We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake’s spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness dependence. We predict fundamental resonance frequencies of these nanodrums in the gigahertz range based on the measured bending rigidity and tension.
Commercially available AFM tips with nominal spring constants or are used. The spring constant is calibrated using the thermal noise method and the deflection sensitivity is obtained by taking an ensemble of force-distance curves on the silicon oxide substrate.
Even when the continuum approximation fails along the direction, it can still be valid in the horizontal direction, as long as the dependence of the induced deformations is not considered. Therefore, the bending rigidity is not expressed in the elastic constants, but it is treated as a fit parameter.
We have calculated the first order correction to for an anisotropic tension: the flake is stiffer than average along the principal direction with the largest tension and weaker along the other. The lines of constant compliance are ellipsoidal instead of circular. As this has not been observed in the measurements, the assumption of isotropic tension is allowed.