Thermodynamic aspects of materials’ hardness: prediction of novel superhard high-pressure phases

Abstract

In the present work, we have proposed a method that allows one to easily estimate the hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, which has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC₅. It has been predicted that the hypothetical forms of B₂O₃, diamond-like boron, BC _x and CO _x , which could be synthesized at high pressures and temperatures, should have extreme hardness.

Keywords:

• superhard materials
• theory of hardness
• thermodynamical properties

Acknowledgements

The authors are grateful to Agence Nationale de la Recherche for financial support (grant NT05-3_42601).

Notes

E.g. for carbon phases, the linear dependence between the hardness and density has been established in paper 44.

The use of this coefficient allows us to establish the hardness of the compounds A ^I B ^VII () and A ^II B ^VI (), i.e. LiF, NaCl, BeO, ZnS, MgO, etc.

For diamond and cBN, the corresponding temperatures of sublimation are 4300 and 3300 K, respectively 21.

The 2 value has been set to a mean (∼51 GPa) of corresponding values for B₆O and B₄C; β=0.79.