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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. jsve@dtu.dk
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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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References

Booth, T.J., Blake, P., Nair, R.R., Jiang, D., Hill, E.W., Bangert, U., Bleloch, A., Gass, M., Novoselov, K.S. & Katsnelson, M.I. (2008). Macroscopic graphene membranes and their extraordinary stiffness. Nano Lett 8(8), 2442–2446.Google Scholar
Boykov, Y. & Kolmogorov, V. (2004). An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans Pattern Anal Mac Intell 26(9), 1124–1137.Google Scholar
Eder, F.R., Kotakoski, J., Kaiser, U. & Meyer, J.C. (2014). A journey from order to disorder – Atom by atom transformation from graphene to a 2D carbon glass. Sci Rep 4, 1–6. doi:10.1038/srep04060.Google Scholar
Efron, B. (2004). Large-scale simultaneous hypothesis testing. J Am Stat Assoc 99(465), 96–104.CrossRefGoogle Scholar
Geim, A.K. & Novoselov, K.S. (2007). The rise of graphene. Nat Mater 6(3), 183–191.Google Scholar
Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6), 721–741.Google Scholar
Girit, C.O., Meyer, J.C., Erni, R., Rossell, M.D., Kisielowski, C., Yang, L., Park, C.-H., Crommie, M.F., Cohen, M.L., Louie, S.G. & Yang, L. (2009). Graphene at the edge: Stability and dynamics. Science 323(5922), 1705–1708.Google Scholar
Hartelius, K. & Carstensen, J. (2003). Bayesian grid matching. IEEE Trans Pattern Anal Mach Intell 25(2), 162–173.Google Scholar
Ising, E. (1925). A contribution to the theory of ferromagnetism. Z Phys 31, 253–258.Google Scholar
Kling, J., Vestergaard, J.S., Dahl, A.B., Stenger, N., Booth, T.J., Bøggild, P., Larsen, R., Wagner, J.B. & Hansen, T.W. (2014). Pattern recognition approach to quantify the atomic structure of graphene. Carbon 74, 363–366.CrossRefGoogle Scholar
Kotakoski, J., Krasheninnikov, A., Kaiser, U. & Meyer, J. (2011). From point defects in graphene to two-dimensional amorphous carbon. Phys Rev Lett 106(10), 105505.Google Scholar
Kotakoski, J., Santos-Cottin, D. & Krasheninnikov, A.V. (2012). Stability of graphene edges under electron beam: Equilibrium energetics versus dynamic effects. ACS Nano 6(1), 671–676.Google Scholar
Kubale, M. (2004). Graph Colorings (vol. 349) American Mathematical Society Providence, RI 02904-2294 USA: American Mathematical Society.CrossRefGoogle Scholar
Lindeberg, T. (1996). Scale-space: A framework for handling image structures at multiple scales, CERN European Organization for Nuclear Research – Reports, 27–38, 1217 Meyrin, Switzerland.Google Scholar
Meyer, J.C., Eder, F., Kurasch, S., Skakalova, V., Kotakoski, J., Park, H.J.J., Roth, S., Chuvilin, A., Eyhusen, S. & Benner, G. (2012). An accurate measurement of electron beam induced displacement cross sections for single-layer graphene. Phys Rev Lett 108, 196102.Google Scholar
Meyer, J.C., Geim, A.K., Katsnelson, M.I., Novoselov, K.S., Booth, T.J. & Roth, S. (2007). The structure of suspended graphene sheets. Nature 446(7131), 60–63.Google Scholar
Meyer, J.C., Kisielowski, C., Erni, R., Rossell, M.D., Crommie, M.F. & Zettl, A. (2008). Direct imaging of lattice atoms and topological defects in graphene membranes. Nano Lett 8(11), 3582–3586.Google Scholar
Nolen, C., Teweldebrhan, D. & Denina, G. (2010). Large-scale automated identification and quality control of exfoliated and CVD graphene via image processing technique. ECS Trans 33(13), 201–209.Google Scholar
Soille, P. (2003). Morphological Image Analysis (vol. 132) New York: Springer.Google Scholar
Stadelmann, P. (2004). JEMS, EMS Java Version. Lausanne, Switzerland: CIME-EPFL.Google Scholar
Wang, M., Liu, Q., Feng, J., Jiang, Q., Zou, X. & Pan, J. (2014). Recognition of defect structure of graphene by image processing technique. J Comput Theore Nanosci 11(2), 391–395.Google Scholar
Wang, Z., Zhou, Y., Bang, J., Prange, M., Zhang, S. & Gao, F. (2012). Modification of defect structures in graphene by electron irradiation: Ab initio molecular dynamics simulations. J Phys Chem C 116(30), 16070–16079.Google Scholar
Warner, J.H., Margine, E.R., Mukai, M., Robertson, A.W., Giustino, F. & Kirkland, A.I. (2012). Dislocation-driven deformations in graphene. Science 337, 209–212.CrossRefGoogle ScholarPubMed
Welsh, D. & Powell, M. (1967). An upper bound for the chromatic number of a graph and its application to timetabling problems. Comput J 10(1), 85–86.Google Scholar
Zhang, Y., Brar, V., Girit, C., Zettl, A. & Crommie, M. (2009). Origin of spatial charge inhomogeneity in graphene. Nat Phys 5(10), 722–726.CrossRefGoogle Scholar
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