Searching superhard cubic phases in ternary B–C–N phase diagram using first-principles calculations

Based on first-principles calculations within a random solid solution model, we investigated the formation energies and mechanical properties (including Young's modulus, Vickers hardness, and ductility) as function of compositions on the ternary phase diagram of B–C–N crystals. According to our calculations, compositions in the C-rich (70–90%) areas possess relatively high Vickers hardness (up to 77.5 GPa), B-rich (30–35%) areas have better ductility, and the sp3 crystalline phase does not exist stably in the N-rich areas (15–35%). As for the formation energies, the most favorable area locates around the C-poor area (30–50%) in the diagram. These theoretical results provide useful insight for designing and synthesizing the ternary B–C–N crystal of desirable mechanical properties.

► Searching potential superhard phases in large areas of the B–C–N diagram.
► Building the relationship of compositions and mechanical properties.
► Finding superhard areas in the B–C–N phase diagram.