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T. W. Ebbesen and P. M. Ajayan, Nature 358, 220 (1992). We caution that different production recipes can yield different results; in particular, defect densities may vary substantially from one laboratory to the next (as is the case with crystal growing). For example, catalytically grown tubes are usually very defective. In contrast, the nanotube material used in this work [including (31)] was from the same stock as was used in our previous work (6, 7) and was of high quality.
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note
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The TEM used was a JEOL 100C (100 kV) at the School of Materials Science and Engineering, Georgia Institute of Technology.
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30
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0344148993
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Di was not measured for all nanotubes, and in those cases it was not included in the calculations. However, the value for E is rather insensitive to Di, because Di/D = 1/4, which is an extreme case, differs only by 7% as compared with Di = 0.
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31
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0345442612
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Microscopy was performed with a Philips CM30 200-kV high-resolution TEM
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Microscopy was performed with a Philips CM30 200-kV high-resolution TEM.
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32
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0026679509
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The ripple mode may be a precursor to buckling, but it should not be confused with bucking. Buckling (in contrast to rippling) is characterized as an instability giving rise to a nonlinear response. It occurs in highly stressed nanotubes (and beams) and manifests as one or several kinks with very small radii of curvature (about 1 to 10 nm). It is accompanied by abrupt change in the effective force constant and may cause irreversible damage. The observed effect may be related to the rippling found in classical beams as a precursor to buckling [see S. Kyriakides and G. T. Ju, Int. J. Solids Struct. 29, 1117 (1992)].
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Ju, G.T.2
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0345442605
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11.
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34
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0027125463
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D. Ugarte, Nature 352, 707 (1992).
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Ugarte, D.1
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0345442604
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Electrical charging due to the electron beam cannot account for the effect, because the charge found to reside on the nanotubes is positive rather than negative. Furthermore, the amplitude of vibration at resonance does not change with electron dose, as it would if electron beam charging were important.
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39
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0345442603
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note
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We thank U. Landman, R. L. Whetten, L. Forro, and A. Zangwill for fruitful discussion and R. Nitsche for his analysis of the static bent nanotube. D.U. thanks the Centre Interdepartemental de Microscopy Electronique, Ecole Polytechnique Federale, for the use of the Philips CM30 microscope for Fig. 3, B through D, and the Brazilian Council for Scientific and Technological Research. Supported by the Army Research Office, grants DAAG 55-97-0133 (W.A.d.H. and P.P.), by NSF9733160 (Z.L.W.), and by NSFDMR-9971412 (W.A.d.H. and Z.L.W.)
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