Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
1 Introduction
What is a glass from a structural standpoint? There are different answers dependent upon whether the emphasis is on structure, preparation methods, or thermodynamic properties. However, a simple structural definition is adopted here, according to which a material must be solid and have a noncrystalline structure to be called a glass.
Put simply, the description of a crystal involves a unit cell, containing a particular arrangement of atoms, which is then replicated periodically in three dimensions to build up the structure as illustrated by the 2‐D (two dimensional) representation of Figure 1. Crystal structures have translational symmetry because, if crystallite boundaries are neglected, the environment of a particular atom is the same as that of all equivalent atoms in all unit cells. Contrastingly, a glass lacks translational symmetry and a detailed understanding of its structure requires as much experimental information as possible. In addition to X‐ray (XRD) and neutron (ND) diffraction, inelastic neutron scattering and various other spectroscopies (X‐ray absorption, infrared, Brillouin, Mössbauer, and X‐ray photoelectron spectroscopies) may be used (Chapter 2.1), along with electron microscopy, physical property data (especially density), and theoretical modeling.
As is clear to any reader of this Encyclopedia, many types of materials can vitrify if they are solidified rapidly enough to avoid crystallization. Leaving aside metallic glasses (Chapter 7.10) or organic polymers (Chapters 8.7 and 8.8), however, the majority of useful glassy materials are formed by oxides or chalcogenides. This is the reason why this chapter is restricted to these materials and to the elementary concepts that are used to describe their structure.
These structures can be understood well in terms of the continuous random network (CRN) model, first propounded by Zachariasen [1], because the atomic bonds have some covalent (directional) character. The basic features of this model will thus be reviewed and related to fundamental structural information gathered for silica glass, the archetypal glass former, and the “mother” of all amorphous silicates. Because microcrystalline descriptions of glass structures in fact preceded Zachariasen's model, their basic limitations will also be summarized. The structural changes induced by the addition of so‐called network modifiers in oxide glasses will then be discussed at short‐ and medium‐length scales, along with the intermediate character of some oxides that may act as glass formers only when combined with some modifiers. Finally, the manner in which network glasses can depart from Zachariasen's model will be illustrated with chalcogenides.
List of Acronyms
2‐Dtwo dimensionalBObridging oxygenCRNcontinuous random networkFSDPfirst sharp diffraction peakIROintermediate‐range orderLROlong‐range orderMDmolecular dynamicsMRNmodified random networkMROmedium‐range orderNBOnon‐bridging oxygenNDneutron diffractionNMRnuclear magnetic resonanceRMCreverse Monte CarloSROshort‐range orderv‐SiO2 vitreous SiO2XRDX‐ray diffraction
Figure 1 Two‐dimensional representation of a crystal structure for a composition A2O3. Small dark spheres: A atoms; large light spheres: oxygens. Unit cell delineated by thick, dashed lines.
2 The Zachariasen–Warren Random Network Model
The structure of oxide and chalcogenide glasses is usually described by the Zachariasen–Warren random network model, thus termed because it was proposed by Zachariasen [1] in 1932 and subsequently supported by early XRD studies of glass structure made by Warren and coworkers (Chapter 10.11, [2]).
This model is easily understood 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),