Atomic Resolution Imaging of Carbon Nanotubes from Diffraction Intensities

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Atomic Resolution Imaging of Carbon Nanotubes
from Diffraction Intensities

• J.M. Zuo1, I.A. Vartanyants2, M. Gao1,
• R. Zhang3, L.A.Nagahara3
• 1Department of Materials Science and Engineering,
  UIUC
• 2Department of Physics, UIUC
• 3Physical Sciences Research Lab., Motorola Labs

Science 300, 1419 (2003)
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Carbon Nanotubes (atomic structure)

• cna1ma2,
• c wrapping vector,
• a1, a2 unit vectors
• nm armchair
• m0 zigzag

STM images of single-walled nanotubes J.
Wildoer, et al, Science, 391, 59 (1998).
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Carbon Nanotubes (imaging)

• Structure
• A armchair
• B - zigzag
• C chiral
• Imaging
• D STM image of 1.3 nm SWNT (J. Wildoer et al.,
  Science 391, 59 (1998))
• E TEM image of MWNT
• F TEM micrograph of 1.4 nm SWNTs in a bundle
  (A. Thess et al., Science 273, 483 (1996)
• G SEM image of MWNTs grown as a nanotube forest

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Coherent Nano-Area Electron Diffraction

• Schematic ray diagram
• CL condenser lens
• CA condenser aperture
• FP front focal plane
• OL objective lens
• D imaging plates

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Electron Scattering on Carbon Nanotubes

• Weak phase object kinematic scattering
• Transmission function

Diffracted intensity
For constant illumination ? (r)const
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Electron wavefront on the sample 10 ?m aperture
Cs and ?f spherical aberration and defocus of
electron lens
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Electron Diffraction pattern from SWNT
Scattering amplitude for SWNT
Experiment diffraction pattern d1.400.02 nm,
?17.0º(0.2º)
Simulated diffraction pattern (n1, n2)(14,
6) d1.39 nm, ?17.0º
M. Gao, J.M. Zuo et al., Appl. Phys. Lett (2003)
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Iterative phase retrieval algorithm
FFT
sk(x)
Ak(q)
Reciprocal Space Constraints
Real Space Constraints
A'k(q)
s'k(x)
FFT-1

• Real space constraints
• finite support
• real, positive

Reciprocal space constraint
R.W.Gerchberg W.O. Saxton, Optic (1972) 35,
237 J.R. Fienup, Appl Opt. (1982). 21, 2758 R.P.
Millane W.J. Stroud, J. Opt. Soc. Am. (1997)
A14, 568
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Reconstruction of SWNT from simulated data
Simulated diffraction pattern
Reconstructed Image
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Model for SWNT (d1.39 nm, ?17º)
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Reconstruction of SWNT
Experimental Diffraction Pattern
Reconstructed Diffraction Pattern
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Reconstructed Image of SWNT
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Far-field diffraction pattern from DWNT
Pixel resolution 0.025 1/nm
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1d reconstruction from DWNT
Equatorial data
Reconstructed electron density
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Electron Diffraction Pattern from DWNT
Experiment
Reconstruction
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Reconstructed Image of DWNT
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Reconstructed Image and model of DWNT
Model Outer tube (n1,n2)(35,25) d14.09
nm Inner tube (n1,n2)(26,24) d23.39 nm
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Possible Applications

• Imaging of biological molecules
• ferritine,
• actines,
• radiation damage
• Imaging of nanostructures
• nanowires
• nanoclusters