Superhard BC2N in cubic diamondlike structure

Cubic ${\mathrm{BC}}_{2}\mathrm{N}$, a superhard material with a slightly lower hardness than diamond, has been synthesized but the determination of its crystal structure has long been elusive, impeding the further understanding of pertinent physics. Here, by employing a first-principles electronic structure framework, we predicted a cubic ${\mathrm{BC}}_{2}\mathrm{N}$ crystal structure (dia-${\mathrm{BC}}_{2}\mathrm{N}$), marking it as the hitherto cubic phase among all previously proposed structures. Our simulated x-ray diffraction patterns of diamondlike ${\mathrm{BC}}_{2}\mathrm{N}$ agree with the experimental data, implying that our predicted structure is likely to be the high-symmetry ${\mathrm{BC}}_{2}\mathrm{N}$ structure synthesized in experiment. Furthermore, the estimated Vicker's hardness of this structure is 77 GPa, demonstrating its intrinsic superhard nature. Our current findings may begin to clarify the long-term unsolved crystal structure of cubic ${\mathrm{BC}}_{2}\mathrm{N}$, and they may pave the way for further design and discovery of superhard materials.