A new theoretical superstoichiometric hard $Ti{N}_x$ crystal

In this article we present the application of a $\mathit{\text{ab}}\mathit{\text{initio}}$ methodology to design new hard materials with crystal behavior. In special, we applied this methodology in the search of new materials of the $Ti{N}_x$ family. This search will find a set of structures super-stoichiometrics $T{i}_3{N}_4$ and properties of the candidate to greatest hardness are evaluated. Hardness model used in this work is described by Anton'in Simunek and Jir'i Vack'ar (2006).