Structural theories of glass formation

3 or 4. Zachariasen clearly states that this requirement is empirical and is based solely on the lack of knowledge of any glasses in which the coordination number of the network cation is neither 3 nor 4. The formation of a network in which the cations are located as far apart as possible, further requires that the oxygen polyhedra be connected only at the corners and do not share either edges or faces. Finally, he states that the network can only be 3-dimensional if at least three corners of each oxygen polyhedron are shared. 

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. 

---

There is no one structure of glass any more than there is one crystal structure. Almost any solid can be produced in a glassy state if the melt is cooled sufficiently quickly. To some extent, glass can be thought of a product of kinetics, and the structure of a glass can depend on the rate at which the hquid is cooled. Theories of glass stracture and formation must consider this (see also Section 6.3). 

The discussion of the large- tail in S(q) in Section 7.4.1.1, which is characteristic for a short-ranged attraction, enables one to formulate a simplified theory of bond formation within MCT with the result that the long-time limit of the dynamic structure factor is controlled by a single interaction parameter, F = fP-(p/b. Bond formation occurs at T, = 3.02... [34]. For small values of F, the dynamic structure factor decays to zero for all wavevectors. Physically, this means that concentration fluctuations decay into equilibrium at long times, just as expected for a colloidal fluid. However, for F > F, the solutions yield a nonzero glass form factor, namely, the system arrests in a metastable state. This simple result requires the approximate expression for S(q) given above and needs to be replaced by a full numerical solution whenever this approximation fails. 

We have carrried out an analysis of the multilevel structure of the tunneling centers that goes beyond a semiclassical picture of the formation of those centers at the glass transition, which was primarily employed in this chapter. These effects exhibit themselves in a deviation of the heat capacity and conductivity from the nearly linear and quadratic laws, respectively, that are predicted by the semiclassical theory. 

---