Hardness ofT-carbon: Density functional theory calculations

We reconsider and interpret the mechanical properties of the recently proposed allotrope of carbon, T-carbon [Sheng et al., Phys. Rev. Lett. 106, 155703 (2011)], using density functional theory in combination with different empirical hardness models. In contrast with the early estimation based on Gao et al.'s model, which attributes to T-carbon a high Vickers hardness of 61 GPa comparable to that of superhard cubic boron nitride (c-BN), we find that T-carbon is not a superhard material, since its Vickers hardness does not exceed 10 GPa. Besides providing clear evidence for the absence of superhardness in T-carbon, we discuss the physical reasons behind the failure of Gao et al.'s and Simunek and Vack\'ar's (SV) models in predicting the hardness of T-carbon, residing in their improper treatment of the highly anisotropic distribution of quasi-$sp$${}³$-like C-C hybrids. A possible remedy for the Gao et al. and SV models based on the concept of the superatom is suggested, which indeed yields a Vickers hardness of about 8 GPa.