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Scanning electron diffraction tomography of strain

Published version
Peer-reviewed

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Authors

Johnstone, Duncan N 
Collins, Sean M 
Lionheart, William R B  ORCID logo  https://orcid.org/0000-0003-0971-4678
Midgley, Paul A 

Abstract

Abstract: Strain engineering is used to obtain desirable materials properties in a range of modern technologies. Direct nanoscale measurement of the three-dimensional strain tensor field within these materials has however been limited by a lack of suitable experimental techniques and data analysis tools. Scanning electron diffraction has emerged as a powerful tool for obtaining two-dimensional maps of strain components perpendicular to the incident electron beam direction. Extension of this method to recover the full three-dimensional strain tensor field has been restricted though by the absence of a formal framework for tensor tomography using such data. Here, we show that it is possible to reconstruct the full non-symmetric strain tensor field as the solution to an ill-posed tensor tomography inverse problem. We then demonstrate the properties of this tomography problem both analytically and computationally, highlighting why incorporating precession to perform scanning precession electron diffraction (SPED) may be important. We establish a general framework for non-symmetric tensor tomography and demonstrate computationally its applicability for achieving strain tomography with SPED data.

Description

Keywords

Paper, transverse ray transform, computed tomography, tensor tomography, scanning precession electron diffraction, 4D-STEM, strain mapping, strain tomography

Journal Title

Inverse Problems

Conference Name

Journal ISSN

0266-5611
1361-6420

Volume Title

37

Publisher

IOP Publishing
Sponsorship
Leverhulme Trust (Breaking the non-convexity barrier ECF-2016-611)
H2020 Marie Skłodowska-Curie Actions (RISE (CHiPS))
University of Leeds (University Academic Fellowship)
Girton College, University of Cambridge (Henslow Research Fellowship)
Engineering and Physical Sciences Research Council (EP/K00428X/1 EP/L016516/1 EP/M00483X/1 EP/M022498/1 EP/N014588/1 EP/P02226X/1 EP/R008779/1)