Conclusion and outlook
Ultra-hard materials - Concepts and modelling

After presenting the context of use of the best-known ultra-hard materials, diamond and cubic boron nitride, and their synthesis routes, the criteria defining hardness were developed, as well as the physico-chemical aspects that can serve as guides to new systems. Particular emphasis was placed on the complementary importance of obtaining incompressibility modulus B and shear modulus G. This was illustrated for C ₃ N ₄ -β, which, while being an ultra-hard material due to its high value of incompressibility modulus, close to that of diamond, nevertheless exhibits interesting elasticity properties through the lower amplitude of its shear modulus G. This provided an opening towards the identification of new compositions in the light element ternary: B, C, N, within which new binary nitrides such as C...