Chiral single-wall carbon nanotubes phonon spectra

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Chiral single-wall carbon nanotubes phonon spectra calculations

The relationship between frequency and diameter basically armchair and zigzag similar 【7]. Low mode frequency increases with the diameter decreases, breathing mode is inversely proportional to the frequency and approximate diameter,[link widoczny dla zalogowanych], high-frequency mode depends on the diameter smaller. Careful observation will find some fine structure. Figure 5 shows the armchair, zigzag and chiral tubes in 860cmI1 frequency vibrational modes near the relationship between frequency and diameter. Can be seen from the dispersion relation into several branches, each branch belong to the bottom-up (n, 0), (n, 1), (n, 2), (n, 3) ... ... (n, n) tube, the figure shows the (n, 0), (n, 4), (n, n) branch. Each branch of the frequency (the relationship with the diameter d can be fitted into the following functional form: WaveVector (26nfr) Fig.2Phonondispersionrelationsof (9,3) tube (dengencymodes) - E1 - Et - E1 - Et - El ----- E .-- E2 - E, - E2 - E2 - E2 a ~ E2Fig.3AIvibrationalmodesof (9,[link widoczny dla zalogowanych],3) tubecu = Aexp (a d / B) + C + Dd will be carefully analyzed found that some phenomena,[link widoczny dla zalogowanych], the frequency of vibrational modes of carbon tubes with diameter of bamboo-shaped relationship between the present distribution of carbon nanotubes on each section is equal to an integer index,[link widoczny dla zalogowanych], ie n + m = 10,11, · 198.12, .... For the other vibrational modes have a similar phenomenon. have specific reasons for this phenomenon needs further analysis and research., summer u.) Ja0 summer; I1} do 3 Wang Yufang: Chiral single-wall carbon nanotubes phonon spectra Calculation of moments of 2006 concluded Chang Wong 2 - 10 Chang Xiao Wavenumber (em) Fig. 4PlotofthevibrationalmodefrequenciesasfunctionofcarbonnanotuberadiusDiameter (nm) Fig. 5Diameterdependenceofthevibrationalmodefrequencies (about866cm) opponents of the tube this phonon dispersion relations were calculated. For (9,3) tube line given the dispersion bleed at the nose and some vibrational modes of vibration mode diagram of the point of the Brillouin zone I1 vibration mode of the relationship between frequency and diameter, and found some fine structure.