Diamond unit structure

Silicon atoms bond strongly with four oxygen atoms to give a tetrahedral unit (Fig. 16.4a). This stable tetrahedron is the basic unit in all silicates, including that of pure silica (Fig. 16.3c) note that it is just the diamond cubic structure with every C atom replaced by an Si04 unit. But there are a number of other, quite different, ways in which the tetrahedra can be linked together. 

The otherl4th group elements, Si, Ge and oSn have the diamond-type structure. The tI4- 3Sn structure (observed for Si and Ge under high pressure) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger and another four at a considerable larger distance. Fig. 7.13 shows the (3Sn unit cell. Lead, at ambient pressure, has a face-centred cubic cF4-Cu type structure. 

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). 

To date, inorganic materials have been used in most semiconductor applications. The most studied and technologically important inorganic semiconductors have the diamond (e.g.. Si) or zinc-blende (e.g., Ga As) crystal structure. Figure 1 shows the zinc-blende crystal structure and the corresponding BrOouin zone. (The symbols label special symmetry points in the zone.) The structure is based on an fee lattice with two atoms per unit cell. The diamond crystal structure is the same as the zinc-blende structure, except that the two atoms in the unit cell are the same for diamond, whereas they are different for zinc blende. The Brillouin zones are the same for the two structures, but for the diamond structure, there is an additional inversion symmetry operator. 

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... 

Silicon will serve as the paradigmatic example of slip in covalent materials. Recall that Si adopts the diamond cubic crystal structure, and like in the case of fee materials, the relevant slip system in Si is associated with 111 planes and 110> slip directions. However, because of the fact that the diamond cubic structure is an fee lattice with a basis (or it may be thought of as two interpenetrating fee lattices), the geometric character of such slip is more complex just as we found that, in the case of intermetallics, the presence of more than one atom per unit cell enriches the sequence of possible slip mechanisms. 

Since the spectra of Ice In and Ice I are identical, it makes sense to analyse the vibration spectrum indicated in fig. 6.4 in terms of the simpler diamond cubic structure of Ice I,.. In fact, since the molecules move as rigid units for the translational modes, the analysis should be very similar to that for the lattice vibrations of diamond, silicon or germanium. All these crystals have two atoms per unit cell (two molecules in the case of Ice Ij.) and the vibrational spectrum has two branches an acoustic branch, in which the two atoms move essentially in phase, and an optical branch, in which their motion is antiphase (Ziman, i960, chapter i). In... 

Fig. 5. Phonon spectra of crystals with a diamond-type structure, plotted for mj = mg. (a) and m2 = 0.43 mg. (b) is in relative units.

Structure of Cubic Diamond. Cubic diamond is by far the more common structure and, in order to simplify the terminology, will be referred to as simply diamond . The covalent link between the carbon atoms of diamond is characterized by a small bond length (0.154nm) andahighbond energy of 711 kJ/mol (170 kcal/mol).l i Each diamond unit cell has eight atoms located as follows 1/8 x 8 at the corners, 1/2 x 6 at the faces and 4 inside the unit cube. Two representations of the structure are shown in Fig. 11.3, /a and (b/.PPl... 

Above 1500 °C, quartz transforms to the mineral cristobalite which has a diamond-like structure with C-C bonds replaced by Si-O-Si units. 

Figure Bl.21.3. Direct lattices (at left) and corresponding reciprocal lattices (at right) of a series of connnonly occurring two-dimensional superlattices. Black circles correspond to the ideal (1 x 1) surface structure, while grey circles represent adatoms in the direct lattice (arbitrarily placed in hollow positions) and open diamonds represent fractional-order beams m the reciprocal space. Unit cells in direct space and in reciprocal space are outlined.

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. 

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.

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