Combined in- and out-of-plane chemical ordering in super-ordered MAX phases (s-MAX)

The challenge of synthesizing stable super-ordered MAX phases (s-MAX), with both in-plane and out-of-plane chemical ordering, lies in the combination of five different elements and the inherent order of them. A plethora of compositions is thus possible for these quinary phases, however finding the most promising ones and their suitable synthesis methods remains challenging. In this study, we address this issue by employing density functional theory (DFT) to investigate the phase stability of s-MAX phases with the general formulae M1₄M2₂M3₆Al₃C₉ (413 MAX) and M1₄M2₂M3₃Al₃C₆ (312 MAX). We identified 26 stable s-MAX phases, with in-plane order of M1 and M2 in the outer layer next to Al and out-of-plane order with M1 + M2 in the outer layer and M3 in the inner layers. An additional 14 s-MAX phases with partial disorder, i.e., M2 with in-plane order in the outer layer whereas disorder of M1 and M3 across outer and inner layers, were also found to be thermodynamically stable. Ideal super-ordered s-MAX is favoured over s-MAX with partial disorder when, among other things, the atomic size of M2 and M3 is larger than M1. These findings provide a framework for designing compositionally tuned s-MAX phases with enhanced functionality, contributing to the development of advanced materials and MXene precursors.