Sodium fullerides NanC60 (n = 2, 3) have been synthesized by a liquid phase reaction and investigated with X-ray diffraction (XRD), nuclear magnetic resonance (NMR), electron paramagnetic resonance, and differential thermal analysis. XRD data indicate that the crystal structure of Na2C60 at 300 K is face centered cubic (FCC). A phase transition from primitive cubic to FCC crystal structure has been observed in this work in Na2C60 fulleride at 290 K. The transition is accompanied by the step-like change of paramagnetic susceptibility. The crystal structure of Na3C60 is more complicated than, and different from, what has been reported in the literature. A nearly seven-fold increase of paramagnetic susceptibility with increasing temperature has been observed in the Na3C60 fulleride at 240–260 K. In the same temperature range, a new line at about 255 ppm appears in the 23Na NMR spectrum, indicating a significant increase of electron density near the Na nucleus. The observed effect can be explained by a metal-insulator transition caused by a structural transition.
In this paper we use symmetry of Single Walled Carbon Nanotubes (SWCNTs) to generate some types of virtual sub-bands that are lower in number than the real sub-bands obtained through conventional-TB. It is shown that the virtual sub-bands maintain the value of band gap. In obtaining the sub bands, the interactions of the nearest and the second and third-nearest neighbors are taken into account. As the consequence of lower number of sub-bands, a significant reduction in computational effort has occurred and made the approach useful.
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