Ab initio calculation of ideal strength and phonon instability of graphene under tension

Graphene-based $s{p}^{2}$-carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Uniaxial tensile strain is applied in the $x$ (nearest-neighbor) and $y$ (second nearest-neighbor) directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young's modulus…