1. 1 Atomic Resolution Imaging of Carbon Nanotubes from Diffraction Intensities J.M. Zuo 1, I.A. Vartanyants 2, M. Gao 1, R. Zhang 3, L.A.Nagahara 3 1 Department of Materials Science and Engineering, UIUC 2 Department of Physics, UIUC 3 Physical Sciences Research Lab., Motorola Labs Science 300, 1419 (2003)

2. 2 Carbon Nanotubes (atomic structure) c=na 1 +ma 2, c – wrapping vector, a 1, a 2 – unit vectors n=m – ‘armchair’ m=0 – ‘zigzag’ STM images of single-walled nanotubes J. Wildoer, et al, Science, 391, 59 (1998).

3. 3 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

4. 4 Coherent Nano-Area Electron Diffraction Schematic ray diagram CL – condenser lens CA – condenser aperture FP – front focal plane OL – objective lens D – imaging plates

5. 5 Electron Scattering on Carbon Nanotubes Weak phase object – kinematic scattering Transmission function Diffracted intensity: For constant illumination:  (r)=const

6. 6 Electron wavefront on the sample 10  m aperture C s and  f – spherical aberration and defocus of electron lens

7. 7 Electron Diffraction pattern from SWNT Scattering amplitude for SWNT: Simulated diffraction pattern (n 1, n 2 )=(14, 6) d=1.39 nm,  =17.0º M. Gao, J.M. Zuo et al., Appl. Phys. Lett (2003) Experiment diffraction pattern d=1.40±0.02 nm,  =17.0º(±0.2º)

8. 8 Iterative phase retrieval algorithm sk(x)sk(x)Ak(q)Ak(q) Reciprocal Space Constraints A'k(q)A'k(q)s'k(x)s'k(x) Real Space Constraints FFT 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

9. 9 Reconstruction of SWNT from simulated data Simulated diffraction patternReconstructed Image

10. 10 Model for SWNT (d=1.39 nm,  =17º)

11. 11 Reconstruction of SWNT Experimental Diffraction PatternReconstructed Diffraction Pattern

12. 12 Reconstructed Image of SWNT

13. 13 Far-field diffraction pattern from DWNT Pixel resolution 0.025 1/nm

14. 14 1d reconstruction from DWNT Equatorial dataReconstructed electron density

15. 15 Electron Diffraction Pattern from DWNT ExperimentReconstruction

16. 16 Reconstructed Image of DWNT

17. 17 Reconstructed Image and model of DWNT Model Outer tube: (n 1,n 2 )=(35,25) d 1 =4.09 nm Inner tube: (n 1,n 2 )=(26,24) d 2 =3.39 nm

18. 18 Possible Applications I.Imaging of biological molecules ferritine, actines, radiation damage II.Imaging of nanostructures nanowires nanoclusters