A first-principle study on the structure, stability and hardness of cubic BC2N

The hardness of cubic BC2N (c-BC2N) has sparked considerable debate in the literature. First-principle calculations, guided by bond counting rules, were engaged to investigate the correlation between the stability of an alloy configuration and its hardness by searching through alloy configurations in all distinct unit cells of size up to 12 atoms. The existence of many low-energy and high-density alloy configurations with formation energies in the order of 100–200 meV/atom suggests that a mixture of high-density alloy configurations in the experimental samples is likely to occur due to the high temperature and non-equilibrium conditions offered by modern growth techniques. Theoretical analysis on elastic stiffness and Vickers hardness confirm that these stable high-density c-BC2N alloy configurations are indeed harder than c-BN.