Predicted phase diagram of boron-carbon-nitrogen

Abstract

Noting the structural relationships between phases of carbon and boron carbide with phases of boron nitride and boron subnitride, we investigate their mutual solubilities using a combination of first-principles total energies supplemented with statistical mechanics to address finite temperatures. Thus we predict the solid-state phase diagram of boron-carbon-nitrogen (B-C-N). Owing to the large energy costs of substitution, we find that the mutual solubilities of the ultrahard materials diamond and cubic boron nitride are negligible, and the same for the quasi-two-dimensional materials graphite and hexagonal boron nitride. In contrast, we find a continuous range of solubility connecting boron carbide to boron subnitride at elevated temperatures. An electron-precise ternary compound ${\mathrm{B}}_{13}\mathrm{CN}$ consisting of ${\mathrm{B}}_{12}$ icosahedra with NBC chains is found to be stable at all temperatures up to melting. It exhibits an order-disorder transition in the orientation of NBC chains at approximately $T=500$ K. We also propose that the recently discovered binary ${\mathrm{B}}_{13}{\mathrm{N}}_{2}$ actually has composition ${\mathrm{B}}_{12.67}{\mathrm{N}}_{2}$.