Cubic diamond structure

Fig. 16.3. Covalent ceramics, (a) The diamond-cubic structure each atom bonds to four neighbours.

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. 

Pure silica contains no metal ions and every oxygen becomes a bridge between two silicon atoms giving a three-dimensional network. The high-temperature form, shown in Fig. 16.3(c), is cubic the tetrahedra are stacked in the same way as the carbon atoms in the diamond-cubic structure. At room temperature the stable crystalline form of silica is more complicated but, as before, it is a three-dimensional network in which all the oxygens bridge silicons. 

Tin exists in two allotropic forms white tin (p) and gray tin (a). White tin, the form which is most familiar, crystallizes in the body-centered tetragonal system. Gray tin has a diamond cubic structure and may be formed when very high purity tin is exposed to temperatures well below zero. The allotropic transformation is retarded if the tin contains small amounts of bismuth, antimony, or lead. The spontaneous appearance of gray tin is a rare occurrence because the initiation of transformation requires, in some cases, years of exposure at —40°C. Inoculation with Ot-tin particles accelerates the... 

Silicon and germanium are the most important elemental semiconductors. They have the diamond cubic structure with sp hybrid bonds. The structure of the low index crystallographic planes, the only ones to be considered here, is shown in Fig. 1. It is seen that in the ill surfaces the atoms are triply bonded to the layer below and thus have one unpaired electron (dangling bond). Each atom of the 110 surfaces also... 

BN. This variety has a diamond cubic structure and is extremely hard like diamond. Its theoretical density is 3.48 gem ... 

In some structures, several planes and directions may be equivalent by symmetry. For example, this is the case for the (100), (010), (001), (100), (010), and (OOl) planes in the diamond cubic structure. Equivalent directions are denoted concisely as a group by using angular brackets. Thus, the (100) directions in a diamond cubic lattice include all of the directions that are perpendicular to the six planes noted above. The Miller index notation thus provides a concise designation for describing the surfaces of semiconductor crystals. 

Several cluster models have been tested to account for patterns of small clusters (p = 1 or 2 bar in Fig. 18). First, clathrate models have been examined. The most popular of these consists of a regular dodedecahedron with one H2O molecule at each of the 20 vertices and possibly one additional molecule at the center. In this model, HjO molecules form regular pentagons with a molecular angle HOH of 108°, which is intermediate between 104.5°, the value for the free molecule, and 109.5°, that for tetrahedral bonding in the diamond cubic structure. Such a clathrate model, stabilized by an additional proton, accounts well for mass spectrometry results, but is found to be far too symmetrical to account for the structure of neutral clusters. An amorphous model,derived from Polk s random dense packing, has been tested. This... 

Figure 1. Local rearrangement of bonds used to generate random networks from the diamond cubic structure, (a) Configuration of atoms and bonds in the diamond cubic structure and (b), relaxed configuration of atoms and bonds after switching bonds.

The choice of the diamond cubic structure (FC-2) as the initial configuration to be randomized is a natural one. It is the most common structure for group IV elements and related semiconductors with tetrahedral bonding and it is the one of highest symmetry. It has periodicity built in from the outset and it allows for the possibility that the randomized structure can in principle return to the initial crystal structure. Indeed, with insufficient randomization, the nearly-randomized structure will sometimes return to the perfect FC-2 crystal structure [34]. Without exactly N = Sn atoms this option is precluded. 

Note that diamond and a metal like copper have quite dissimilar structures, although both are based on a face-centered cubic Bravais lattice. To distinguish between these two, the terms diamond cubic and face-centered cubic are usually used. The industrially important semiconductors, silicon and germanium, have the diamond cubic structure. 

Stillinger-Weber Energy for Si in Diamond Cubic Structure... 

In eqn (4.51) we derived an expression for the total energy of a two-dimensional triangular lattice. That expression was for a geometrically umealistic structure for a covalently bonded material. Derive an analogous expression for the total energy of Si when in the diamond cubic structure. 

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. 

Grayish-white, lustrous, brittle metalloid. Diamond-cubic structure when cryst. Poor conductor of electricity. dj 5.323. Reported melting points range from 925-975 best value 937.2 (Hassion). Vol smaller by a few % when molten, bp 2700. Thermal expansion coefficient (at 25 ) 6.1 X 10 / C. Thermal conductivity (at 25 ) 0.14 cal/sec... 

Given the information given in Table 3.3, draw the zinc blende structure. What, if anything, does this structure have in common with the diamond cubic structure Explain. 

Calculate the number of broken bonds per square centimeter for Ge (which has a diamond cubic structure identical to the one shown in Fig. 3.16 except that all the atoms are identical) for the (100) and... 

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... 

If we left the half-plane 1234 where it is but removed the other half, we would create a dislocation with the opposite b, but instead of the last atom being R(S) it would be T(U) Zn instead of S The core of the dislocation is fundamentally different it is still a shuffle dislocation. These two dislocations are fundamentally different because the zinc blende structure does not have a center of symmetry. Similar considerations will hold for materials such as AIN and GaN, which also lack a center of symmetry but have the wurtzite structure crystal structure. The stacking fault in the diamond-cubic structure is described as AbBbCcBbCcAaBb the pair of planes Aa behaves just as if it were one fee plane in this case. Two possible SFs are shown in Figure 12.11d. 

Estimate the polarization of diamond. Diamond has a diamond-cubic structure with a = 0.357 nm. 

Silicon (Si) with an atomic number of 14 is a covalent material with wide-ranging application as a semiconductor in industry in devices and solar panels. Here our interest is primarily limited to the structure of amorphous Si and its mechanical behavior in its glassy range. In its crystalline form Si has a diamond-cubic structure with an atomic coordination number of 4 and has a relatively low density of Po = 2330 kg/m at room temperature. The diamond-cubic crystal structure of Si, for purposes of crystal plasticity, acts very similarly to fee metals and has most of the deformation characteristics of the fee structure. These characteristics, which have been studied intensively, are of no interest here. A summary of the low-temperature crystal plasticity of crystalline Si can be found elsewhere (Argon 2008). 

The Stillinger-Weber potential, so far the most widely used interaction potential for silicon, comprises a two- and a three-body interaction potential. The crystalline phase of silicon at low pressures is in the diamond cubic structure, and it melts into a high-density liquid phase. Stillinger and Weber, after a search through a class of interaction potentials with two- and three-body interactions, defined their empirical potential as follows ... 

Ceramics with cubic F structures and lllKHO) slip systems exhibit the same hardness anisotropy as fluorite structure solids with 001 (110) slip systems in the sense that the hardest directions on 100 are (100) and the softest are (110). Thus in order to determine which system is operative, a combination of the analysis given in Section 3.6.1 and other techniques, such as slip line analysis, is necessary. Ceramics with the diamond cubic structure have this slip system, and the parallel of their hardness anisotropy with that of fluorites can be seen by comparing the results for cubic boron nitride, BN, with the InP data in Figure 3.7. 

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