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Structure Identification in High-Resolution Transmission Electron Microscopic Images: An Example on Graphene

Published online by Cambridge University Press:  12 November 2014

Jacob S. Vestergaard Open the ORCID record for Jacob S. Vestergaard [Opens in a new window] ,
Jens Kling ,
Anders B. Dahl ,
Thomas W. Hansen ,
Jakob B. Wagner  and
Rasmus Larsen
Jacob S. Vestergaard*
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 324/130, Richard Petersens Plads, 2800 Kgs Lyngby, Denmark
Jens Kling
Affiliation:
Center for Electron Nanoscopy, Technical University of Denmark, Fysikvej, Building 307, 2800 Kgs Lyngby, Denmark Center for Nanostructured Graphene, Technical University of Denmark, Ørsteds Plads 345E, 2800 Kgs Lyngby, Denmark
Anders B. Dahl
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 324/130, Richard Petersens Plads, 2800 Kgs Lyngby, Denmark
Thomas W. Hansen
Affiliation:
Center for Electron Nanoscopy, Technical University of Denmark, Fysikvej, Building 307, 2800 Kgs Lyngby, Denmark Center for Nanostructured Graphene, Technical University of Denmark, Ørsteds Plads 345E, 2800 Kgs Lyngby, Denmark
Jakob B. Wagner
Affiliation:
Center for Electron Nanoscopy, Technical University of Denmark, Fysikvej, Building 307, 2800 Kgs Lyngby, Denmark
Rasmus Larsen
Affiliation:
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 324/130, Richard Petersens Plads, 2800 Kgs Lyngby, Denmark
*
*Corresponding author. [email protected]
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Abstract

A connection between microscopic structure and macroscopic properties is expected for almost all material systems. High-resolution transmission electron microscopy is a technique offering insight into the atomic structure, but the analysis of large image series can be time consuming. The present work describes a method to automatically estimate the atomic structure in two-dimensional materials. As an example graphene is chosen, in which the positions of the carbon atoms are reconstructed. Lattice parameters are extracted in the frequency domain and an initial atom positioning is estimated. Next, a plausible neighborhood structure is estimated. Finally, atom positions are adjusted by simulation of a Markov random field model, integrating image evidence and the strong geometric prior. A pristine sample with high regularity and a sample with an induced hole are analyzed. False discovery rate-controlled large-scale simultaneous hypothesis testing is used as a statistical framework for interpretation of results. The first sample yields, as expected, a homogeneous distribution of carbon–carbon (C–C) bond lengths. The second sample exhibits regions of shorter C–C bond lengths with a preferred orientation, suggesting either strain in the structure or a buckling of the graphene sheet. The precision of the method is demonstrated on simulated model structures and by its application to multiple exposures of the two graphene samples.

Keywords

graphenestructure identficationgrid matchingMarkov random fieldsHRTEM
Type
Materials Applications
Information
Microscopy and Microanalysis , Volume 20 , Issue 6 , December 2014 , pp. 1772 - 1781
Copyright
© Microscopy Society of America 2014 

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