Interpenetration of Nets

In this article we shall use the term e-fold interpenetration to describe systems with z independent nets - Zn(CN)2 therefore displays 2-fold interpenetration. 

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Figure 18 Interpenetration of nets of different dimensions (a) 1D/2D inclined interpenetration (b) 1D/3D interpenetration (c) 2D/3D interpenetration ...

Fig. 11 (Top) Perspective view of an [Fe]4 rhombus in the [Fe(bpe)2(NCS)2]-CH3OH 2D polymer. (Bottom) Schematic representation of the interpenetration of a layer lying in the plane of the sheet and three orthogonal layers (left). Perspective view of the crossing of two independent net systems defining the rectangular channels (right). Balls and sticks represent iron atoms and bpe ligands, respectively...

All structures in this family contain icosahedra and at least one other coordination type. Frank and Kasper demonstrated that structures formed by the interpenetration of the four polyhedra contain planar or approximately planar layers of atoms primary layers made by tessellation of triangles with hexagons and/or pentagons, and intervening secondary layers of triangles and/or squares. For a classification and coding of the nets and of their stacking, see Pearson (1972) and also Shoemaker and Shoemaker (1969) or Frank and Kasper (1958, 1959). 

The net coulombic attractions of the ions for one another are counterbalanced at their equilibrium separation ro by the short-range repulsions due to interpenetration of the electronic clouds of ions in contact. This short-range repulsion falls off sharply with increasing r. Max Born suggested that it could be represented by B/rn, where B is a constant and n can be estimated from the compressibility of the crystal. As a rule of thumb, for ions having the electron configurations of Ne, Ar, Kr, and Xe, n 7, 9, 10, and 12, respectively,... 

A useful concept in the consideration of framework structures and, in particular, in the consideration of their various modes of interpenetration, is that of a net. A net is a collection of points with some clearly defined connectivity. We shall be concerned with infinite nets and shall refer to the interconnected points as nodes and to the connecting units either as connecting rods or simply as connections or rods. For a fuller account of nets the reader is referred to monographs by Wells [2]. 

Figure 11. The parallel interpenetration of (6,3) nets in the [Cu2(CN) N(CN)2 2r polyanion. Large circles represent Cu, small circles C and N.

A mode of parallel interpenetration of two (4,4) nets topologically different from that in Figure 10 is seen in [Cu(tcm)(bipy)], where bipy is 4,4 -bipyridine [11]. In this case the tern- ligands act as bent 2-connectors, as shown in Figure 12. 

We know of only two examples of parallel 2D interpenetration involving nets other than (6,3) and (4,4). One is Hittorf s phosphorus, in which two 82-10 nets, composed entirely of phosphorus atoms, interpenetrate [15], The other example, considered in the next section, differs from all the other parallel interpenetrating cases in that the composite formed is a three-dimensional interlocked structure. 

Parallel Interpenetration of 2D Nets to Give a 3D Interlocked Composite... 

We classify the modes of interpenetration of 3D nets in terms of the topologies of the individual nets. 

Figure 25. (a) Three interpenetrating (10,3)-b nets with T-shaped 3-connecting nodes in the structure of [Ag(bipy)]N03. Circles represent Ag atoms. Long connections are via bridging bipy units and short connections are direct Ag... Ag interactions, (b) An idealized version of the mode of interpenetration of three (10,3)-b nets, of the type seen in [Ag(bipy)]N03. 

Figure 31. Threefold interpenetration of a-Po-related nets in the structure of Rb[Cd Ag(CN)2 3]. Circles in order of decreasing size represent Cd, Ag, N, and C. Intercalated Rb atoms are omitted for clarity.

Interpenetrating 3D Nets Each Containing Two Types of Nodes with Different Connectivities... 

Figure 37. Schematic representation of the interpenetration of one NbO-like Bi604 net ( open connections) and two independent diamond-like (Ga Sh /s Og nets (one heavy die other fine ) in the structure of BisGaSbOn. Smaller circles represent the centers of (Ga b Oe clusters, larger circles represent the centers of Bi404 cube-like clusters.

Figure 11.25. Parallel interpenetration of two 4.82 nets of ([ Ag(20) C104 , crystal structure...

L= l,2-bis(2-pyrimidinylthio)ethane), the large macrocyclic size leads to the interpenetration of the diamondoid nets and a host-guest arrangement of the ligands within the cycles. 

For a rather complex example of a structure in which there are two interpenetrating ThSi2 nets see neptunite (p. 824). 

Structures based on systems of interpenetrating diamond nets. In the structures we have been describing it is possible to trace a path from any atom in the crystal to any other along bonds of the structure, that is, along C-C bonds in diamond, Si-O-Si bonds in cristobalite, etc. In CU2O (the mineral cuprite) each Cu atom forms two collinear bonds and each 0 atom four tetrahedral bonds, and these atoms are linked together in exactly the same way as the 0 and Si atoms... 

Further examples of structures based on two interpenetrating diamond nets are the anions in the borates LI2B4O7, CsBsOg, and Ag2BgOi 3 (Table 3.14) which are described in Chapter 24. 

This produces a net force for all non-imiform density distributions so that for the bell-shaped distribution in Figure 1.3 there will be a net force of expansion of the chain. When the melt is considered, every chain is surrounded by a chain of the same type, so the concentration is constant in all directions (the dotted line in Figure 1.3). No distinction is drawn between repeat units on the same or different chains. (As noted above, there will be interpenetration of chains in all but dilute solutions.) The result is that there is no gradient in potential and there are no forces of expansion. In effect, the polymer chain in the melt behaves as if the forces of expansion due to excluded volume were screened from each chain and the dimensions are those for the unperturbed chain. 

Fig. 13, Structure of Be(NH j, . The large tetrahedra are made up of the groups shown in l it. 12. The topology is that of two interpenetrating diamond nets...

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