Mechanical properties and hardness of new carbon-rich superhard C11N4 from first-principles investigations

The structural, mechanical properties and hardness of the new carbon-rich material C₁₁N₄ are studied by first-principles total energy calculations based on the density-functional theory. We use the empirical equations of state (EOS) to investigate the lattice properties and bulk modulus. It is found that the calculated lattice constants and bulk modulus are in good agreement with previous calculations. And the full set elastic constants are calculated using the stress-strain method. The Voigt-Reuss-Hill approximation is used to evaluate the mechanical moduli. The elastic constants show that the two phases of C₁₁N₄ are mechanically stable. The tetragonal-C₁₁N₄ (α-C₁₁N₄) exhibits larger mechanical moduli than the orthorhombic-C₁₁N₄ (β-C₁₁N₄). The mechanical anisotropy is calculated of several different anisotropic indexes and factors, such as universal anisotropic index (A^U), the percent anisotropy (A_G and A_B) and shear anisotropic factors (A₁, A₂ and A₃). Furthermore, the hardness of α-C₁₁N₄ and β-C₁₁N₄ are evaluated according to the intrinsic hardness calculation theory. α-C₁₁N₄ is predicted to be a superhard material with the Vickers hardness of 67.17 GPa, which is slightly higher than that of the cubic boron nitride. And the β-C₁₁N₄ is also a superhard material with the calculated Vickers hardness of 45.63 GPa. C₁₁N₄ can be considered as candidate superhard compounds.