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Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Published online by Cambridge University Press:  27 July 2021

Scott D. Findlay Open the ORCID record for Scott D. Findlay [Opens in a new window] ,
Hamish G. Brown ,
Philipp M. Pelz ,
Colin Ophus ,
Jim Ciston  and
Leslie J. Allen
Scott D. Findlay*
Affiliation:
School of Physics and Astronomy, Monash University, Clayton, VIC3800, Australia
Hamish G. Brown
Affiliation:
National Center for Electron Microscopy Facility, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA Ian Holmes Imaging Center, Bio21 Molecular Science and Biotechnology Institute, University of Melbourne, Parkville, VIC3052, Australia
Philipp M. Pelz
Affiliation:
National Center for Electron Microscopy Facility, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA Department of Materials Science and Engineering, University of California, Berkeley, CA94720, USA
Colin Ophus
Affiliation:
National Center for Electron Microscopy Facility, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA
Jim Ciston
Affiliation:
National Center for Electron Microscopy Facility, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA
Leslie J. Allen
Affiliation:
School of Physics, University of Melbourne, Parkville, VIC3010, Australia
*
*Author for correspondence: Scott D. Findlay, E-mail: [email protected]
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Abstract

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

Keywords

4D STEMphase retrievalscattering matrix
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 27 , Issue 4 , August 2021 , pp. 744 - 757
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of the Microscopy Society of America

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