We report the calculations of the Vickers hardness of five predicted C3N4 polymorphs by using the microscopic model of hardness. The hardest phase, cubic C3N4, has the hardness of 92.0GPa, softer than diamond, although its modulus is higher than that of diamond. The densest phase, cubic spinel C3N4, has the lowest hardness of 62.3GPa in the five polymorphs. Our analysis suggests that the hardness of simple-structured covalent materials might not exceed that of diamond.

The hardness of cubic spinel Si3N4 was calculated by using our microscopic model of hardness combined with first principles calculation. The calculated Vickers hardness is only 33.3GPa in good agreement with its experimental values reported recently, indicating that the cubic spinel Si3N4 is not a superhard material. Our calculation results also implicate a more important fact that predicting the hardness of a material based on its bulk modulus or shear modulus is impertinent.

An assumed B 2 CN crystal system containing seven possible diamondstructured configurations in boron-carbonitride B-C-N compounds has been studied by using an ab initio pseudopotential density functional method. After structural relaxation, the lattice constant, bulk modulus and shear modulus, and electronic band structures as well as the electron density of states are calculated for the derived B 2 CN structures. A unique type t-B 2 CN phase deduced from the diamond structure contains only B-N and B-C bonds in a tetragonal cell, and it has the lowest total energy and an electron-deficiency structure with nonvanishing density of states at the Fermi energy. Unlike diamond and c-BN, the t-B 2 CN phase may show metallicity.

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