In this paper, we suggest a novel potential superhard material, a new carbon nitride phase consisted of sp3 hybridized bonds, possessing a cubic P213 symmetry (8 atoms/cell, labeled by cg-CN) which is similar to cubic gauche nitrogen (cg-N) by first-principles calculations. It is a metallic compound, while most of other superhard materials are insulators or semiconductors. The Vickers hardness of cg-CN is 82.56 GPa, and if we considered the negative effect of metallic component on hardness, it is 54.7 GPa, which is much harder than any other metallic materials. It is found that a three-dimensional C–N network is mainly responsible for the high hardness. Both elastic constant and phonon-dispersion calculations show that this structure remains mechanically and dynamically stable in the pressure ranges from 0 to 100 GPa. Furthermore, we compared our results with many other proposed structures of carbon nitride with 1:1 stoichiometry and found that only cg-CN is the most favorable stable crystal structure. Formation enthalpies calculations demonstrate that this material can be synthesizable at high pressure (12.7–36.4 GPa).

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