Theoretical study of thermodynamic and magnetic properties of transition metal carbide and nitride MAX phases

We systematically perform density-functional theory (DFT) calculations for all possible ${\mathrm{M}}_{n+1}{\mathrm{AX}}_{n}$ (MAX) phases with transition metal M=Sc to Au (excluding Tc), A in group IIIA-IVA, X=C, N, and $n=1,2,3$, a total of about 1200 systems. The thermodynamic stability is determined by comparing the formation enthalpy (at 0 K) against all possible combinations of unary, binary, and ternary boundary phases (available from online DFT databases). Thereby, we identify 124 so far unknown phases (in terms of both experimental synthesis and other theoretical predictions), of which 54 are carbides and 70 are nitrides. Among all stable MAX phases, we identify nine with magnetic properties. In addition to already known and synthesized magnetic phases $({\mathrm{Cr}}_{2}\mathrm{AlC},$ ${\mathrm{Cr}}_{2}\mathrm{GeC},$ ${\mathrm{Cr}}_{2}\mathrm{GaN},$ and ${\mathrm{Mn}}_{2}\mathrm{GaC})$, we predict five more MAX phases with magnetic ordering $[{\mathrm{Mn}}_{2}\mathrm{A}(=\mathrm{Ge}, \mathrm{Sn})\mathrm{C}, {\mathrm{Cr}}_{3}\mathrm{A}(=\mathrm{Ga}, \mathrm{Ge}){\mathrm{N}}_{2}, \mathrm{and} {\mathrm{Cr}}_{4}\mathrm{A}(=\mathrm{Ge}){\mathrm{N}}_{3}]$. Evaluating previously suggested descriptors for the stability of MAX phases [valence electron concentrations (VECs), differences in atomic radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{at}}$, and differences in electronegativities $\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}$], we find that $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{at}}$ does not correlate with stability and stable phases are characterized by $\text{VEC}<5.5$, $\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}>1.5$. The reverse is, however, not true; for example, a MAX phase with $\text{VEC}<5.5$ and $\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}>1.5$ is not necessarily stable.