Planar nets

Anti-MoSj Pt.jB No Trigonal prism Defect planar net... 

Planar nets of five-and seven-membered B rings trigonal prism... 

Other ideas found useful in describing complex crystal structures are planar nets and rod packing. The idea of planar nets, which has been explored at length by O Keeffe Hyde (1980), is to regard complex crystal structures as stackings of two-dimensional... 

Figure 16.5. A hexagonal planar net is generated by the fundamental translations a1 a2 (each of length a) and a12 — 2n/3. To generate a space lattice with three-fold rotational symmetry, the second and third layers must be translated so that Pi lies over the points marked P2 and P3, respectively, that is at (1/3 2/3 1/3) and (2/3 1/3 2/3). If using hexagonal coordinates a3 is normal to the plane of a1 a2 and lies along e3, so that this unit cell (3R) contains three lattice points (Figure 16.4).

Equations (21) and (23) showthat M is invariant under C3Z and C2x- Therefore the compatible point groups are those that contain a proper or improper three-fold axis, with or without proper or improper two-fold axes normal to the principal axis. These point groups are 3,3,32, 3m, 3m (or C3, S6, D3, C3v, D3d). To generate a 3-D lattice with three-fold rotational symmetry, the second and third layers of the hexagonal planar net in Figure 16.5 must be translated so that Pj lies over P2 and P3, respectively, i.e. at (i/3 2/3 y3) and (2/3 /3 2/3). 

The one form of tellurium is silvery-white, semimetallic, and isomorphous with grey Se. Like the latter it is virtually insoluble in all liquids except those with which it reacts. Even though Te8 rings are not found in elemental tellurium, they do occur in the compound C Te, 5 which also contains unusual planar nets of Te atoms. 

Rafts, that is, large, triangulated, planar nets. Thus far this sort of structure has been found only for some osmium species. 

The gross structure of collagen in many tissues, for example tendons, involves wave-like curved fibrils, which provide elasticity. This sort of curvature occurs also when fibrils in two directions are linked into a planar net. A highly ordered collagen structure is fovmd in the so-called "decemats membrane", which is the basement membrane of corneal endothelial cells. Stacks of hexagonal lattices have been observed which are parallel to the basement membrane [17]. 

Smith has already described the zeolite frameworks in terms of 3-connected 2-D nets.[15] The 3-D framework is formed by the addition of a fourth bond to each node of the planar net. The nature of the inter-sheet bonding is automatically defined by the stacking operator, with bonds being formed between nodes within the Si—O—Si-allowed bonding distance. 

INFINITE PLANAR NETS OF sp2-HYBRIDIZED CARBON ATOMS... 

Two other semiregular nets examined in 1968 [1] and 1994 [8 were [3, 9 and (4, 6, 12 with resonance energies per electron -0.007 and -0.0744 eV, respectively. Other 3-connected planar nets, but without regular polygons, were analyzed. From... 

For icosahedral symmetry, the whole net is completely specified by one lattice vector, i.e, by an ordered pair of integers a, ft). The atom count of the fullerene is proportional to the area of the planar net, and so it is easily shown that at least one icosahedral fullerene C exists for... 

For linear chains d = 1, for planar nets 2, and for three-dimensional stackings d = 3. The parameter d can also be a noninteger in solids that have a special microstructure. 

Lee, E. Jeong, Y.-H. Kim, J.-K. Lee, M. Controlled self-assembly of asymmetric dumbbeU-shaped rod amphiphiles transition from toroids to planar Nets. Macrvmolecules 2007,40, 8355-8360. 

Figure 12 Honeycomb networks in BTC (a) puckered net in pure BTC, llA, and (b) planar net in BTC crystals with small guest molecules such as halogens or alkanes, IIB (guest molecules omitted).

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