In this work we systematically explore a class of atomically laminated materials,
Mn+1AXn (MAX) phases upon alloying between two transition metals, M´ and M´´,
from Group 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 do 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 group 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 group 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.