3.4). Of direct practical interest, the densities of glasses and melts and their temperature and pressure derivatives are then reviewed by M. Toplis who also presents empirical models predicting these properties as a function of chemical composition (Chapter 3.5). A similar approach is followed by P. Richet and D. de Ligny in the next chapter, which is mainly devoted to heat capacity and entropy from near 0 K to superliquidus temperatures: at lower temperatures, the properties of glasses are exclusively vibrational and mainly determined by the oxygen coordination of cations, whereas the picture is markedly more complicated above the glass transition by configurational contributions to the properties of liquids, whose nature remains largely elusive (Chapter 3.6).
After these overviews of key physical properties, the ground is ready for a thorough discussion of relaxation processes. Relying mainly on calorimetric measurements, U. Fotheringham describes how the concept of fictive temperature can be incorporated into various relaxation models to predict accurately features of great practical interest such as thermal shrinkage and index of refraction changes as a function of time and temperature (Chapter 3.7). Because of extreme metastability, a special case of relaxation is that of glasses quenched at rates of the order of 106 K/min. As revealed by calorimetric experiments examined by Y. Yue, these hyperquenched glasses do show unusual features related to structural heterogeneities and to the existence of fragile‐to‐strong rheological transitions in glass‐forming systems (Chapter 3.8).
The existence of polyamorphism, i.e. transitions from one amorphous phase to another, has recently been an unexpected discovery because the structure and properties of glasses were instead thought to vary continuously as a function of the quench temperature and pressure. As reviewed by P. McMillan and M. Wilding, these abrupt phase changes akin to first‐order transitions in crystals have been extensively investigated and their origin accounted for in terms of the topology of configurational‐energy landscapes (Chapter 3.9). Amorphous phases can also be prepared by high‐pressure compression of crystals that undergo structural collapse when their elastic limits are exceeded. As explained again in terms of configurational‐energy landscape by P. McMillan, D. Machon, and M. Wilding, the similarity of these phases with the dense polyamorphs formed at high pressures is not fortuitous (Chapter 3.10).
From the standpoint of mechanical stability, amorphous phases display a much greater variety of compression mechanisms than crystals, thanks to the lack of structural constraints imposed by the symmetry of a crystal lattice. In addition, the intrinsic strength 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 Tg (Chapter 3.2). Under typical cooling rates of the order of 10 K/s, the standard Tg 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, Tg is always significantly lower than the melting (or liquidus) temperature Tm. It can be roughly estimated with the Kauzmann formula Tg ≈ 2Tm/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
