Nearest-neighbor bond network

Figure 1. Scheme of the formation of B — B bonds in binary metal borides B(0), borides with isolated B atoms 1b(2), borides with one-dimensional infinite B chains, each B atom having two nearest-B-neighbor atoms iB(3), borides with infinite two-dimensional B nets (three B neighbors for each B atom) formation of a three-dimensional B network (more than three nearest-neighbor B atoms for each B atom). 

In random bond percolation, which is most widely used to describe gelation, monomers, occupy sites of a periodic lattice. The network formation is simulated by the formation of bonds (with a certain probability, p) between nearest neighbors of lattice sites, Fig. 7b. Since these bonds are randomly placed between the lattice nodes, intramolecular reactions are allowed. Other types of percolation are, for example, random site percolation (sites on a regular lattice are randomly occupied with a probability p) or random random percolation (also known as continuum percolation the sites do not form a periodic lattice but are distributed randomly throughout the percolation space). While the... 

All BaCvN nanotubes are made of a hexagonal network of sp2 bonded atoms, with three nearest neighbors to each atom (15, 55, 69, 78, 79). In the case of BC2N nanotubes, two different arrangements of the sheet are possible, leading to two isomers with different structures and with distinct electrical properties (78b). 

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

Covalent Solids. These are substances such as graphite, diamond, and quartz in which the atoms are bonded to nearest neighbors by covalent linkages forming a macromolecular, two- or three-dimensional network. Atoms at the surfaces and edges of such crystals may be chemically unsaturated and can thus act as centers for initiating free radical or redox reactions. 

Using a weak definition of the bond, a greater number of hydrogen bonds than the natural is obtained, and the quantity tends to the number of nearest neighbors of a molecule. This is only sli tly dependent on temperature." Statistical data have been reported recently" for the H-bond network obtained at 2S°C using various different potentials and a weak definition of the bond = —2.25 kcal/mol). The values obtained from computer simulation data with different potentials are listed in Table I. 

The randomizaton takes place by a a diffusion of atoms that is implicit in our earlier description of the initial randomization process as being akin to melting [1]. Later it was shown that the root-mean-square displacement of each atom must be of the order of the nearest-neighbor distance in order that the network lose all memory of the original crystal structure as measured by the structure factor S q) [21]. In this context, the melting point can be defined as that temperature for which the mean square displacement increases linearly with time. It appears, though, that a sequence of bond switches as illustrated in Fig. 1 is not the primary mechanism for self-diffusion in silicon [31,32]... 

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