Phase stability of boron carbon nitride in a heterographene structure: A first-principles study

Phase stability for monolayer boron-carbon-nitride (BNC) (l-BNC) ternary system was examined by Monte Carlo simulations and the cluster expansion technique based on first-principles calculations. All the possible atomic arrangements exhibit positive formation energies, indicating phase separation into monolayer BN and graphene. The atomic arrangements in lowest formation energy have strong preferences for B-N and C-C atoms while disfavor with B-C, C-N, B-B, and N-N bonds along the first-nearest-neighbor coordination, which have a similar tendency for cubic BNC ternary alloys predicted in our previous study. Lattice vibration significantly enhances solubility limits for l-BNC: within the framework of harmonic approximation, complete miscibility achieves at around $T=3500\text{ }\text{K}$, which is below melting lines between hexagonal BN and graphite.