Prediction of the stability of the Mn₊₁AXn phases from first principles

One of the unusual features of the Mn₊₁AXn phases (where M is a transition metal, A is a group A element, X is carbon or nitrogen, and n=1,2,3…) is that for a given M-A-X system, only certain values of n are found to occur and there is no systematic behavior between the different systems. Density-functional theory was used to verify the stability of the different phases by comparing their total energy to that of the appropriate competing phases. Five systems (Ti-Al-C, Ti-Si-C, Ti-Al-N, Ti-Si-N, and Cr-Al-C) were studied for n=1–4. Complete agreement with observed occurrences of these phases was found. Very small energy differences suggest that it may be possible to fabricate Ti₂SiC, Ti₂SiN, and Ti₃AIN₂ as metastable phases. None of the M₅AX₄ phases were predicted to occur and in all cases the α phases were found to be more energetically favorable than the β phases.