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.