Theoretical model of intrinsic hardness

Intense theoretical and experimental interest has been focused on the possibility of new materials with hardness exceeding that of diamond. However, building the link between the information that first-principles calculations can produce and the hardness of materials remains one of the challenges of computational materials science. In this paper, a calculated method of hardness based on the Mulliken overlap population analysis in first principles has been presented. In particular, the effects of stress strain on intrinsic hardness were studied, and a formula of hardness under stress is established. It can be employed to explain the hardening phenomenon resulting from the stress of film and grain boundary and nanoeffects. The theoretical results revealed that nanodiamond films obtained by careful experiments can be harder than bulk single-crystal diamonds.

Figure 1

(Color online) Correlation between calculated hardness $H_v^{\mu }$ and a bondlength of a $\mu$-type bond of some crystals.