Phase stability and mechanical properties of Mo1-xNx with 0 ≤ x ≤ 1

First-principle 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 molybdenum nitride compound phases are found to be thermodynamically stable: tetragonal β-Mo3N, hexagonal δ-Mo3N2, cubic γ-Mo11N8, orthorhombic ε-Mo4N3, cubic γ-Mo14N11, monoclinic σ-MoN and σ-Mo2N3, and hexagonal δ-MoN2. 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 Mo1-xNx indicates that cubic structures are preferred for molybdenum rich (x 0.3) compounds, and 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. The volume per atom Vo of the thermodynamically stable Mo1-xNx phases decreases from 13.17 to 9.56 Å3 as x increases from 0.25 to 0.67, with plateaus at Vo = 11.59 Å3 for hexagonal and cubic phases and Vo = 10.95 Å3 for orthorhombic and monoclinic phases. The plateaus are attributed to the changes in the average coordination numbers of molybdenum and nitrogen atoms, which increase from 2 to 6 and decrease from 6 to 4, respectively, indicating an increasing covalent bonding character with increasing x. The change in bonding character and the associated phase change from hexagonal to cubic/orthorhombic to monoclinic cause steep increases in the isotropic elastic modulus E = 387–487 GPa, the shear modulus G = 150–196 GPa, and the hardness H = 14–24 GPa in the relatively narrow composition range x = 0.4–0.5. This also causes a drop in Poisson's ratio from 0.29 to 0.24 and an increase in Pugh's ratio from 0.49 to 0.64, indicating a ductile-to-brittle transition between x = 0.44 and 0.5.