Graphite band structure

As an example of a nanotube representative of the diameters experimentally found in abundance, we have calculated the electronic structure of the [9,2] nanotube, which has a diameter of 0.8 nm. Figure 8 depicts the valance band structure for the [9,2] nanotube. This band structure was calculated using an unoptimized nanotube structure generated from a conformal mapping of the graphite sheet with a 0.144 nm bond distance. We used 72 evenly-spaced points in the one-... 

The interpretation of thermoelectric power data in most materials is a delicate job and this is particularly true for the case of carbons and graphites. In the case of SWCNTs the data are not consistent with those calculated from the known band structure which leads to much smaller values than observed. Hone et al. [11] suggest from their data that they may indicate that the predicted electron-hole symmetry of metallic CNTs is broken when they are assembled into bundles (ropes). 

First reported by Fredenhagen in 1926 F3, F4), the graphite-alkali-metal compounds possess a relative simplicity with respect to other intercalation compounds. To the physicist, their uncomplicated structure and well defined stoichiometry permit reasonable band-structure calculations to be made S2,12) to the chemist, their identity as solid, "infinite radical-anions frequently allows their useful chemical substitution for such homogeneous, molecular-basis reductants as alkali metal-amines and aromatic radical anions N2, B5). 

Although residue compounds are difficult to characterize experimentally, they should constitute only a minor perturbation on the band structure of pure graphite. Efforts to model the electronic properties in the dilute-concentration limit by perturbing the Slonczewski-Weiss-McClure model for graphite have been made (D5). 

Raman spectroscopy A nondestructive method for the study of the vibrational band structure of materials, which has been extensively used for the characterization of diamond, graphite, and diamond-like carbon. Raman spectroscopy is so far the most popular technique for identifying sp bonding in diamond and sp bonding in graphite and diamond-like carbon. 

In the left panel of Figure 8 we show the band structure calculation of graphite in the repeated zone scheme, together with a drawing of the top half of the first Brillouin zone. The band structure is for the 1 -M direction. As the dispersion is very small along the c-axis we would find a similar result if we add a constant pc component to the line along which we calculate the dispersion [17]. The main difference is that the splitting of the a 1 and % band, caused by the fact that the unit cell comprises two layers, disappears at the Brillouin zone boundary (i.e. if the plot would correspond to the A-L direction). 

Figure 8. In the top left panel we show the band structure in the repeated zone scheme for the T -M direction. In the lower left panel we show the top half of the graphite Brillouin zone. The measurement presented in the central and right panel are for the T-M and A-L directions. Darker shading corresponds to larger intensities. Note that the n band is visible in the latter but absent in the first.

Takahashi T, Tokailin H, Sagawa T (1985) Angle-resolved ultraviolet photoelectron spectroscopy of the unoccupied band structure of graphite. Phys Rev B32 8317-8324... 

Band structure calculations of MgB2 show that the a states are unfilled and hence metallic, whereas for graphite a states are completely filled (An Pickett, 2001). It is sometimes useful to consider the geometrical and electronic structure of graphite when studying MOMs, because it summarizes the main features carbon-based, 2D and electrical conductivity given by nr-electrons. 

Band structure cesium auride, 25 240-241 graphite-alkali metal compounds, 23 287 Band theory, for one-dimensional electrical Conductors, 26 237-241 Barbituric acid, 18 187 Barium... 

Sketch the band structure of graphite intercalated with (a) an electron donor and (b) an electron acceptor. 

Figure 1. a) Schematic band structure illustrating transitions from the valence band to the conduction band (black arrow) and from core levels to the empty states above Fermi level (grey arrow).b) comparison, for graphite, (top) of LELS with optic measurements (optic data from [3]) and (bottom) of Core Losses with XAS (XAS data from [4])... 

Let us recall that nanotubes can be considered as graphene sheets rolled up in different ways. If we consider the so-called chiral vectors c = nai + na2, in which a and a2 are the basis vectors of a 2D graphite lattice, depending on the value of the integers n and m, one can define three families of tubes armchair tubes (n = m), zig-zag tubes (n or m = 0), and chiral tubes (n m 0). Band structure calculations have demonstrated that tubes are either metallic compounds, or zero-gap semiconductors, or semiconductors [6,7]. More commonly, they are divided into metallic tubes (when n-m is a multiple of 3) or semiconducting ones. 

---