Lattice structure of graphite

FIGURE 6.10 Lattice structure of graphite. The unit cell has four carbon atoms (a, P, a, P ). The positional vectors measured from atom a are denoted by x2,and x4 for P, a, and P atoms, respectively. 

Graphite is another solid form of carbon. In contrast to the three-dimensional lattice structure of diamond, graphite has a layered structure. Each layer is strongly bound together but only weak forces exist between adjacent layers. These weak forces make the graphite crystal easy to cleave, and explain its softness and lubricating qualities. 

Fig. 11. Crystal structure of graphite. The unit cell is shaded in green, (a) Top view of the surface layer. The hexagonal surface lattice is defined by two unit vectors u and v in the xy-plane with a length of 246 pm and an angle of 120° forming a honeycomb web of hexagonal rings. The basis of the lattice consists of two carbon atoms a, (white) and /3 (red) with a distance of 142 pm. (b) Perspective view, showing the layered structure. The distance between layers is 2.36 times the next-neighbor distance of atoms within one layer, and the bond between layers is weak. The a-atoms (white) are directly above an a-atom in the layer directly underneath at a distance of 334.8 pm the /3-atoms (red) are over hollow sites (h). The unit vector w is parallel to the z-axis with a length of 669.6pm.

Structure of Graphite. Figure 11 displays the structure of graphite, a layered structure with a hexagonal lattice of carbon atoms linked by strong sp2 bonds with a next neighbor distance of only 142 pm. 

If GO is used as a host lattice for Li+ in aprotic electrolytes, reversibility is improved [577]. The potential level is distinctly more positive than with donor GIC, at about —1 V vs. SHE. An all-solid-state Li/GO battery with PE0/LiC104 as solid electrolyte was reported by Mermoux and Touzain [578], but rechargeability is poor. Recently, the structure of graphite oxide was studied by its fluorination at 50-2()0 °C [579]. C-OH bonds were transformed into C-F bonds. The examples, in conjunction with Section 2, show that the formation or cleavage of covalent C-O (C-F) bonds makes the whole electrochemical process irreversible. Application was attempted in lithium primary batteries, which have a voltage of 2-2.5 V. Really reversible electrodes are only possible, however, with graphite intercalation compounds, which are characterized by weak polar bonds. 

If there is no change in molecular radius, this corresponds to a reduction in intermo-lecular spacing from 2.9 to 2.5 A. The a-axis compressibility —(/(In a)/dP is 2.3 x 10 cm /dyne, essentially the same as the interlayer compressibility -d(ln c)/dP of graphite within our combined 10% experimental error on P and a. The system retains the fee structure up to at least 1.2 GPa, so it is reasonable to assume that all the volmne reduction is accommodated by decreasing the VDW separation between molecules rather than by compressing or deforming the spheres. This is also consistent with the fact that a pressure of 1.2 GPa has no measurable effect on the in-plane lattice cottstant of graphite (9). 

Structure characterization is the basis for property study and application development. Therefore, structure of graphite oxide and GO is an important research topic. The difference between graphite oxide and GO is the number of layers. Here, we focus on the intralayer structure. Therefore, we will not distinguish graphite oxide and GO in this review unless it is necessary. The four early GO structure models include the Hoffman model [29], the Ruess model [30], the Scholz-Boehm model [31], and the Nakajima-Matsuo model [32, 33] (Fig. 5.1). These models are based on regular lattices with discrete repeat units. 

Figure 1.9 The lattice structure of hexagonal diamond. The arrangement of atoms in the horizontal crystal plane somewhat resembles a wavy graphite structure.

Studies with crystals indicate that the specificity, so often encountered in adsorption, can depend on mutual relations between the lattice structure of the solid and the configuration of the adsorbed substance. Methylene Blue is adsorbed by crystals of lead nitrate, but not by potassium sulfate. Nellensteyn1 found that diamond powder adsorbs Methylene Blue but not succinic acid, whereas graphite adsorbs succinic acid but not Methylene Blue. 

Pure diamond is a crystalline form of only carbon atoms. The crystal lattice is three-dimensional, and all carbon atoms are attached to four other carbon atoms in a perfect tetrahedral geometry. Because the lattice repeats in all three dimensions, there is no easy way to distort the structure, making it a very hard material. The structure of graphite, for comparison, is many stacked-up layers of carbon atoms. These two-dimensional sheets can slide relative to one another, making graphite relatively soft in comparison to diamond. 

Thus, in the 2D lattice of Figure 2.22, the superior unit cell actually has 4 (1/4)=1 effective point provided by the tops contributions, and one other effective point from the internal contribution, and with a total of two effective points on the cell it cannot be elementary or primitive. Instead, the inferior unit cell of Figure 2.22 is a primitive because the two atoms (physical) of the middle of the cell are assimilated with a motif (base of the lattice), i.e., generating 1 inferior effective motif-point on the cell, and there are not other. It s easy to imagine that the translating of this primitive cell in either direction along the parallels of its sides reproduces the planar structure of graphite. 

FIGURE 2.22 The lattice 2D for the structure of graphite after Heyes (1999). 

Figure A. 11a shows a schematic image of the atomic structure of graphite plane - graphene, and shows how from it can be obtained the nanotube. The nanotube is fold up with the vector connecting two atoms on a graphite sheet. The cylinder is obtained by folding this sheet so that were combined the beginning and end of the vector. That is, to obtain a carbon nanotube from a graphene sheet, it should turn so that the lattice vector R has a circumference of the nanotube in Fig. A. 11b. This vector can be expressed in terms of the basis vectors of the elementary cell gra-...

Figure 6.1 Schematic illustration of the layered lattice structures of (a) graphite and (b) molybdenum disulfide...

Lattice structure of diamond and graphite are shown in Figure A2. Graphite crystals are built of planes parallel to each other, in which carbon... 

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