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A Comparative Theoretical Study of Carbon and Boron-Nitride Single-wall Nanotubes

B. Akdim, X. Duan, and R. Pachter
Air Force Research Laboratory, Materials & Manufacturing Directorate, US

Keywords: Nanotubes, Density Functional Theory, Computational Study

Abstract:
In this study, we focus on a comprehensive theoretical comparison between CNTs and BN-NTs, particularly for the radial breathing modes (RBMs), which are characteristic of nanotubes and do not have any corresponding modes in the graphite structure. Raman spectroscopy is a well-known technique for measuring RBMs and characterizing tube radii, e.g., by experiment as well as by theory. In our comprehensive theoretical study of CNTs and BN-NTs using all-electron and plane-wave pseudopotential first-principle methods, we calculated the RBMs, optimizing the geometry and cell parameters in all calculations, also evaluating the equilibrium inter-tube distance in bundles. We find that the RBM values depend on the inter-tube distance in tube bundles, and are important to optimize, both for CNTs and BN-NTs (cf. Table 1). Note that the nanotube crystalline-rope interaction energies in bundles were found to be, on average, 0.2 (eV/Å) and 0.17 (eV/Å), for armchair and zigzag tubes, respectively. These results agree well with a previous theoretical study. The RBM values were fitted to A/R, where R is the tube radius and A the fitting constant, as summarized in Table 2. For CNT’s, for example, with an optimized crystalline-rope structure we calculate a RBM value of 287 (cm-1) at an intertube distance of (2R+3.4)(Å) for C(6,6), which is the value obtained for an isolated tube. Therefore, the value of the interlayer graphite distance as the intertube separation should be chosen with care. It is interesting to note that our RBMs for isolated tubes are in good agreement with experiment. Recent measurements show a 10 cm-1 decrease in the RBM due to the intertube coupling, contrary to our and other calculations. This inconsistency is due to an expansion of the van Hove singularities in tube bundles leading to an excitation, by the same laser energy, of different diameter tubes in the sample.

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