2004-02-15454A

Supplementary Figures

Fig.S1 A HR-TEM image of a SWNT in which the zig-zag chains of carbon atoms in graphitic network (inset figure) are clearly visible. Scale bar is 2 nm. Bottom inset figure indicates the contrast transfer function (CTF) chosen to enhance the contrast made of the zig-zag chain (0.213nm apart). This experimental condition generates the CTF in red chart, comparing to the blue chart under Scherzer condition. We can fabricate this CTF under the following observation condition: a spherical aberration coefficient (Cs) measured at 0.5 mm, a chromatic aberration coefficient (Cc) estimated at 1.1 mm and a defocus value set at -32 nm, while the Scherzer focus is -47 nm. The defocus value was determined with an accuracy of a few nanometers during experiments by the live FFT of the HR-TEM images (see Fig. S2). The targeted CTF peak is extremely sharp with a width comprising between 0.21 and 0.23 nm. The obtained contrast is then highly sensitive to the projected spacing of the graphitic network and consequently to the local strain field within the structure even though the inter-chain distance (0.213 nm) is beyond the Scherzer limit (0.24 nm) of the microscope as illustrated by the blue chart in Fig. S1 bottom. It should be recalled that the image recorded using such a fabricated CTF does not exactly correspond to the atomic potential of the examined object especially in higher frequency components. This does limit the applicability of this technique and image simulations knowing all the microscope parameters must be accompanied to interpret precisely the observed images. See for example D. B. Williams and C. B. Carter, Transmission Electron Microscopoy, Plenum Press, New York, 1996.

Fig.S2 A fast Fourier transform of the presented HR-TEM image of a graphene layer. The peaks corresponding to the zig-zag inter-chain distances (0.469 nm-1) appear in the second bright-band after the Scherzer limit, which confirms the defocus value is correctly set to the desired one (~32 nm) (See the CTF in the Fig. S1).

Fig.S3 Relationship between the true diameter (dtrue) and the apparent diameter (dapp) measured by the distance of the two minima in the image contrast. A series of image simulation have been systematically performed for various nanotubes and two defocus conditions (f = -32 and -47 nm).

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