The thermal and mechanical stability of graphene is important for manypotential applications in nanotechnology. We calculate the temperaturedependence of lattice parameter, elastic properties and heat capacity by meansof atomistic Monte Carlo simulations that allow to go beyond the quasiharmonicapproximation. We predict an unusual, non-monotonic, behavior of the latticeparameter with minimum at temperature about 900 K and of the shear modulus withmaximum at the same temperature. The Poisson ratio in graphene is found to besmall ~0.1 in a broad temperature interval.
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