Diamond cubic unit cell

The ultimate covalent ceramic is diamond, widely used where wear resistance or very great strength are needed the diamond stylus of a pick-up, or the diamond anvils of an ultra-high pressure press. Its structure, shown in Fig. 16.3(a), shows the 4 coordinated arrangement of the atoms within the cubic unit cell each atom is at the centre of a tetrahedron with its four bonds directed to the four corners of the tetrahedron. It is not a close-packed structure (atoms in close-packed structures have 12, not four, neighbours) so its density is low. 

Figure 8.3 Structure of diamond showing the tetrahedral coordination of C the dashed lines indicate the cubic unit cell containing 8 C atoms.

Several superstructures and defect superstructures based on sphalerite and on wurtzite have been described. The tI16-FeCuS2 (chalcopyrite) type structure (tetragonal, a = 525 pm, c = 1032 pm, c/a = 1.966), for instance, is a superstructure of sphalerite in which the two metals adopt ordered positions. The superstructure cell corresponds to two sphalerite cells stacked in the c direction. The cfla ratio is nearly 1. The oP16-BeSiN2 type structure is another example which similarly corresponds to the wurtzite-type structure. The degenerate structures of sphalerite and wurtzite (when, for instance, both Zn and S are replaced by C) correspond to the previously described cF8-diamond-type structure and, respectively, to the hP4-hexagonal diamond or lonsdaleite, which is very rare compared with the cubic, more common, gem diamond. The unit cell dimensions of lonsdaleite (prepared at 13 GPa and 1000°C) are a = 252 pm, c = 412 pm, c/a = 1.635 (compare with ZnS wurtzite). 

Figure 4.13. The 3 2PT structure of diamond. The packing (P) layers are in a ccp pattern. All sites are occupied by C, but here the balls in the T layers are lighter. The cubic unit cell is outlined by double lines.

There are two polymorphic structures of ZnS, zinc blende (or sphalerite) (3 2PT) and wurtzite (2 2PT). In zinc blende there is a ccp arrangement of S atoms with Zn atoms filling one of the two T layers as shown in Figure 6.1. The diamond has the same structure, with the sites of P and one T layer filled by C atoms (Section 4.3.3). The structure of zinc blende has six (3 2) layers in the repeating unit. This structure is encountered for many binary compounds with significant covalent character as shown in Table 6.1. The space group for zinc blende is T%, F43m, and a0 = 5.4093 A, for the cubic unit cell. ... 

In diamond, each carbon atom is tetrahedrally surrounded by four equidistant neighbours (see Figure 9.1). In this case, the C-C distance is 0.154 nm and four interlinked tetrahedra make up the cubic unit cell of eight carbon atoms. The tetrahedral bond symmetry is the result of sp3 hybridization. Diamond is an extremely poor conductor of electricity since the energy of the empty conduction band lies considerably above the filled valence band. 

Figure 1-26 The diamond structure seen from two points of view, (a) The conventional cubic unit cell, (b) A view showing how layers are stacked these layers run perpendicular to the body diagonals of the cube.

Zinc blende (sphalerite, ZnS) has a diamond-type structure. The space group is F43m for a cubic unit cell with a = 5.42 A. The structure is illustrated in Figure 14.20. Parallel to the (100) face of zinc blende... 

Note There are three allotropes of carbon graphite, diamond, and buckminsterfullerene (Cgo) the latter, discovered in 1985, is composed of soccer-ball-shaped molecules. The thermodynamic stability of buckminsterfullerene has not yet been determined. The validity of its inclusion on the C phase diagram is, therefore, uncertain. (Metastable phases, such as supercooled water, do not appear on phase diagrams.) The crystal structure is face-centered cubic with Ceo molecules at the corners and faces of a cubic unit cell. The unit cell is shown below. 

The structures of the principal allotropic forms of all the elements will be discussed in detail as the chemistry of each element is treated. For illustrative purposes,-we shall mention here only one such structure, the diamond structure, since this is adopted by several other elements and is a point of reference for various other structures. It is shown from two points of view in Fig. 2-8. The structure has a cubic unit cell with the full symmetry of the group Td. However, it can, for some purposes, be viewed as a stacking of puckered infinite layers. It will be noted that the zinc blende structure (Fig. 2-3) can be regarded as a diamond structure in which one-half of the sites are occupied by Zn2 + (or other cation) while the other half are occupied by S2 (or other anion) in an ordered way. In the diamond structure itself all atoms are equivalent, each being surrounded by a perfect tetrahedron of four others. The electronic structure can be simply and fairly accurately described by saying that each atom forms a localized two-electron bond to each of its neighbors. 

Fig. 31. Conventional cubic unit cell of RAl. The R ions form a diamond-type sublattice. The Al ions are placed on the comers of tetrahedrons. For CeAlj the lattice constant is a = 8.062 A.

The simple cubic unit cell. When we arrange the first layer of spheres in vertical and horizontal rows, large diamond-shaped spaces are formed (Figure 12.24A, cutaway portion). If we place the next layer of spheres directly above the first, we obtain an arrangement based on the simple cubic unit cell (Figure 12.24B). The spheres occupy only 52% of the unit-cell volume, so 48% is empty space between them. This is a very inefficient way to pack spheres, so neither fruit nor atoms are typically packed this way. 

The hexagonal and face-centered cubic unit cells. Spheres are packed most efficiently in these cells. First, in the bottom layer (labeled a, orange), we shift every other row laterally so that the large diamond-shaped spaces become smaller triangular spaces. Then we place the second layer (labeled b, green) over these spaces (Figure 12.24D). 

Diamond adopts a face-centered cubic unit cell, with each C tetrahedrally bonded to four others in an endless array. Throughout the crystal, strong single bonds make diamond the hardest natural substance known. Like most network covalent solids, diamond does not conduct electricity because the bonding electrons are localized. 

In Table 2.5 we give general information about all the cubic structures under consideration prototype name, Pearson and strukturbericht designations, space group and Wyckoff positions occupations, and possible equivalent description of the structure. All these structures contain one formula unit in the primitive unit cell Z=l). For the structures cF with a face-centered cubic lattice the number of atoms is given for the cubic unit cell consisting of four primitive unit cells (this is traditional for crystal-structure databases). In computer calculations only the atoms inside the primitive unit cell have to be included two atoms for diamond, rocksalt, zincblende and cesium... 

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