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 Tg 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 Tg 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 Tg 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 Tg [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 Tg 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 produced industrially is not a practical concern as most of them are stable for times much longer than any imaginable timescales of use. In practice, that there is no stress relaxation at room temperatures is indicated by the fact that high permanent internal stresses are preserved in glass articles made more than several millennia ago, and even in billion‐year‐old extraterrestrial glasses (Chapter 7.1).
The reason for this stability is that relaxation processes are controlled by viscosity. The characteristic time τ required to achieve time‐independent parameters can be derived from Maxwell's simple relaxation model, which predicts that τ = η/G, where G is the shear modulus and η the viscosity (Chapter 3.7). The higher the viscosity, the longer the relaxation time. Besides, viscosity changes are thermally activated. Glass‐forming oxides are characterized by high activation energies and very high viscosities under normal conditions. As an extreme example, fused silica has an activation energy for viscous flow of QH of 759 kJ/mol at lower temperatures and a shear modus of about 31 GPa, which implies relaxation times τM as long as 1098 years at room temperature, an immeasurably longer time than even the 14∙109 years lifetime of the universe.
3 Kinetic Theory of Vitrification
As already stated, vitrification on cooling is tantamount to bypassing crystallization, which would bring the material to an ordered state of matter of lower energy and, thus, of greater stability. If cooled quickly enough, virtually any material can vitrify. Hence, an important question is to know how fast the melt should be cooled to avoid detectable crystallization. Actually, the cooling rates of good glass formers range from 1 to 10 K/s and those of poor ones are higher than ~100 K/s. Familiar glass‐forming materials such as SiO2‐rich silicates thus do not require fast cooling. An extreme example is supercooled NaAlSi3O8, which did not crystallize at all after five years spent 90 K below the melting point of the albite feldspar mineral [4]. Even though the quenching rate of a liquid medium can be increased to about 103 K/s, such high values may not be fast enough to avoid partial or complete crystallization. In silicates, SiO2‐poor olivine compositions (e.g. Mg2SiO4) are notorious examples of liquids that are difficult to vitrify at such rates [5]. Quickly crystallizing liquids such as metals may require still faster cooling. For instance, early metallic glasses (Chapter 7.10) had to be splat quenched in the form of thin ribbons at about 106 K/s to avoid crystallization, mainly because their viscosities remain very low with decreasing temperatures (Figure 1).
An added complication is that melts can be good glass formers only within limited composition regions as indicated in Figure 2 for aluminosilicates. Compilations of glass‐forming regions of phase diagrams are available [6–8]. As a rule, however, glass formation is enhanced in more complex systems. Oxide systems containing a variety of cations are easier to obtain in a glassy state as their liquidus temperature is lower and their complexity necessitates longer times for diffusion‐controlled redistribution of their diverse constituents before crystal nucleation and growth can take place.
Figure 1 Critical cooling rates for glass formation. Reduced glass transition temperature Trg defined as Tg/Tm, where Tm is the liquidus temperature.
Figure 2 Glass formation ranges in aluminosilicate systems (shaded areas).
Source: After [6], courtesy P. Richet.
If crystallization is bypassed, the melt undergoes the glass transition in a temperature range that shifts to higher temperatures for higher cooling rates. Both the width of this range and the value of Tg within it may vary by typically several tens of degrees. As the width and variation are small compared with Tg, it is therefore possible to manage a cooling schedule rapid enough to keep the degree of crystallization negligible. Volume fractions considered to be negligible are lower than 1 ppm, which is the typical instrumental limit for detecting the presence of crystals by
