Mechanical properties of graphene and boronitrene

We present an equation of state (EOS) that describes how the hydrostatic change in surface area is related to two-dimensional in-plane pressure ($\mathcal{F}$) and yields the measure of a material's resilience to isotropic stretching (the layer modulus $\ensuremath{\gamma}$) as one of its fit parameters. We give results for the monolayer systems of graphene and boronitrene, and we also include results for Si, Ge, GeC, and SiC in the isostructural honeycomb structure for comparison. Our results show that, of the honeycomb structures, graphene is the most resilient to stretching with a value of ${\ensuremath{\gamma}}_{\text{C}}$ = $206.6$ N m${}^{\ensuremath{-}1}$, second is boronitrene with ${\ensuremath{\gamma}}_{\text{BN}}$ = $177.0$ N m${}^{\ensuremath{-}1}$, followed by ${\ensuremath{\gamma}}_{\text{SiC}}$ = 116.5 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{GeC}}$ = 101.0 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{Si}}$ = 44.5 N m${}^{\ensuremath{-}1}$, and ${\ensuremath{\gamma}}_{\text{Ge}}$ = 29.6 N m${}^{\ensuremath{-}1}$. We calculate the Young's and shear moduli from the elastic constants and find that, in general, they rank according to the layer modulus. We also find that the calculated layer modulus matches the one obtained from the EOS. We use the EOS to predict the isotropic intrinsic strength of the various systems and find that, in general, the intrinsic stresses also rank according to the layer modulus. Graphene and boronitrene have comparable strengths with intrinsic stresses of 29.4 and 26.0 N m${}^{\ensuremath{-}1}$, respectively. We considered four graphene allotropes including pentaheptite and graphdiyne and find that pentaheptite has a value for $\ensuremath{\gamma}$ comparable to graphene. We find a phase transition from graphene to graphdiyne at $\mathcal{F}$ = $\ensuremath{-}7.0$ N m${}^{\ensuremath{-}1}$. We also consider bilayer, trilayer, and four-layered graphene and find that the addition of extra layers results in a linear dependence of $\ensuremath{\gamma}$ with $\mathcal{F}$.

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