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Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities

Science  30 May 2003:
Vol. 300, Issue 5624, pp. 1419-1421
DOI: 10.1126/science.1083887

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Abstract

Atomic imaging of three-dimensional structures has required a crystal in diffraction or a lens in electron imaging. Whereas diffraction achieves very high resolution by averaging over many cells, imaging gives localized structural information, such as the position of a single dopant atom. However, lens aberrations limit electron imaging resolution to about 1 angstrom. Resolution is reduced further by low contrast from weakscattering or from the limitations on electron dose for radiation-sensitive molecules. We show that both high resolution and high contrast can be achieved by imaging from diffraction with a nanometer-sized coherent electron beam. The phase problem is solved by oversampling and iterative phase retrieval. We apply this technique to image a double-wall carbon nanotube at 1-angstrom resolution, revealing the structure of two tubes of different helicities. Because the only requirement for imaging is a diffraction pattern sampled below the Nyquist frequency, our technique has the potential to image nonperiodic nanostructures, including biological macromolecules, at diffraction intensity–limited resolutions.

  • On leave from Institute of Crystallography Russian Academy of Science, Leninsky Prospekt. 59, 117333 Moscow, Russia.

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