Graphite unit cell

A carbon SWNT can be visualized as a hollow cylinder formed by rolling a planar sheet of hexagonal graphite (unit-cell parameters a = 0.246, c = 0.669 nm). It can be uniquely described by a vector C = nn + m 2, where ai and a2 are reference unit vectors as defined in Fig. 14.1.9. The SWNT is generated by rolling up the sheet such that the two end-points of the vector C are superimposed. The tube is denoted as (n, m) with n>m, and its diameter D... 

Crystallite parameters La, crystallite diameter in the plane of the a axis Lc, crystallite thickness in the C axis a, graphite unit cell dimension in the plane of the layers C, twice the interlayer spacing in the graphite matrix. 

They measured changes in the forces acting to maintain a constant current as the tip scans from one part of the graphite unit cell to another one. 

FIGURE 1.54 Hexagonal graphite unit cell. When the origin is set on a carbon atom, the positions of the four atoms of the cell, measured from a lattice point, are (0,0,0) ... 

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

Crystal Structure. Diamonds prepared by the direct conversion of well-crystallized graphite, at pressures of about 13 GPa (130 kbar), show certain unusual reflections in the x-ray diffraction patterns (25). They could be explained by assuming a hexagonal diamond stmcture (related to wurtzite) with a = 0.252 and c = 0.412 nm, space group P63 /mmc — Dgj with four atoms per unit cell. The calculated density would be 3.51 g/cm, the same as for ordinary cubic diamond, and the distances between nearest neighbor carbon atoms would be the same in both hexagonal and cubic diamond, 0.154 nm. 

Fig. 8. Lattice distortions in a graphite sheet. For an in-plane distortion (left), the bond denoted by a thin line becomes shorter and that denoted by a thick line becomes longer, leading to a unit cell three times as large as the original. For an out-of-plane distortion (right), an atom denoted by a black dot is shifted down and that denoted by a white circle moves up.

Doping of alkali-metals into CNTs has been examined [11]. The X-ray powder diffraction (XRD) patterns of the K- or Rb-doped CNTs show that alkali-metals are intercalated between the CNT layers. The hexagonal unit cell is essentially the same as that of the stage-1 alkali-metal intercalated graphite ACg (A=K, Rb). For a sample doped with Rb, the observed lattice parameter of the perpendicular... 

Graphite forms extended two-dimensional layers (see Fig. 5.22). (a) Draw the smallest possible rectangular unit cell for a layer of graphite, (b) How many carbon atoms are in your unit cell (c) What is the coordination number of carbon in a single layer of graphite ... 

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 5. Current voltage curve of hexadodecylsubstituted HBC 33 on graphite. Symmetric curve a for the aliphatic part. Diode-like curve b for the aromatic part of the molecule. The inset shows STM image of 33 with unit cell depicted. A and B indicate the aliphatic and the aromatic part. Picture taken from ref. [24],...

Figure 11. STM image of a monolayer of (a) c/s-C12(AZO)C12ISA 61 and (c) frans-C12(AZO)C12ISA 60 on graphite. The molecular models for the two-dimensional packing of 61 and 60 with proposed unit cells are represented in (b) and (d). Pictures taken from ref. [40],...

Different varieties, however, of graphite may be considered. The actual structure and unit cell dimensions and layer stacking can vary depending on the preparation conditions, degree of crystallinity, disorientation of layers, etc. 

Figure 7.15. hP4-C (graphite) structure. The unit cell and a carbon atom layer are shown. 

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