Diamond, cubic

Tin exists in two ahotropic 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 stmcture and may be formed when very high purity tin is exposed to temperatures well below zero. The ahotropic transformation is retarded if the tin contains smah 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 a-tin particles accelerates the transformation. 

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. 

D. L. Woodraska, J. A. Jaszczak. A Monte Carlo simulation method for [111] surfaces of silicon and other diamond-cubic materials. Surf Sci 574 319, 1997. 

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... 

Figure 5.1. Illustration of a unit cell of the diamond cubic lattice. The arrows designate the [001], [010], and [100] directions. Both silicon and germanium crystallize into the diamond cubic lattice structure, where each atom is bonded to four neighboring atoms in a tetrahedral geometry. Figure reproduced from Ref. [30] with permission.

Figure 5.4. The highest occupied molecular orbital of a Si911,2 dimer cluster. The top two silicon atoms comprise the surface dimer, and the remaining seven Si atoms contain three subsurface layers which are hydrogen terminated to preserve the sp3 hybridization of the bulk diamond cubic lattice. The up atom is nucleophilic and the down atom is electrophilic.

In its crystalline state, germanium, similar to silicon, is a covalent solid that crystallizes into a diamond cubic lattice structure. Like for Si, both the (100) and (111)... 

Manufactured abrasives include silicon carbide, fused aluminum oxide, sintered aluminum oxide, sol-gel sintered aluminum oxide, fused zirco-nia-alumina, synthetic diamond, cubic boron nitride, boron carbide, slags, steel shot, and grit. 

At room temperature tin has a body-centered tetragonal structure. This is called fi or white tin. Below 13 °C, the equilibrium structure is diamond cubic and is called gray tin. The transformation of white tin to gray tin results in disintegration into a powder because the volume expansion is very large (27%) and the gray-tin phase is very brittle. It would ruin any part made from or joined by tin. However, the transformation is extremely sluggish and inhibited by common impurities. There is an apocryphal story that attributes Napoleon s defeat at Moscow to this transformation. It is said that the cold Russian winter caused the tin buttons on... 

Cubic zirconia (Zr02), with a Mohs hardness of 8, is a beautiful, usually colorless, stone that is made synthetically. Although not as hard as diamond, cubic zirconia has much fire and brilliance, and it is popular as an imitation diamond. Zirconia normally has a monoclinic crystalline structure at room temperature, but when heated to about 2,300°C (4,172°F), it takes on a cubic structure. Ordinarily, it would revert to the monoclinic structure on cooling, but the addition of yttrium oxide (Y203) or calcium oxide (CaO)... 

Bogatyreva G.P., Marinich M.A., Gvyazdovskya V.L., Bazalij G.A. (2003) Prospects for Using Diamonds as Adsorbents Proc. An International Technical Conference on Diamond, Cubic Boron Nitride and their Applications (INTERTECH 2003), 48. 

Structural data are available (Table 30) for a range of binary, ternary and quaternary sulfides of manganese, almost invariably Mn", and these set the scene for the structures to be expected in the compounds with the more discrete polyhedra.319 Indeed, the structural pattern is established in the simple binary compound MnS. Whereas, the stable modification of this (a-MnS) is green and has the cubic rock salt structure with [MnS6] octahedra, the well-known flesh-coloured precipitates of the qualitative analysis system are metastable / - and y-modifications, which have [MnS4] tetrahedra with respectively the zinc blende or diamond (cubic) and wurtzite (hexagonal) structures. And so, in the rest of the known solids, there are almost equal numbers of four-coordinate tetrahedra and six-coordinate octahedra with no other polyhedra having been detected. 

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 ... 

The element crystallizes in a diamond cubic lattice. It is brittle, and has a bright metalhc luster. Ge can absorb H2,02,... 

The materials described below include diamond, cubic BN (the hardest material next to diamond), SrCu02 (from which two types of superconductors have been derived by compositional modification), MgSiOs (a geologically interesting perovskite), and Ge02 (amorphized underpressure at room temperature). 

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. 

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