Crystal structures and mechanical properties of superhard BC$_2$N and BC$_4$N alloys: First-principles calculations
Shiyou Chen, X. G. Gong, and Su-Huai Wei

Using first-principles calculation, we have investigated the structural and mechanical properties of the cubic (c) BN/C$_2$ alloy systems, which are currently considered as strong candidates for superhard materials. We show that there is a sublinear dependence of the physical properties of the c-BC$_2$N alloy on the number of C-C and B-N bonds in the system. Structures that maximize the number of C-C and B-N bonds have low energy, high density, and high bulk and shear moduli. Structures with unstable B-B and N-N bonds are expected to have higher energy, lower density, and elastic moduli. Based on the ``bond counting rule,'' we have identified a series of low-energy $(C_2)_n/(BN)_m$ (111) superlattices whose structural parameters are similar to the recently synthesized high-density BC$_2$N and BC$_4$N samples [Y. Zhao $\textit{et al.}$, J. Mater. Res., {\bf 17}, 3139 (2002).] The calculated bulk and shear moduli and ideal shear strengths under normal compression show that these BC$_2$N and BC$_4$N (111) superlattices are very strong in resistance to elastic distortion at equilibrium and plastic distortion under nanoindentation. Furthermore, we show that the calculated shear modulus and ideal shear strength under normal compression also have a sublinear relationship with the measured Vickers hardness for these high-density BN/C$_2$ alloy systems, and thus could be used as a good indicator for the hardness of these alloys.

© 2008 The American Physical Society.