Phase diagram, mechanical properties, and electronic structure of Nb-N compounds under pressure

Niobium-nitrogen compounds, which are potential candidates for superhard multifunctional materials, may possess multiple stoichiometries and structures under pressure. Based on ab initio evolutionary structural searches, we predict three ground states (oP6-Nb2N, CW-NbN, and hP22-Nb5N6) and six stable high pressure phases (e-NbN, AsNi-NbN, U2S3-Nb2N3, oC24-NbN2, mP8-NbN3, and mP20-NbN4) for Nb-N compounds at pressures up to 100 GPa. Among them, the oP6-Nb2N, oC24-NbN2, mP8-NbN3, and mP20-NbN4 have never been reported, and N-rich oC24-NbN2, mP8-NbN3, and mP20-NbN4 high pressure phases are recoverable to ambient pressure. We find that the structure of N-rich Nb-N compounds consists of NbNx polyhedral stacking configurations and connected with N-n (n = 2, 3, 4, and n) polymerizations, which can remarkably improve the elastic modulus. It is found that CW-NbN and mP20-NbN4 are two potential ultra-incompressible and hard materials with the hardness calculated to be 24.56 and 19.86 GPa, respectively, while other N-rich phases such as U2S3-Nb2N3, oC24-NbN2, and mP8-NbN3 are soft materials. Detailed electronic structure and chemical bonding analysis proved that the high hardness of CW-NbN and mP20-NbN4 stems from the strong covalent bonding and the fullfilled Nb-N bonding and antibonding states.