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 (AU), the percent anisotropy (AG and AB) 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.