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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