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

Jiong Zhao,Thuc Hue Ly,Gang Hee Han,Mark H Rümmeli,Qingming Deng,Gorantla Sandeep

doi:10.1038/ncomms9935

Abstract

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, 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.

Highlights

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties
Out-of-plane bending properties are of great significance for graphene as well as two-dimensional (2D) transition metal dichalcogenide (TMD) membranes such as 2H-MoS2, WS2 and WSe2, because it can explain the morphology of such materials under external fields and is important with regards to their use in applications[2]
A quantitative comparison with the continuum mechanics shell model confirms that all the bending behaviour of the investigated 2D materials can be well explained by the linear elastic shell model

Summary

Introduction

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. Nano-indentation tests on suspended membranes using atomic force microscope tips[4] or direct in-plane tensile testing involving microelectromechanical systems gave rather scattered results for the Young’s modulus and strength, which suggest many unknown factors in sample preparation, loading system and, in particular, identifying the correct thickness for these membranes[5]. In most of these measurements, a linear and isotropic elasticity were assumed. In this study, based on a 3D atomic mapping by using high-resolution HRTEM and scanning TEM (STEM), we confirmed the continuum mechanics model and derived the bending rigidity of 2D materials

Methods

Results

Conclusion