Figure 5 The strong contrast between the potential energy changes induced by variations of Si–O distances and S–O–Si angles indicated by the calculated surfaces of constant energy of H6Si2O7 clusters.
Source: After [23].
2 Some Basic Concepts of Glass Science
2.1 From Metastability to Relaxation
The silica issue illustrates how answers to apparently simple problems can require in‐depth analyses for which theoretical concepts presented in various chapters of the Encyclopedia should prove useful. To help readers whose knowledge of the glassy state is minimal, however, the rest of this introduction will be devoted to a brief presentation of some basic concepts pertaining to glass and nonequilibrium systems, which will thus not need to be commented upon in specific chapters.
In preamble, it would be useful to define precisely what a glass is before discussing any of its properties. In accordance with its intrinsically disordered nature, however, glass might be pleasantly defined as a material that is difficult to define in an unambiguous or fully consistent manner. In Chapter 10.11, a glass is nonetheless defined as a macroscopically homogeneous amorphous solid whose properties (physical, chemical, or structural) vary with its preparation conditions. Usual definitions differ depending on whether the emphasis is put on the disordered atomic structure of the material or on the existence of a glass transition separating a solid material at lower temperature from a supercooled liquid at higher temperatures. Because glass structures depend on the type of system considered, they are described in widely different ways for oxides, metals, or organic polymers so that they do not lend themselves to a brief, general presentation.
Although a glass transition cannot always be observed, its phenomenology and its implications on glass properties are in contrast common not only to all glass‐forming liquids, but also to partially disordered systems such as plastic crystals. In view of their dual practical and theoretical importance, the main features of the glass transition will thus be summarized here in a qualitative way. Without making any reference to recent advances in the field, the purpose is simply to describe the phenomenology of vitrification and its effects on physical properties, to introduce some of the groundbreaking concepts that have been proposed to account for them, and to highlight some simplifying features thanks to which intrinsically complex glass problems become more tractable.
A main source of difficulty is that the time parameter must be considered because of the kinetic nature of the glass transition. In the backdrop is the way in which the Gibbs free energy of a glass‐forming liquid would be minimized under given experimental conditions and, thus, the kinetics at which physical properties relax after changes in intensive thermodynamic variables (Chapter 3.7). The largest and most rapid decrease of the Gibbs free energy would of course be ensured by crystallization. To bypass it, it has been known from time immemorial that a melt must be cooled rapidly enough. Other things being equal, vitrification is favored by large freezing‐point depressions near eutectic compositions, which result in increased viscosities and reduced thermodynamic driving forces for crystallization.
With very few exceptions (e.g. [25]), however, supercooled liquids do crystallize more or less rapidly upon prolonged annealing. Perhaps also influenced by the early twentieth‐century conception that glasses were supercooled liquids (Chapter 10.11), a commonly held assumption is that any glass would eventually crystallize. This assumption is in fact plainly contradicted by the 4.6‐billion year old glasses found in meteorites (Chapter 7.1). What has ensured their long‐term preservation has been the extremely dry conditions of extraterrestrial space, which have prevented them from weathering. Since their SiO2‐poor compositions would make them prime candidates for ready devitrification, the almost infinite metastability enjoyed by these glasses is especially significant. The crystallization issue will thus be left aside in the following.
2.2 Relaxation: Phenomenological Aspects
Atomic mobility is the hallmark of the molten state as illustrated by the ready flow of a liquid adjusting to the shape of its container. Contrary to crystals where atomic positions are fixed and strongly constrained by long‐range symmetry, liquids are characterized by dynamic disorder, i.e. by unceasing atomic rearrangements. This structural incompatibility between a crystal and a liquid makes any progressive transformation of one phase into the other impossible. In contrast, the vitrification of liquids is clearly a continuous process during which disordered structures become frozen in as revealed by progressively increasing viscosities, which eventually becomes so high that the materials have mechanically become a solid.
At high temperatures, the liquid is in internal thermodynamic equilibrium because its properties are time independent and uniquely determined by two intensive variables, usually taken to be pressure and temperature. At high viscosities, however, this simplicity no longer holds true as seen if one exerts a stress on the liquid at constant temperature or change the temperature at constant stress (Figure 6a). For a window glass [26], a constant, equilibrium shear viscosity is, for example, reached more rapidly in the former case than in the latter but this difference does not need to be commented upon here because pressure and temperature changes are of a different nature. Of greater importance is that Boltzmann superposition principle (Chapter 10.11) applies because, if both perturbations are simultaneously exerted, the response of the system is the sum of the two individual responses (Figure 6a).
Figure 6 Viscosity relaxation of window glass
(Source: Data from [26]).
(a) Time dependence of the viscosity at 788 K after: (1) application of a 110 MPa stress; (2) a temperature change from 819 to 788 K with this stress; (3) exerting simultaneously these stress and temperature changes. (b) Attainment of the equilibrium viscosity; sample equilibrated at 795 K, then quickly brought for equilibration at 788 K and at 777 K (open symbols) before following the same procedure for reversing the equilibrium values first measured at 788 and 795 K (open symbols).
In practice, temperature changes matter most. When high viscosities are measured at successively lower temperatures and then at higher temperatures (Figure 6b), two conclusions follow: (i) the time needed to reach the constant equilibrium values increases tremendously