Raman spectra of filled carbon nanotubes
Introduction
Ever since the discovery of the carbon nanotubes by Iijima in 1991 [1] in the cathode of the same arc-discharge apparatus that was used to produce fullerenes, various other methods have been used to produce both single-wall and multi-wall nanotubes [2], and high-quality aligned nanotubes bundles [3]. Graphitic hexagons forming a nanotube usually form a helix about the tube axis. Earlier it was shown theoretically that nanotubes with non-zero helicity are predominantly semiconducting whereas nanotubes of zero helicity are metallic [4]. Recent experiments have verified these assertions [5].
Nanotubes have many unusual properties that make them very attractive for industrial applications [6]. For example, the strong field emission property has already been used to produce more efficient electron guns and field emission lamps. The huge tensile strength and resilience may some day be used to produce earthquake resistant buildings and dent resistant cars. The possibility of storing hydrogen and lithium in nanotubes is being pursued, as it may lead to production of super batteries. Nanotubes also propose to bring a revolution in the electronic industry as nanosize p–n junctions, metal–semiconductor heterostructures, and field-effect transistors (FET) using carbon nanotubes have already been produced. Nanotube-tipped atomic force microscopes are now being used to trace ultra-thin strands like the DNA. Use of nanotubes will also lead to sharper scanning probe microscopes. Large change in the electrical resistance of nanotubes due to doping will lead to production of supersensitive sensors. These are only a few examples of the plethora of applications that the carbon nanotubes will eventually have.
One recent advancement in carbon nanotube research has been the production of nanotubes filled with a variety of metallic and non-metallic materials along the nanotube axis. Initial filling of the nanotubes by Pb and Bi was achieved by capillary action [7]. The process of filling nanotubes with other foreign materials was greatly aided by two important discoveries. First, Tsang et al. [8] showed that the nanotube tips can be opened with treatment of nitric acid and second, Guerret-Piecourt et al. [9] showed that filled carbon nanotubes can be synthesized by adding the filling material to the electrode used in the carbon arc of the arc discharge tube. Using these and other related techniques carbon nanotubes filled with Ag [10], C60 [11], Ni [12], Co [13], TiC [14], Se, S, Sb, and Ge [15], MnC [16], LaC [17] and other materials have been produced. The electronic and other other properties of the filled nanotubes are now being studied extensively. Electrical and thermal properties of C60 filled single-wall carbon nanotubes or carbon peapods as they are called, have been investigated by Vavro et al. [18]. The magnetic and hysteritic properties of Fe-filled nanotubes have been examined by Prados et al. [19]. Catalytic properties and possible applications in electrochemical energy storage of some filled carbon nanotubes have been studied by Che et al. [20]. The electronic structure and optical properties of filled nanotubes have been investigated theoretically by Ostling et al. [21] and Garcia-Vidal et al. [22], respectively.
In a previous article, we have studied theoretically the effect of electron–phonon interaction on the Raman spectra of pristine metallic carbon nanotubes [23]. We have shown that excitation of a plasmon due to the azimuthal motion of the electrons on the surface of a carbon nanotube will split a nanotube Raman line into two via the electron–phonon interaction. In the present article, we study the Raman spectra of a filled carbon nanotube. Here, we include both the electron–phonon interaction effect as well as the effect of the presence of the phonons of the filling atoms. We find a three-way splitting of the Raman lines. In Section 2 we present the formulation of the present problem and in Section 3, we provide the results of our calculation and a brief discussion.
Section snippets
Calculation of Raman intensity
When light is incident on a medium, most of it is scattered elastically with no change in frequency. Some of it is, however, scattered with a lower frequency because it gives up some of its energy to the lattice vibrations or to excite a phonon (Stokes lines) and some of it may be scattered with a higher frequency because of absorption of a phonon (anti-Stokes lines). This phenomenon is commonly known as the Raman effect. The Raman scattering process can be understood at the microscopic level
Results and discussion
The Raman intensity as given by , , will depend on the parameters λ, a/aB, μ, and We have plotted the Raman intensity as a function of the frequency for several representative sets of these parameters. In all our plots we have taken μ=1 as we expect that this will be the easiest mode to excite.
In Fig. 1, the Raman spectra have been plotted for aB/a=0.3, and two values of λ=0.05 (solid curves) and λ=0.1 (dashed curves). Notice that in both
Acknowledgements
One of us (SNB) would like to acknowledge the hospitality of the Physics Department of Drexel University where bulk of the work was carried out. SNB and SMB would like to acknowledge a visit to University of Duisburg-Essen for collaboration. The authors thank Dr S. Gayen for his valuable assistance with the plotting of the figures.
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Currently at Berhampur University, Bhanja Bihar, Berhampur-760007, Orissa, India.