Phase stability, chemical bonding and mechanical properties of titanium   nitrides: A first-principles study
  We have performed first-principles evolutionary searches for all stable titanium nitrides and have found, in addition to the well-known rocksalt-type TiN, new ground states Ti$_3$N$_2$, Ti$_4$N$_3$, Ti$_6$N$_5$ at atmospheric pressure, and Ti$_2$N and TiN$_2$ at higher pressures. The latest nitrogen-rich structure presents encapsulated N$_2$ dumbbells with a N-N distance of 1.348 {\AA} at 60 GPa and TiN$_2$ is predicted to be mechanically stable (quenchable). Our calculations of the mechanical properties (bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and hardness) are in excellent agreement with the available experimental data and show that the hardness of titanium nitrides increases with increasing nitrogen content. The hardness of titanium nitrides is enhanced by strengthening directional covalent bonds and disappearance of Ti-Ti metallic bonds. Among the predicted compounds, TiN$_2$ has the highest hardness of 27.2 GPa. 
Shuyin Yu, Qingfeng Zeng, Artem R. Oganov, Gilles Frapper and Litong   Zhang
cond-mat.mtrl-sci