Two-dimensional graphite

From the two-dimensional, graphite-like clusters, the extension to three-dimensional structures is obvious. Symmetric structures developed in a similar fashion to the planar systems would grow in three dimensions with increasing N, and the number of atoms would increase faster. In this work clusters of T symmetry were studied, resembling a small fragment of a diamond structure. Only systems with saturated external bonds were considered. The number of carbon and hydrogen atoms in such a structure is given by... 

Figure 10.47. Structure (j) (truncated icosahedron) is well known to the chemical community as buck-minsterfullerene, C6o, comprising hexagons and pentagons. It has been well established, both chemically and geometrically, that the pentagons in the structure are necessary to effect three-dimensional closure, and without them only open, two-dimensional graphitic layers are formed. All fullerenes, and even the topical Bucky tubes (Figure 10.2), that consist of fused hexagons are open at both ends unless pentagons are incorporated into the structure.

Zheng, Y. and T. Ando. 2002. Hall conductivity of a two-dimensional graphite system. Phys. Rev. B65 245420-1-11. 

Canfado LG, Pimenta MA, Saito R, Jorio A, Ladeira LO, Griineis A, Souza Filho AG, Dresselhaus G, Dresselhaus MS (2002) Stokes- and anti-stokes double resonance Raman scattering in two-dimensional graphite. Phys Rev B 66(3) 035415... 

The vibrational modes of an individual SWCNT can be derived from the phonon structure of two-dimensional graphite (graphene) by applying a zone-folding procedure that considers the one-dimensionality of CNTs and a chirality-dependent confinement [33], Due to CNT s complex stmcture, their Raman spectra show many size- and chirality-dependent features. In this section, however, only the most prominent first and second order Raman features will be discussed. 

According to Section 3.2, the nanotube structure can entirely be deduced from the two-dimensional graphite by symmetry considerations and the appHcation of geomehical operations. The same is true now for the physical properties of... 

Many of the structural and physical properties of single-walled nanotubes can easily be understood based on a the picture of a strip of a two-dimensional graphite sheet rolled into a cylindrical form. Adapted to this symmetry, we will use the real space unit vectors ai, 2 of a hexagonal lattice in x,y coordinates ... 

To obtain further the number N of hexagons per unit cell of a nanotube we have to divide the unit cell area Ch x T by the area of one hexagon of our two-dimensional graphite sheet aj x a2, which gives... 

A single-walled carbon nanotube (SWCNT). SWCNTs can be regarded as a two-dimensional graphite sheet rolled into a cylinder. Credit The single-walled carbon nanotube in Figure 11.6 is from the Spartan model provided by Dr. Warren J. Hehre of Wavefunction, Inc. 

Some polymeric films such as polyimide (Kapton), polyacrylonitrile (PAN) and polyfurfural alcohol, when carbonized between sheets of the mineral montmoiilionite, form a two-dimensional graphitic structure with highly oriented layer planes which graphitizes readily... 

Valence-band diagram for two-dimensional graphite. (Adapted from Painter and... 

For two-dimensional graphite, sketch the Bloch sums at F and M resulting from a bonding pair of 2px AOs in each unit cell. Let x be the bisector of ai and U2. Which of these COs would you expect to have higher energy ... 

Cassagne D., Jouanin C., Bertho D. Photonic band gaps in a two-dimensional graphite structnre. Phys. Rev. B 1995-B 52 R2217-R2220... 

Pure structured carbon exists in nature predominantly in the form of the three-dimensional diamond (all sp ) and two-dimensional graphite (all sp see also Real Life 15-1). The onedimensional version of a polymeric acetylene chain (all sp) has remained elusive, but synthetic chemists have come close by making well-defined oligomers containing up to 44 contiguous ip-hybridized carbons The NMR spectrum shows a range of peaks centered around 63.7 ppm, extrapolated to be the likely chemical shift of the infinite polymer. 

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