Phase stability, structural and mechanical properties of transition metal nitrides using first principles calculations

Abstract

Phase stability of Mo 1-x N x system: First-principles density-functional calculations coupled with the USPEX evolutionary phase-search algorithm are employed to calculate the convex hull of the Mo-N binary system. Eight Mo 1-x N x compound phases are found to be thermodynamically stable: tetragonal β-Mo 3 N, hexagonal δ-Mo 3 N 2 , cubic γ- Mo 11 N 8 , orthorhombic ε-Mo 4 N 3 , cubic γ-Mo 14 N 11 , monoclinic σ-MoN and σ-Mo 2 N 3 and hexagonal δ-MoN 2 . The convex hull is a straight line for 0 ≤ x ≤ 0.44 such that bcc Mo and the five listed compound phases with x ≤ 0.44 are predicted to co-exist in thermodynamic equilibrium. Comparing the convex hulls of cubic and hexagonal Mo x N 1-x indicates that cubic structures are preferred for molybdenum rich (x < 0.3) compounds, hexagonal phases are favored for nitrogen rich (x > 0.5) compositions, while similar formation enthalpies for cubic and hexagonal phases at intermediate x = 0.3 – 0.5 imply that kinetic factors play a crucial role in the phase formation.