Ground-state structures, physical properties and phase diagram of carbon-rich nitride C₅N

Using the ab initio evolutionary algorithm, four thermodynamically stable C₅N phases ([Formula: see text], [Formula: see text]-1, [Formula: see text]-2 and C2/m) are uncovered. The structures of the [Formula: see text], [Formula: see text]-1 and [Formula: see text]-2 phases possess layered features. The dense C2/m phase with 3D strong covalent bond network is calculated to be superhard with hardness of 75.4 and 83.9 GPa by Chen and Gao models. The electronic properties of the C₅N is diverse including conductor ([Formula: see text]), indirect semiconductor ([Formula: see text]-1 and [Formula: see text]-2) and direct semiconductor (C2/m). Pressure-induced phase transition sequences and critical pressure points are calculated to be [Formula: see text]  →  [Formula: see text]-1  →  [Formula: see text]-2 at 2.7 and 34 GPa, respectively. Though the C2/m phase is metastable at zero temperature, our established pressure-temperature phase diagram of C₅N shows that the C2/m becomes stable under high temperatures and pressures. The pressure-temperature phase diagram will give theoretical guidance for further experimental synthesis of different C₅N phases.