Theoretical hardness of the cubic BC2N

Vickers hardness of the cubic BC₂N has been investigated using the microscopic hardness model, in which the parameters have been obtained using first principles calculations. Ionicities of the chemical bonds in the cubic BC₂N depend on their surrounding chemical environments, which are included in the hardness calculations of the cubic BC₂N using the population ionicity scale. For the four selected configurations of the cubic BC₂N, the theoretical Vickers hardness has been found to lie between 70 and 72 GPa, consistent with the experimental value of 76 GPa. According to our calculations, it should be the cubic BC₂N that ranks second among the superhard materials instead of the cubic BN.