Hardness of T-carbon: Density functional theory calculations

TL;DR

This study reevaluates the hardness of T-carbon using density functional theory and finds it is not superhard, contrasting earlier estimates, and discusses the limitations of existing hardness models for this material.

Contribution

It provides a detailed DFT-based analysis of T-carbon's mechanical properties and highlights the shortcomings of empirical hardness models for anisotropic carbon allotropes.

Findings

T-carbon's Vickers hardness is below 10 GPa, not superhard.

Empirical models like Gao's and SV's overestimate hardness due to anisotropy.

A superatom-based correction yields a hardness around 8 GPa.

Abstract

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