Abstract:
In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors $\mu$, analytical expressions have been obtained for three third-order independent elastic constants $c_{ijk}(\mu,\zeta)$ of single-layer graphene, where $\zeta=(2\alpha-\beta)/(4\alpha+\beta)$ is the Kleinman internal displacement parameter and $\alpha$ and $\beta$ are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure $p$ have been determined. It has been shown that the moduli $c_{11}$ and $c_{22}$ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.
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