Zachariasen model

Figure 7.10. (a) Zachariasen s two-dimensional model of an AiOj glass, after Zachariasen (1932). (b) Two-dimensional representation of a sodium silicate glass,... 

This parabolic trend can be surmised from Eq. (15), where the occupation numbers n are proportional to Z (the parabola should have a minimum at Cm, i.e. or the half-filling of the 5f shell). The same parabolic trend exists in d-transition metals, and is explained in Friedel s model in a similar way. This fact had seemed to early theorists (see, in Chap. A, the discussion of Zachariasen s model) to suggest that the actinides were 6 d-transition metals. In reality, it means that the light actinides are 5f-transition metals, with the 5 f wavefunctions playing the role of d-wavefunc-tions. 

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 ... 

Figure 1.43 Zachariasen s random network model for AjBj glass.

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. 

The broad approach used by Zachariasen in the network model of liquid silicates is to break down the network present in the pure fused nonmetallic oxide thus... 

Further the Zachariasen requirement that energy difference between crystalline and amorphous phases of a glass forming oxide should not be very high, has also been proved to be incorrect. In the case of the archetypal Si02 glass, cm model (Figure 2.06) has been found to be... 

We need to note that the phenomenon that Zachariasen indicates could perfectly well come from not including appropriate terms for systematic error in the model fitted. Since it is important to understand why this is so, we will illustrate something of what can happen. 

J.F. Shackelford and B.D. Brown, Triangle rafts - extended Zachariasen schematics for structure modeling, J. Non-Cryst. Solids, 49, 19-28 (1982). 

Space models of these alcohols shows immediately how important must be the steric influences on the association processes. One can see how difficult it is for molecules such as pentamethylethanol to form linear hydro-gen-bonded chains of the Zachariasen type. The alkyl groups of alternate molecules can be seen to be close together if no bending occurs in the hydrogen bond chain, and when alkyl substitution occurs in the a position, there is certain to be some hindrance to free rotation around the —C—O— bond. Accordingly, from the lack of a multimer band in the infrared spectrum and the linearity of the curve of NMR chemical shift vs. concentration out to 0.35M we can presume that only dimers are formed initially in pentamethylethanol, with possibly cyclic multimers at higher concentrations. 

A number of other statements by Zachariasen have become the basis for the models for glass structures termed the Random Network Theory. These ideas will be discussed later under the topic of glass structure. It is interesting to note, however, that the term random network does not occur in the original work of Zachariasen, who referred to the glass structure as a vitreous network . Furthermore, Zachariasen specifically states that the vitreous network is not entirely random due to the restriction of a minimum value for the internuclear distances. As a result, all internuclear distances are not equally probable, and X-ray patterns of the type observed for glasses are a natural consequence of the vitreous network. 

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