First-principles-based phase diagram of the cubic BNC ternary system

The phase diagram for the cubic BNC ternary system in a heterodiamond structure was examined by Monte Carlo simulations and the cluster expansion technique based on first-principles calculations. All the atomic arrangements exhibit positive formation energies, indicating phase separation into cubic BN (c-BN) and diamond. These arrangements show a strong preference for B-N and C-C bonds and disfavor B-C, C-N, B-B, and N-N bonds along the first nearest neighbor coordination. This can be naturally attributed to the oversaturation and undersaturation of the number of electrons for respective first nearest neighbor bonds. First-principles-based lattice-dynamics calculations reveal that the formation of a solid solution between c-BN and diamond decreases vibrational free energy, resulting in a significant enhancement of the solubility for both c-BN and diamond-rich phases. Complete miscibility is achieved over T=45000.3em0exK, which is higher than the melting points of both diamond and c-BN.