with reference to the structure of a 2‐D A2O3 oxide glass (Figure 2), where the local structure is very well defined in terms of rigid triangular AO3 units within which there is almost no variation in the bond lengths and angles. The way in which the units connect together to form a noncrystalline structure is described by a set of rules for glass formation, postulated by Zachariasen:
1 An oxygen atom (O) is not linked to more than two network‐forming cations (A).
2 The coordination number, nAO, of oxygen around the network‐forming cations must be small, i.e. 3 or 4 (where the coordination number of an atom simply means the number of other atoms that are within a certain distance from it).
3 The oxygen polyhedra should share corners with each other, not edges or faces.
4 For a three‐dimensional network, at least three corners of each polyhedron must be shared.
For the 2‐D illustration of Figure 2, the coordination number for the triangular AO3 units is three, thus satisfying the second rule. Two AO3 units are connected to each other by the sharing of a common oxygen atom, so that the first rule is satisfied. The third rule is also satisfied, since each pair of connected units shares only one common oxygen, not two (edge‐sharing), or three (face‐sharing). Even though this example is a 2‐D structure, it also satisfies the fourth rule, since the AO3 units are three‐connected. In fact, it is well established that real glasses such as B2O3 [3] and As2O3 [4] can form three‐dimensional structures based on three‐connected structural units.
Figure 2 Two‐dimensional representation of a random network for a composition A2O3 [1]. Small dark spheres: A atoms; large light spheres: oxygens.
It should be emphasized that the random nature of the structure does not arise from disorder within the basic structural units because the distributions of bond lengths and bond angles within them can be very narrow, as in a crystal structure. Instead, there is a wide distribution of bond angles (e.g. A–Ô–A in Figure 2) leading to a distribution in sizes and shapes of the rings formed by the connections between the AO3 units. The noncrystalline nature of the structure arises from this wide distribution of bond angles.
As will become clear later, not all real network glasses obey all of Zachariasen's rules. Nevertheless, these rules provide a basic philosophical framework and a valuable starting point from which the structure of real glasses can be described.
A comparison of the crystalline structure of Figure 1 with the random network of Figure 2 shows the similarity and difference between the two. Both types of structure have short‐range order (SRO) when distances similar to the bond lengths are considered. In fact, SRO arises naturally from the finite sizes of atoms and their mutual bonding so that it exists in all condensed phases, be they liquid, glassy, or crystalline. The fundamental difference is that only crystals exhibit long‐range order (LRO), extending over distances that are large compared to interatomic spacings (Figure 1), whereas glasses (Figure 2) and liquids are by definition isotropic because their structure is on average the same in any direction.
3 Silica – The Archetypal Glass
Vitreous silica, v‐SiO2, is the archetypal example of an oxide glass. Its basic structural unit is a highly regular tetrahedron, with a silicon atom at the center and an oxygen atom at each of the four vertices, which is denoted as SiO4/2 because each oxygen is bonded to two different silicons. The Si─O bonds are all very close in length to 1.608 Å [5], and the O─
Figure 3 Connection of two corner‐sharing SiO4/2 tetrahedra by a bridging oxygen, defining the Si─Ô─Si bond angle, θ, at the bridging oxygen, and the torsion (or dihedral) angles for the two tetrahedra, δ1 and δ2. Small dark spheres: silicons; large light spheres: oxygens. Shortest interatomic distances indicated by dashed arrows.
Initially, it was not clearly established whether a CRN constructed in this way could indeed fill three‐dimensional space without the development of strains or the eventual breaking of bonds. An important step thus occurred in the 1960s when the construction of large ball‐and‐stick models showed that it is indeed possible to build a large tetrahedral network that is both continuous and random. The most influential was constructed by Bell and Dean [6] for silica with a total of 614 atoms (Figure 4), which appeared to form a three‐dimensional CRN structure through the sharing of oxygen bridges between SiO4/2 tetrahedra (Figure 4, inset). Ball‐and‐stick methods of modeling the atomic structure of glasses are rarely used nowadays, and computer‐based methods are extensively used, for example, Monte Carlo, molecular dynamics (MD), or reverse Monte Carlo (RMC) simulations (Chapter 2.8, [7]).
Experimentally, evidence for a random SiO2 network is provided by the diffraction patterns measured by both XRD [2, 8] and ND [5, 9], which has some advantages over XRD for the study of disordered materials (Chapter 2.2). Whereas the peaks observed in the diffraction patterns of crystals are sharp, those for glasses are broad (Figure 5a). These patterns are conventionally displayed as a function of momentum transfer, Q, otherwise known as the magnitude of the scattering vector. A standard analysis [10] is to obtain a correlation function from a suitable Fourier sine transform of the experimental data from reciprocal to real space (
