Graphite lattice structure

Fig. 5.10. Schematic drawing of graphite lattice structure. After Singer (1989).

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. 

Studies of intercalates have also been reported in recent years. In their EXAFS investigation of Btj in graphite, Heald Stern (1978) have found that while the intercalate retains its molecular structure, the Br-Br distance increases so as to match the periodicity of the graphite lattice. In the series of pseudo-stoichiometric alkali... 

This minimum is responsible for the diamond and graphite lattices with = 109° and 120° respectively having the smallest and second smallest values of the normalized fourth moment, and hence the shape parameter, s, in Fig. 8.7. This is reflected in the bimodal behaviour of their densities of states in Fig. 8.4 with a gap opening up for the case of the diamond cubic or hexagonal lattices. Hence, the diamond structure will be the most stable structure for half-full bands because it displays the most bimodal behaviour, whereas the dimer will be the most stable structure for nearly-full bands because it has the largest s value and hence the most unimodal behaviour of all the sp-valent lattices in Fig, 8.7, We expected to stabilize the graphitic structure as we move outwards from the half-full occupancy because this... 

Proof. Such tori can be obtained as quotients of a ( 5, b], 3)-plane. We will get again such a plane from the graphite lattice 6,3 with added structure on it On any vertex of the structure below, which is incident to an boldfaced edge, we put a (5,3>-polycycle D, while on other vertices we put a (5,3)-polycycle E. The obtained ( 5, b, 3)-plane is bR. ... 

Proof. Consider the graphite lattice 6,3 and put a 5-gon in every vertex of it The obtained structure is, clearly, a ( 5,8, 3)-plane, which is 8/ 2- In order to obtain ( 5, b, 3)-planes with b > 8, we need to modify the structure. The 5-gons can be organized into pairs of adjacent ones. Every such pair, which is highlighted in the diagram below, can be changed into a (5,3)-polycycle E2n with n > 1. 

Silicon and germanium as elemental substances are found only in the diamond-type form. The reluctance of Si and Ge to enter into pre-p bonding prohibits a graphite-type structure as a plausible allotrope. These are rather more reactive than diamond the weaker Si-Si and Ge-Ge bonds make disruption of the lattice kinetically easier. Tin occurs in both a metallic form (white tin) and a covalent (diamond-type) form the latter is slightly more stable at low temperatures. Lead forms only a metallic elemental substance. 

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. 

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. 

Raman spectra were recorded using a Spex Triplemate spectrograph equipped with a diode array detector. The 514 nm line of an Ar+ laser was used for excitation. The Raman spectra displayed a band at approximately 1600 cm-1 due to C-C vibrations of graphite-like structures and a band at 1365 cm 1 due to imperfections of the graphite lattice and to amorphous carbon. The width of the 1600 cm"1 band in the Raman spectra has been reported to be inversely proportional to the degree of graphitization [5,6]. 

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