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

of glasses should in principle be limited only by that of interatomic bonds since it is not reduced by grain boundaries. As explained by R. Hand, however, the actual strength is hundred times smaller because of the existence of surface flaws where the accumulation of stresses triggers breakage; whereas the abundance of flaws increases with time and their effects have to be treated statistically, their creation can be limited in various ways (Chapter 3.11). Strategies for strengthening glass are described in more detail by S. Karlsson and L. Wondraczek; in addition to elimination of flaws by mechanical polishing or flame finishing, these involve the creation of compressive stresses at the glass surfaces by either physical or chemical means, i.e. tempering by rapid, homogenous cooling (Figure 1) or exchange of smaller by bigger ions, e.g. replacement of Na⁺ by K⁺ (Chapter 3.12). Irradiation by energetic photons or subatomic particles is another source of defects reviewed by N. Ollier, S. Girard, and S. Peuget who describe their effects on optical and mechanical properties and the ways in which these can be reduced (Chapter 3.13).

The last chapter is devoted to the special case of amorphous ices, which have recently received much attention not so much because of their cosmochemical importance, but because they are prime illustrations of polyamorphism. Their formation and properties are thus reviewed by R. Tournier who goes into the details of a thermodynamic model of nucleation and growth originally designed for crystals – including numerical applications – to account for the formation of these amorphous ices and, in addition, to throw valuable light on the general problem of the glass transition in terms of transformations between supercooled liquids of different densities (Chapter 3.14).

3.1 Glass Formation

       Michael I. Ojovan

       Department of Materials, Imperial College London, London, UK

1 Introduction

      Glasses can be formed by various methods, including physical vapor deposition, solid‐state reactions, thermochemical and mechanochemical treatments, or liquid‐state reactions with sol–gel techniques (Chapter 8.1). Amorphous solids can also be prepared under the action of high pressure (Chapter 3.10) or by irradiation of crystals (Chapter 3.13). In industry or in Nature (Chapters 7.1 and 7.2), however, vitrification most frequently relies on the extremely strong viscosity increases when melts are cooled until the glass transition eventually takes place before nucleation and crystal growth have developed (Chapter 5.4). The topic dealt with in this chapter will thus be glass formation by melt cooling.

      In a first approximation, the glass transition is conveniently characterized by a single parameter, the glass transition temperature T_g (Chapter 3.2). Under typical cooling rates of the order of 10 K/s, the standard T_g is the temperature at which the viscosity is about 10¹² Pa.s (10¹³ P) at the macroscopic observational timescales of 10²–10³ seconds that are relevant to actual glass formation. As defined in this way, T_g is always significantly lower than the melting (or liquidus) temperature T_m. It can be roughly estimated with the Kauzmann formula T_g ≈ 2T_m/3 [1].

      In principle, any liquid vitrifies if the melt is cooled sufficiently fast to prevent crystallization from happening. This is by definition the case of the vast bulk of commercially used glasses, which are made up of oxides. In glass technology, SiO₂, GeO₂, B₂O₃, and P₂O₅ are archetypal glass formers in that they easily form glass networks by themselves or in combination with other oxides. But in practice it is not obvious to predict which materials readily vitrify and under what conditions they do so. As a matter of fact, the high viscosities that favor vitrification are related to structural factors whereas configurational complexity also contributes to frustrate crystallization. Here, particular attention will thus be paid not only to the kinetics of vitrification and its theoretical aspects but also to these factors.

      In preamble, however, it is useful to examine the way in which glass is defined because of the possibly surprising fact that there is no generally accepted definition of this state of matter. Likewise, a few fundamental points will be summarized about relaxation, the process by which the structure and properties of an amorphous substance tend to reach their equilibrium values to vanish below the glass transition (Chapter 3.7).

      Acronyms

BObridging oxygenCCRcritical cooling rateCNcoordination numberCPTconfiguron percolation theoryDSCdifferential scanning calorimetryDTAdifferential thermal analysisICGInternational Commission on GlassIUPACInternational Union of Pure and Applied ChemistryNBOnon‐bridging oxygenTTTtime temperature transformation

2 Glass and Relaxation

      According to the International Commission on Glass (ICG, Chapter 9.11), a glass is a homogeneous amorphous solid material produced when a viscous molten material is cooled rapidly enough through the glass transition range without leaving sufficient time for the formation of a regular crystal lattice. As for the International Union of Pure and Applied Chemistry (IUPAC), its Compendium of Chemical Terminology puts instead the emphasis on the process through which a glass is produced by defining it as a second‐order transition taking place upon cooling of a supercooled melt [2]. Additionally, IUPAC states that below T_g the physical properties of glasses vary in a manner like those of crystalline phases.

      Of more serious consequences that this divergence is the fact that the nature of the glass transition is not yet well understood in spite of its fundamental importance (Chapter 3.3). One reason is the almost undetectable structural differences noted between the supercooled liquid and glass phases, which contrast with the marked changes observed in mechanical and other physical properties associated with the extremely large changes in the timescale of relaxation processes at T_g and below.

      Specifically, a glass has a topologically disordered distribution of atoms or molecules, like a liquid, but it has also the elastic properties of an isotropic solid. Moreover, the translation‐rotation symmetry at T_g is unchanged as the glass retains the topological disorder of the fluid from which it formed. This symmetry similarity of both liquid and glassy phases generally leaves unexplained the basic differences observed between their properties. An exception is the qualitative difference that has been demonstrated in the symmetries of liquid and glasses in terms of Hausdorff dimensionality for the system of bonds which shows a stepwise change exactly at T_g [3]. The reason is that broken bonds in glasses are present as point defects, thus forming a set of zero‐Hausdorff dimensionality, whereas in liquids just above the T_g they are associated in macroscopic percolating clusters that form sets characterized by the Hausdorff dimensionality ≈2.5 [3].

      Although glasses are metastable materials with respect to isochemical crystals, their transformation to a thermodynamically stable crystalline structure is kinetically impeded. The metastability of silicate glasses commonly