Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping

The great application potential for two-dimensional (2D) membranes (MoS 2 , WSe 2 , graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes on the atomic scale, using high-resolution (S)TEM images. After quantitative comparison with continuum mechanics shell model, it is verified that the bending behaviour of the studied 2D materials can be well explained by the linear elastic shell model. And the bending rigidities can thus be derived by fitting with our experimental results. Recall almost only theoretical approaches can access the bending properties of these 2D membranes before, now a new experimental method to measure the bending rigidity of such flexible and atomic thick 2D membranes is proposed. The out-of-plane bending of 2D materials is an important factor to consider for applications, but is challenging to probe experimentally. Here, the authors map the out-of-plane bending in graphene and other 2D materials using high resolution electron microscopy.