1 atomic resolution imaging of carbon nanotubes from diffraction intensities j.m. zuo 1, i.a....
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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, UIUC2Department of Physics, UIUC
3Physical Sciences Research Lab., Motorola Labs
Science 300, 1419 (2003)
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Carbon Nanotubes (atomic structure)
c=na1+ma2,
c – wrapping vector,
a1, a2 – unit vectors
• n=m – ‘armchair’
• m=0 – ‘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
)U(i1)U(iexp)T( rrr Diffracted intensity: 2
2
)iexp()T()()I( rkrrk
For constant illumination: (r)=const
rkrk
kkk
iexp)U()F(
)F()()()I(
2
22
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Electron wavefront on the sample 10 m aperture
20 nm20 nm
||||2||
22||
2|| 2exp
2exp)()( dkrikfk
CkikA s
r
k
Cs and f – spherical aberration and defocus of electron lens
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Electron Diffraction pattern from SWNT
Scattering amplitude for SWNT:
j
n
/cπlz2nφiexp
R)πr(2J2π/Φinexpl)Φ,F(R,
jj
0n
Simulated diffraction pattern(n1, n2)=(14, 6)d=1.39 nm, =17.0º
M. Gao, J.M. Zuo et al., Appl. Phys. Lett (2003)
Experiment diffraction patternd=1.40±0.02 nm, =17.0º(±0.2º)
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Iterative phase retrieval algorithm
sk(x) Ak(q)
Reciprocal Space Constraints
A'k(q)s'k(x)
Real Space Constraints
FFT
FFT-1
Real space constraints:•finite support•real, positive
Reciprocal space constraint:
)(I)(A expk qq
R.W.Gerchberg & W.O. Saxton, Optic (1972) 35, 237J.R. Fienup, Appl Opt. (1982). 21, 2758R.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 (d=1.39 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)d1=4.09 nm
Inner tube:(n1,n2)=(26,24)d2=3.39 nm
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Possible Applications
I. Imaging of biological molecules
• ferritine,
• actines,
• radiation damage
II. Imaging of nanostructures
• nanowires
• nanoclusters