Anisotropies of elasticity and thermal conductivity in some novel superhard materials

• We calculated the hardness and elastic constants of four hexagonal compounds.
• A shape of ‘8’ was observed for the 3D Young’s modulus.
• We explained why the anisotropic graphics of Young’s modulus is in the shape of ‘8’.
• The minimum thermal conductivities at high temperature were calculated.
• We found that the conditions for the preparation of r3m-B2CN are most difficult.

The first principles calculations based on density functional theory are performed to investigate the anisotropies of four superhard materials (w-BN, w-BC2N, r3m-BC2N, and r3m-B2CN). By calculating Poisson’s ratio, we found that the atomic binding forces of the first three materials are non-central forces, whereas that of r3m-B2CN is a central force. According to the elastic percentage anisotropy (AB, AG, and AE) and the calculated values of shear anisotropic factor A, the four materials are proven to have elastic anisotropy. Moreover, the different shapes in the three-dimensional stereograms of Young’s modulus on all surfaces, as well as the tensile and shear stress–strain curves in different crystal orientations can further account for the anisotropies of these materials. In addition, the anisotropic factors of acoustic wave and thermal conductivities in the propagation directions of [0 0 0 1] and (0 0 0 1) are also calculated. w-BN, w-BC2N, and r3m-BC2N have similar calculated values, which explain why they have similar properties. By contrast, r3m-B2CN has a large degree of anisotropy, and the three-dimensional diagram of its Young’s modulus has an “8” shape.