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2 Glass and Relaxation

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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.

Encyclopedia of Glass Science, Technology, History, and Culture

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