Low-dimensional materials

Other Inorganics. Inorganic species in solution have been studied very effectively by Raman spectroscopy. Work in this area includes the investigation of coordination compounds (qv) of fluorine (qv) (40), the characterization of low dimensional materials (41) and coordinated ligands (42), and single-crystal studies (43). Several compilations of characteristic vibrational frequencies of main-group elements have been pubflshed to aid in the identification of these species (44,45). 

In this chapter the results of detailed research on the realistic electronic structure of single-walled CNT (SWCNT) are summarised with explicit consideration of carbon-carbon bond-alternation patterns accompanied by the metal-insulator transition inherent in low-dimensional materials including CNT. Moreover, recent selective topics of electronic structures of CNT are also described. Throughout this chapter the terminology "CNT stands for SWCNT unless specially noted. 

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

An interesting point concerns polarisation effects in the Raman spectra, which are commonly observed in low-dimensional materials. Since CNTs are onedimensional (ID) materials, the use of light polarised parallel or perpendicular to the tube axis will give information about the low dimensionality of the CNTs. The availability of purified samples of aligned CNTs would allow us to obtain the symmetry of a mode directly from the measured Raman intensity by changing the experimental geometry, such as the polarisation of the light and the sample orientation, as discussed in this chapter. 

Michalowicz, A., Verdaguer, M., Mathey, Y., and Clement, R. Order and Disorder in Low Dimensional Materials Beyond the First Coordination Sphere with E.X.A.F.S., 145, 107-149 (1987). Montanari, F., Landini, D., and Rolla, F. Phase-Transfer Catalyzed Reactions. 101, 149-200 (1982). 

The equations discussed above are reliable for phases where the compressibility does not change too fast with pressure, more specifically for 3.4 < K t q < 7. The equations are thus suitable for a large range of crystalline substances but not for liquids or low-dimensional materials, where K T 0 is often larger than 7. In the latter cases the universal Vinet equation of state seems more appropriate [28],... 

Taube, H. "Synthesis and Properties of Low-Dimensional Materials" Epstein, A. J. Miller, J. S., Eds. New York Academy of Sciences p 481 and references cited therein. 

Anderson localization is the localization of electrons on low-dimensional materials, which is induced by the irregularity of the periodic potential field [43]. Figure 17 gives a schematic representation of Anderson localization of a particle in one-dimensional box. The same is true for an electron on a polymer skeleton. A localized state in a completely periodic... 

This topic featured strongly in our last review and has continued to be important because high magnetic fields are essential in the study of low dimensional materials. A shortened form of the introduction to the theory required to understand the properties of these materials is repeated here from the last review. A review article,63 that emphasizes the importance of HFEPR to this topic, should be consulted for further details. 

Zhang, Z., Chen, L. S. Zhou, G. W. Low dimensional materials and their microstructures studied by high resolution electron microscopy. Springer Ser. Surf. Sci. 39, 105-169 (2001). 

T. Ogawa and Y. Kanemitsu, Optical Properties of Low-Dimensional Materials (World Scientific, Singapore, 1995). 

W. Jaegermann, A. Klein, C. Pettenkofer, in Electron Spectroscopies Applied to Low-Dimensional Materials, ed. by H.I. Hughes, H.P. Starnberg, Physics and Chemistry of Materials with Low-Dimensional Structure (Kluwer, Dordrecht, 2000), pp. 317-402... 

J. P. Pouget, in Organic and Inorganic Low-Dimensional Materials, NATO ASI B 168 (P. Delhaes and M. Drillon, eds.), Plenum Press, New York, 1987. 

Puchkov, A. V. Shen, Z.-X. In Hughes, H. P., Stamberg, H. I., Eds. Electron Spectroscopies Applied to Low-Dimensional Materials, Kluwer Academic Publishers, 2000. 

It has been well known that HRTEM is a powerful tool to investigate structures of low-dimensional oxides, such as nanoparticles, nanowires, nanorods and nanotubes, while the information from powder dilfraction of these low-dimensional materials is normally very Hmited merely because their small crystaUite sizes. For the nanoscale oxides, HRTEM can give useful information on particle size, crystal structure, particle morphology, structural defects and possible inter-particle connections. 

Future studies should concentrate on four types of silicon-based polymers semiconducting polymers, functional polymers, metallic polymers, and ideal low-dimensional materials for pure physics. The range of Si-based polymers should be expanded rapidly to include high-dimensional polymers, one-dimensional superlattices, and unsaturated polymers. 

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