Continuous random network

The stmcture of vitreous siUca is a continuous random network of SiO tetrahedra, linked through the sharing of corners. It differs from crystalline sihca ia having a broader distribution of Si—O—Si bond angles and a more random distribution of one tetrahedron with respect to another (44). The density is 2.2 g/cm. ... 

The first theory of the structure of glass to become widely accepted was that of Zachariasen (1932), called the random network theory [now commonly referred to as the continuous random network (CRN) theory]. This arose... 

Fig. 42 a. Continuous random network predictions for IR and Raman absorption in Si(as) and experimental data (from Prof. R. Alben)... 

Alben and Boutron suggest that the peak in the X-ray and neutron scattering functions at 1.7 A-1 is indicative of an anisotropic layer structure extending over at least 15 A in Polk type continuous random network models. To show this better Fig. 52 displays the radial distribution function of the Alben-Boutron modified... 

Fig. 50. Continuous random network fit to the X-ray diffraction pattern of H20(as) (from Ref. 82>). Experimental data and X Theory---...

Finally, we remark that the few thermodynamic data available are consistent with a simple continuous random network structure for high temperature H20(as). 

If the different continuous random network models of high and low temperature H20(as) are valid, the following tests are worthy of attention ... 

Clearly, any measurement that differentiates between the properties of high and low temperature forms of H20(as), and/or delineates the relationship between H20(as) and liquid H20, can be used to test the hypotheses advanced vis a vis their structures. These and the experimental tests suggested, together with the construction of continuous random network models more sophisticated than that for Ge(as), the increased use of computer simulation, and exploitation of the available experimental information to guide the choice of appproximations in a statistical mechanical theory should increase our understanding of H20(as) and, uitimately, liquid H20. 

One of the early models to describe the amorphous state was by Zachariasen (1932), who proposed the continuous random network model for covalent inorganic glasses. We are now able to distinguish three types of continuous random models ... 

Continuous random network (applicable to covalent glasses)... 

The short range order and long range disorder lead to the model of the continuous random network, introduced by Zachariasen (1932) to describe glasses such as silica. The periodic crystalline structure is replaced by a random network in which each atom has a specific number of bonds to its immediate neighbors (the coordination). Fig. 

A real crystal contains defects such as vacancies, interstitials and dislocations. The continuous random network may also contain defects, but the definition of a defect has to be modified. Any atom... 

Fig. 1.3. An example of a continuous random network containing atoms of different bonding coordination, as indicated.

The major source of the disorder energy is the bond strain within the random network. Phillips (1979) proposed a model to explain the relation between network coordination and disorder. A four-fold continuous random network is overcoordinated, in the sense that there are too many bonding constraints compared to the number of degrees of freedom. The constraints are attributed to the bond stretching and bending forces, so that for a network of coordination Z , their number, NciZJ is. 

This latter result should put to rest the once-expressed idea that distortions in a continuous random network model would increase as the size of the model is increased, leading eventually to such a build-up in strain as to limit the size of the model. Of course, for a hand-built model, there may well be a limit to the size. There is no way to return to the interior of a hand-built model to make rearrangements that would reduce the strain for surface atoms. 

Figure 2.06 Continuous random network model simulating the structure of amorphous Si02 (After Bell and Dean, 1966).

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