Manifestation of ripples in free-standing graphene in lattice images obtained in an aberration-corrected scanning transmission electron microscope

The shape of ripples in free-standing graphene is derived from bond length distributions in high-angle annular-darkfield (Z-contrast) images, obtained in an aberration-corrected scanning transmission electron microscope (superSTEM). Local undulation patterns can readily be visualized by applying fast Fourier transform procedures to the lattice images, using a spatial frequency filter which passes the precise graphitic a-plane spacing. Using aberration-corrected STEM presents the unique opportunity to correlate atomic resolution imaging with the undulations. Values for projected bond lengths, and hence bond inclinations, can be obtained by adjusting the filter to the appropriate band pass. Ripples with amplitude ∼0.5 nm and width ∼5 nm were observed. Their patterns modify in repeated image scans, with prolonged scanning introducing vacancies. These, in conjunction with adatoms which are also revealed in Z-contrast, induce highly localized changes in the mechanical properties of graphene. Ripples in defected graphene remain dynamic, with changes occurring together with redistribution of defects.