Abstract

Convergent beam electron diffraction is routinely applied for studying deformation and local strain in thick crystals by matching the crystal structure to the observed intensity distributions. Recently, it has been demonstrated that CBED can be applied for imaging two-dimensional (2D) crystals where a direct reconstruction is possible and three-dimensional crystal deformations at a nanometre resolution can be retrieved. Here, we demonstrate that second-order effects allow for further information to be obtained regarding stacking arrangements between the crystals. Such effects are especially pronounced in samples consisting of multiple layers of 2D crystals. We show, using simulations and experiments, that twisted multilayer samples exhibit extra modulations of interference fringes in CBED patterns, i. e., a CBED moiré. A simple and robust method for the evaluation of the composition and the number of layers from a single-shot CBED pattern is demonstrated.

Highlights

  • Convergent beam electron diffraction (CBED) has been known almost since the beginning of electron microscopy [1] and has been utilized for the study of crystallographic deformation in thick samples [2,3,4,5,6,7,8]

  • Unlike in a conventional selected area electron diffraction pattern, in a CBED pattern each diffraction peak is turned into a finite-size CBED spot with an interference pattern-like intensity distribution that can be directly related to the three-dimensional (3D) deformations, local atomic mispositions and strain in the crystal, as well as the sample thickness

  • We investigated the CBED imaging of samples consisting of multiple layers of 2D crystals by simulations and experiments

Read more

Summary

Introduction

Convergent beam electron diffraction (CBED) has been known almost since the beginning of electron microscopy [1] and has been utilized for the study of crystallographic deformation in thick samples [2,3,4,5,6,7,8]. Unlike in a conventional selected area electron diffraction pattern, in a CBED pattern each diffraction peak is turned into a finite-size CBED spot with an interference pattern-like intensity distribution that can be directly related to the three-dimensional (3D) deformations, local atomic mispositions and strain in the crystal, as well as the sample thickness. CBED has been demonstrated for 2D crystals and van der Waals structures where the diffraction pattern analysis is different from that for thick samples, since it is more straightforward and allows for direct structure reconstructions, such as the distance between the layers and 3D displacement of atoms [11,12,13,14]. The atomic arrangement and displacement along the z-direction are not trivial for reconstruction from diffraction patterns despite recent advances in imaging techniques, such as "Big Bang" tomography [15] and electron ptychography [16, 17]. We present simulated CBED patterns of multilayer twisted samples and compare them with the experimentally acquired CBED patterns of multilayer van der Waals structures

Transmission function
Diffraction patterns
CBED interference and moiré
Relation between diffraction and CBED patterns
Estimation of number of layers from a single CBED pattern
Experimental
Discussion and conclusions

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.