@article{c5707eba8b714f02bb96944d9864a594,
title = "Imaging Polarity in Two Dimensional Materials by Breaking Friedel's Law",
abstract = "Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events within thick, non-centrosymmetric crystals. However, two-dimensional (2D) materials such as a single monolayer of MoS2 can also violate Friedel's law, with unexpected contrast between conjugate Bragg peaks. We show analytically that retaining higher order terms in the power series expansion of the scattered wavefunction can describe the anomalous contrast between hkl and hkl¯peaks that occurs in 2D crystals with broken in-plane inversion symmetry. These higher-order terms describe multiple scattering paths starting from the same atom in an atomically thin material. Furthermore, 2D materials containing heavy elements, such as WS2, always act as strong phase objects, violating Friedel's law no matter how high the energy of the incident electron beam. Experimentally, this understanding can enhance diffraction-based techniques to provide rapid imaging of polarity, twin domains, in-plane rotations, or other polar textures in 2D materials.",
keywords = "2D Materials, Diffraction, Non-centrosymmetric, Pixelated detector, Polar",
author = "Pratiti Deb and Cao, {Michael C.} and Yimo Han and Holtz, {Megan E.} and Saien Xie and Jiwoong Park and Robert Hovden and Muller, {David A.}",
note = "Funding Information: This work was supported by the National Science Foundation ( NSF ) through the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM; DMR-1539918) (PD) and the Air Force Office of Scientific Research through the 2D Electronics MURI grant FA9550-16-1-0031 (MC). Support for the EMPAD development was provided by the U.S. Department of Energy, grant DE-FG02-10ER46693. The adaptation to the STEM was supported by the Kavli Institute at Cornell for Nanoscale Science. YH, electron microscope and facilities were supported by the Cornell Center for Materials Research , through the National Science Foundation MRSEC program, award # DMR 1719875. Funding Information: The authors acknowledge microscopy support from John Grazul and Mariena Silvestry Ramos. We thank Kayla X. Nguyen, Mark Tate, Prafull Purohit, and Sol Gruner for help with the pixel array detector. Funding Information: This work was supported by the National Science Foundation (NSF) through the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM; DMR-1539918) (PD) and the Air Force Office of Scientific Research through the 2D Electronics MURI grant FA9550-16-1-0031 (MC). Support for the EMPAD development was provided by the U.S. Department of Energy, grant DE-FG02-10ER46693. The adaptation to the STEM was supported by the Kavli Institute at Cornell for Nanoscale Science. YH, electron microscope and facilities were supported by the Cornell Center for Materials Research, through the National Science Foundation MRSEC program, award #DMR 1719875. Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",
year = "2020",
month = aug,
doi = "10.1016/j.ultramic.2020.113019",
language = "English (US)",
volume = "215",
journal = "Ultramicroscopy",
issn = "0304-3991",
publisher = "Elsevier",
}