Four modern theoretical models have been used to predict the Vickers hardness (H V ) of new phases. The thermodynamic (T) model , which is based on thermodynamic properties and crystal structure, generally shows good agreement with experiment, and is therefore recommended for hardness evaluation of superhard and ultrahard phases . The Vickers hardness and bulk modulus values calculated using this model are summarized in Table . The Lyakhov-Oganov (LO) model takes into account the topology of the crystal structure, the strength of covalent bonding, the degree of ionicity and directionality; and the empirical models, Mazhnik-Oganov (MO) and Chen-Niu (CN) , are based on elastic properties, namely, bulk and shear moduli. As shown previously , in the case of superhard (H V ≥ 40 GPa) compounds of light elements, the Lyakhov-Oganov model gives slightly underestimated values of hardness, while empirical models are not reliable. Fracture toughness (K Ic ) was evaluated using the Mazhnik-Oganov model . Table shows the hardness and other mechanical properties of the dense carbon, BN and SiC phases calculated using all four models.