Hardness and elastic properties of covalent/ionic solid solutions from first-principles theory

Most of the engineering materials are alloys (solid solutions) and inevitably contain some impurities or defects such as vacancies. However, theoretical predictions of the hardness of this kind of materials have rarely been addressed in literature. In this paper, a hardness formula for multicomponent covalent solid solution is proposed based on the work of Simunek and Vackar [Phys. Rev. Lett. 96, 085501 (2006)]. With this formula, the composition dependence of the hardness is investigated for titanium nitrogencarbide (TiN1-xCx), off-stoichiometric transition-metal nitrides (TiN1-x and VN1-x), and B-doped semiconductors. The predicted hardness is in good agreement with experiments. To investigate the most frequently quoted correlation between hardness and elastic modulus, the elastic moduli of the systems involved in this paper have also been calculated. The results show that the elastic moduli cannot be used for rigorous predictions of the hardness of the solid solutions. (c) 2008 American Institute of Physics.