Journal of Superhard Materials

, Volume 32, Issue 3, pp 167–176

Thermodynamic model of hardness: Particular case of boron-rich solids


  • V. A. Mukhanov
    • LPMTM-CNRSUniversité Paris Nord
  • O. O. Kurakevych
    • IMPMCUniversité P & M Curie
  • V. L. Solozhenko
    • LPMTM-CNRSUniversité Paris Nord
Theory of Hardness and Superhard Materials Production, Structure, Properties

DOI: 10.3103/S1063457610030032

Cite this article as:
Mukhanov, V.A., Kurakevych, O.O. & Solozhenko, V.L. J. Superhard Mater. (2010) 32: 167. doi:10.3103/S1063457610030032


A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one to predict hardness of known or even hypothetical solids from the data on Gibbs energy of atomization of the elements, which implicitly determine the energy density per chemical bonding. The only structural data needed is the coordination number of the atoms in a lattice. Using this approach, the hardness of known and hypothetical polymorphs of pure boron and a number of boron-rich solids has been calculated. The thermodynamic interpretation of the bonding energy allows one to predict the hardness as a function of thermodynamic parameters. In particular, the excellent agreement between experimental and calculated values has been observed not only for the room-temperature values of the Vickers hardness of stoichiometric compounds, but also for its temperature and concentration dependencies.

Key words

superhard materialsborontheory of hardness

Copyright information

© Allerton Press, Inc. 2010