Revealing the 3D structure of graphene defects

Abstract

We demonstrate insights into the three-dimensional (3D) structure of defects in graphene, in particular grain boundaries, obtained via a new approach using two transmission electron microscopy images recorded at different angles. The structure is revealed through an optimization process where both the atomic positions as well as the simulated imaging parameters are iteratively changed until the best possible match to the experimental images is found. We first demonstrate that this method works using an embedded defect in graphene that allows direct comparison to the computationally predicted 3D shape. We then apply the method to a set of grain boundary structures with misorientation angles spanning nearly the whole available range (2.6°–29.8°). The measured height variations at the boundaries reveal a strong correlation with the misorientation angle with lower angles resulting in stronger corrugation and larger kink angles. Our results allow for the first time a direct comparison to theoretical predictions for the corrugation at grain boundaries, revealing the measured kink angles are significantly smaller than the largest predicted ones.