Stability trends of MAX phases from first principles

We have developed a systematic method to investigate the phase stability of Mn+1AXn phases, here applied for M=Sc, Ti, V, Cr, or Mn, A=Al, and X=C or N. Through a linear optimization procedure including all known competing phases, we identify the set of most competitive phases for n=1-3 in each system. Our calculations completely reproduce experimental occurrences of stable MAX phases. We also identify and suggest an explanation for the trend in stability as the transition metal is changed across the 3d series for both carbon- and nitrogen-based systems. Based on our results, the method can be used to predict stability of potentially existing undiscovered phases.