Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов

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 SiO_4/2 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──O bond angles are all very close to the ideal tetrahedral value of 109.47°. Because SiO_4/2 tetrahedra are connected together by the sharing of a bridging oxygen (BO) atom (Figure 3), the Si─O─Si bridge is characterized by three angles: the Si─Ô─Si bond angle, θ, and the two torsion (dihedral) angles, δ₁ and δ₂. There is a broad distribution of bond angles (centered at ~144°), but little or no preference for any particular value of the torsion angle. Hence, the tetrahedra connect together to form a network that is both continuous (i.e. it can fill all of three‐dimensional space without a break in the continuity of the network) and random (i.e. it is not periodically repeating and, thus, not crystalline). This is why a structure of this type is often called a CRN.

Figure 3 Connection of two corner‐sharing SiO_4/2 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 SiO_4/2 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 (Figure 5b). The result essentially shows the distribution of interatomic distances in the measured sample, each of its peaks corresponding to a commonly occurring interatomic distance. For v‐SiO₂, the first two peaks in the correlation function arise from the Si─O bond length and the O─O distance within SiO_4/2 tetrahedra, respectively. Since these peaks are as sharp as for α‐quartz, both distances are as well defined in the glass as in the crystal. Within the limits of what is achievable experimentally, the Si─O and O─O coordination numbers determined from the areas of these peaks are essentially four and six, as expected for a fully connected CRN of SiO_4/2 tetrahedra (Figure 3).

Figure 4 Ball‐and‐stick model constructed by Bell and Dean for SiO₂ glass [6]. Upper part: complete 614‐atom model; lower part: small portion with higher magnification. Small dark spheres: silicons; large light spheres: oxygens.

Figure 5 Diffraction results for α‐quartz and v‐SiO₂. (a) Neutron diffraction measurements of their distinct scattering [9] compared with the X‐ray diffraction data for v‐SiO₂ [8]. Position of the first sharp diffraction peak indicated at Q₁ ≈ 1.52 Å⁻¹. (b) Neutron correlation function for α‐quartz and v‐SiO₂, and X‐ray correlation function for v‐SiO₂. Approximate positions of the short distances for a pair of connected tetrahedra indicated as (Si─O)₁, and so on (same notation as in Figure 3).

Because of LRO, there are further sharp peaks at longer distances in the correlation function of a crystal (Figure 5b). In contrast, these features rapidly become less well defined for a glass so that it becomes harder to determine structural information involving longer correlation lengths. For instance, the third peak in the function of v‐SiO₂ arises from the two silicon atoms in a connected pair of SiO_4/2 tetrahedra. This peak is broadened due to variations in the angle θ (Figure 3), which lead to the random nature of the structure. The distribution of Si─Ô─Si bond angles, θ, has been extensively investigated. From fits made to their X‐ray correlation function, Mozzi and Warren [11], for instance, found a most probable bond angle of 144° with an average value of 147.9° and a standard deviation of 12.7° (Figure 6). In a recent nuclear magnetic resonance (NMR) study, a narrower distribution was deduced with values of 147.1 and 11.2°, respectively [12].