Hardness of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>-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 $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{\mathrm{S}}$im$\stackrel{\ifmmode \mathring{}\else \r{}\fi{}}{\mathrm{u}}$nek and Vack\'a$\stackrel{\ifmmode \check{}\else \v{}\fi{}}{\mathrm{r}}$'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.

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