Hardness of materials at high temperature and high pressure

The intrinsic character of the correlation between hardness and thermodynamic properties of solids has been established. The proposed thermodynamic model of hardness allows one to easily estimate hardness and bulk moduli of known or even hypothetical solids from the data on Gibbs energy of atomization of the elements or on the enthalpy at the melting point. The correctness of this approach is illustrated by an example of the recently synthesized superhard diamond-like BC₅ and orthorhombic modification of boron, γ-B₂₈. The pressure and/or temperature dependences of hardness were calculated for a number of hard and superhard phases, i.e. diamond, cBN, B₆O, B₄C, SiC, Al₂O₃, β-B₂O₃ and β-rh boron. Excellent agreement between experimental and calculated values is observed for temperature dependences of Vickers and Knoop hardness. In addition, the model predicts that some materials can become harder than diamond at pressures in the megabar range.