Phonon vibrational frequencies of all single-wall carbon nanotubes at the lambda point: reduced matrix calculations.
With a simple method-the reduced matrix method, we simplified the calculation of the phonon vibrational frequencies according to SWNTs structure and their phonon symmetric property and got the dispersion properties of all SWNTs at Gamma point in Brillouin zone, whose diameters lie between 0.6 and 2.5 nm. The calculating time is shrunk about 2-4 orders. A series of the dependent relationships between the diameters of SWNTs and the frequencies of Raman and IR active modes are given. Several fine structures including "glazed tile" structures in omega approximately d figures are found, which might predict a certain macro-quantum phenomenon of the phonons in SWNTs.
Wang
Yufang
Y
College of Physics, Nankai University, 94 Weijin Road, Tianjin 300071, PR China.
Wu
Yanzhao
Y
Feng
Min
M
Wang
Hui
H
Jin
Qinghua
Q
Ding
Datong
D
Cao
Xuewei
X
D008956:Models, Chemical; D015394:Molecular Structure; D036103:Nanotechnology; D037742:Nanotubes, Carbon / Q000737:chemistry*; D011789:Quantum Theory; D013055:Spectrophotometry, Infrared; D013059:Spectrum Analysis, Raman; D013816:Thermodynamics; D014732:Vibration
D037742:Nanotubes, Carbon