference between M ' and M '' is small, and (iii) the difference in electronegativity between M ' and Al is large. Preference for chemical disorder is favoured when the size and electronegativity of M ' and M '' is similar, in combination with a minor difference in electronegativity of M ' and Al. We also propose guidelines to use in the search for novel o-MAX; to combine M ' from group 6 (Cr, Mo, W) with M '' from groups 3 to 5 (Sc only for 312, Ti, Zr, Hf, V, Nb, Ta). Correspondingly, we suggest formation of disordered MAX phases by combing M ' and M '' within groups 3 to 5 (Sc, Ti, Zr, Hf, V, Nb, Ta). The addition of novel elemental combinations in MAX phases, and in turn in their potential two-dimensional MXene derivatives, allow for property tuning of functional materials.