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The radial breathing mode frequency in double‐walled carbon nanotubes: an analytical approximation
Author(s) -
Dobardžić E.,
Maultzsch J.,
Milošević I.,
Thomsen C.,
Damnjanović M.
Publication year - 2003
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200301825
Subject(s) - carbon nanotube , tube (container) , phonon , materials science , graphite , breathing , mode (computer interface) , molecular physics , phase (matter) , coupling (piping) , condensed matter physics , atomic physics , physics , nanotechnology , composite material , quantum mechanics , medicine , computer science , anatomy , operating system
We study the breathing‐like phonon modes of double‐walled carbon nanotubes in a simple analytical model by considering the tube walls as coupled oscillators. The force constant of the oscillator coupling is found to be proportional to the inner tube diameter. Thus, only for small‐diameter tubes, the shift of the breathing‐like phonon mode frequencies (relative to the radial breathing modes of the isolated layers) scales with the tube diameter D . For tubes with larger diameter the in‐phase breathing‐like phonon mode frequency is inversely proportional to the diameter (like the radial breathing modes of the single wall carbon nanotubes), while the out‐of‐phase mode approaches asymptotically, as 1/ D 2 , the graphite B 2g phonon mode frequency.