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V doped nanotubes of Ge have also been studied recently and similar results have been obtained. For details see A. K. Singh, V. Kumar, and Y. Kawazoe, Eur. Phys. J. D (to be published). Similar results could be expected for Ta doping.
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note
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5). This is very much expected as the ground state energies of Nb clusters (Ref. 21) increase much more rapidly compared with the energies of Ge clusters (Ref. 22) as well as the nanotubes with the increase in the number of atoms. Nanotubes are metastable structures and in the infinite nanotube limit the cohesive energy is expected to be lower than the corresponding bulk material as it is the case for carbon nanotube and the bulk graphite. However, the important point is the nucleation of these structures and appropriate conditions for their growth. In the case of metal doped nanotubes, the small nanotubes or appropriate clusters are important as these could act as the nucleation centers for larger nanotubes.
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25
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15744401902
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note
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7 show antiprism-prism stacking to be most preferred similar to the case of Nb. In these nanotubes the Ge-Ge BL's in each hexagonal ring are equal, leading to the sixfold-symmetric nanotubes. The HOMO-LUMO gaps are much larger as compared to Nb doping. This is due to the stronger hybridization of the W 5d states with the valence states of Ge. The states near the highest occupied level are significantly shifted downwards in W-doped nanotubes while for the other states this shift is small as compared to the case of Nb doping. This results in a higher BE of the W-doped nanotubes (Table I).
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