Planar networks/lattices

Figure 8-27 shows three planar networks based on the same plane lattice. Two and only two lines intersect in each point of all three networks. Accordingly, the parallelograms of all three networks have the same area. All of them are unit cells, in fact, primitive cells. Each of these parallelograms is determined by two sides a and b, and the angle y between them. These are called the cell parameters. 

To proceed, consider two finite planar networks, a regular Euclidean triangular lattice (interior valence v — 6, but with boundary defect sites of valence v = A and v = 2) of dimension d — 2, and a fractal lattice... 

The diamond lattice (Figure 3a) contains tetrahedral carbon atoms in an infinite three-dimensional network. Graphite is also an infinite three-dimensional network, but it is made up of planar offset layers of trigonal carbons forming fused hexagonal rings (Figure 3b). The C-C bonds within... 

The closed but boundless network of hexagons embedded as an all-hexagon toroidal polyhex can be represented by an infinite planar lattice, on which the set of hexagons forms a parallelogram which repeats itself endlessly in two dimensions (i.e., it is doubly periodic). Figure 14 shows an example of a torus with nine hexagons (A-I). 

The PtS lattice contains both the square-planar (Pt) and tetrahedral (S) centres. A square-planar Pt complex Pt(CN)4, when interconnected with tetrahedral Cu centres (CN CuO, affords an infinite network similar to the PtS structure [40]. Tetra(4-pyridyl)- (3 X=N and M = Cu 0 and tetra(4-cyanophenyl) porphyrin (3 X=C-CN and M = Cu O provide a huge square-planar site. They are also assembled with Cu (CUBF4) to give a similar structure 14 having porphyrin-walled channels in the two directions shown by the arrows (Fig. 2) [25]. 

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