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33646619970
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note
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In Ref. 24 some evidence was presented that, while for the small and moderate radii the strain energy is clearly smaller in the case of BN compared to C nanotubes, the opposite could be true for larger tubes (r > 30 Å). However, this seems quite unlikely if, as pointed out here, a smaller flexular rigidity of BN can already be deduced from the behavior of the ZA phonon band of the flat sheet. Unfortunately, the parameter δ is quite sensitive to the fit procedure and to numerical uncertainities, and the values for C and BN are close enough so that no definitive conclusion can be given here.
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57
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33646627737
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note
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2) with a value of 0.284 TPa nm and v being the Poisson ratio.
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58
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68
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33646605297
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note
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See EPAPS Document No. E-PRBMDO-66-235415 for the tables containing the numerical values of the vibrational frequencies at Γ, including the Raman- and IR-active modes, for all the tubes studied in this work. The frequencies have been classified according to their symmetries. A direct link to this document may be found in the online article's HTML reference section. The document may also be reached via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more information.
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Similarly to the case of the monolayer, the main changes on the phonon band structure of the single-walled tubes induced by the long-range dipolar interactions are relatively small and restricted to the high-frequency modes: the in-plane optical modes extend over a somewhat larger energy range, and some of the longitudinal modes (with atomic displacements parallel to the tube axis) exhibit a larger dipersion with k. These changes are directly related to the larger overbending of the LO band of the BN monolayer when the electrostatic interactions are included.
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