Abstract
We have studied the low frequency vibrational modes and the structural rigidity of long graphitic carbon tubules consisting of 100, 200, and 400 atoms. Our calculations have been performed using an empirical Keating Hamiltonian with parameters determined from first principles. We have found the “beam bending” mode to be one of the softest modes in these structures. The corresponding beam rigity of a “bucky tube” is compared to an found to exceed the highest values found in presently available materials.
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Krätschmer, W., Lamb, L.D., Fostiropoulos, K., Huffman, D.R.: Nature347, 354 (1990)
Kroto, H.W., Heath, J.R., O'Brien, S.C., Curl, R.F., Smalley, R.E.: Nature318, 162 (1985)
Sumio Iijima: Nature354, 56 (1991); Sumio Iijima, Toshinari Ichihashi, Yoshinori Ando: Nature356, 767 (1992)
Ball, Philip: Nature354, 18 (1991)
Bacon, R.: In: Proceedings of the Cambridge Conference on Strength of Whiskers and Thin Films (1958)
Mintmire, J.W., Dunlap, B.I., White, C.T.: Phys. Rev. Lett.68, 631 (1992); Hamada, N., Sawada, S.-I., Oshiyama, A.: Phys. Rev. Lett.68, 1579 (1992); Kikuo Harigaya: Phys. Rev. B45, 12071 (1992); Saito, R., Fujita, M., Dresselhaus, G., Dresselhaus, M.S.: Phys. Rev. B46, 1804 (1992); Tanaka, K., Okahara, K., Okada, M., Yamabe, T.: Chem. Phys. Lett.191, 469 (1992)
Ross, Philip E.: Scientific American, December 1991, p. 24
Fowler, P.W., Cremona, J.E., Steer, J.I.: Theor. Chim. Acta73, 1 (1988)
Keating, P.N.: Phys. Rev.145, 637 (1966)
Kane, E.O.: Phys. Rev. B31, 7865 (1985)
Jones, R.: J. Phys. C20, L271 (1987)
Schlüter, M., Lannoo, M., Needels, M., Baraff, G.A., Tománek, D.: Phys. Rev. Lett.68, 526 (1992). The phonon modes of the C60 solid are based on the Keating potential and force constants of (1) and Table 1 in this publication
Wooten, F., Weaire, D.: Solid State Phys.40, 2 (1987)
Hohenberg, P., Kohn, W.: Phys. Rev.136, B864 (1964); Kohn, W., Sham, L.J.: Phys. Rev.140, A1133 (1965)
Overney, G., Tománek, D., Zhong, W., Sun, Z., Miyazaki, H., Mahanti, S.D., Güntherodt, H.-J.: J. Phys.4, 4233 (1992)
Hamann, D.R., Schlüter, M., Chiang, C.: Phys. Rev. Lett.43, 1494 (1979)
The vibrational modes of graphite are explained in: Dresselhaus, M.S., Dresselhaus, G.: Adv. Phys.30, 139 (1981)
Onida, G., Benedek, G.: Europhys. Lett.18, 403 (1992); ibid19, 343 (1992) (E)
Sarid, D.: Scanning force microscopy, Oxford Series in Optical and Imaging Sciences, pp. 1–7. Oxford: Oxford University Press 1991; Landau, L.D., Lifshitz, E.M.: Theory of elasticity, p. 81. New York: Pergamon Press 1986; Cook, R.D., Young, W.C.: Advanced mechanics of materials, p. 258. New York: Macmillan 1985
The larger radius would appear as more appropriate when comparing Ir with multi-walled carbon tubules, where an atomic volume and density can be reasonably defined
[3]; Ebbesen, T.W., Ajayan, P.M.: Nature358, 220 (1992); Ugarte, D.: Nature359, 707 (1992)
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Overney, G., Zhong, W. & Tománek, D. Structural rigidity and low frequency vibrational modes of long carbon tubules. Z Phys D - Atoms, Molecules and Clusters 27, 93–96 (1993). https://doi.org/10.1007/BF01436769
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DOI: https://doi.org/10.1007/BF01436769