one of the strongest engineering materials at ordinary temperatures. However, their practical strengths are lowered significantly due to the development of microscopic surface cracks produced by abrasives and chemicals. Griffith (1921) tackled this issue and explained the low strength of glass objects.
The glass that we see through from the windows of automobiles and trains, watch and admire in shimmering skyscrapers, and consider the pride of our cities is not a simple transparent material. It is a unique amorphous material, toughened and/or laminated with layers of polymers. The mechanical and optical properties of glass depend not only on their chemical compositions, but also on structural transformation induced during processing at high temperatures and subsequent thermal treatments. To understand the thermal tempering or toughening process, a detailed knowledge of the rheological properties of glass is required. This will be treated in Chapter 5, which deals with the fundamentals of creep. It is appropriate to mention here that the creep and failure models for polycrystalline materials, to be presented later in this book, have actually been developed on the basis of the primary author's investigations on the rheo‐optical behavior of a common window glass. There is, therefore, a need to describe the basic features of the structure of real glass, the science of the glassy state, and industrial processes.
2.4.1 Glass Transition
The classical glass transition is the transformation of a material from a hard, brittle state into a soft, rubbery or viscous state as temperature increases. The transition is characterized by the glass transition temperature, T g. However, T g is defined as a transition temperature by convention and actually represents a range of temperatures. The reverse transition is called vitrification and is achieved by cooling a viscous liquid into the glassy state.
The different uses of amorphous materials are often characterized by their operating temperature relative to their glass transition. For example, oxide glasses used in windows and hard plastics, like polystyrene used in food packaging, are utilized well below their glass transition temperature, i.e. when they are in a hard phase. On the other hand, rubber elastomers, like polyisoprene used in rubber bands, are utilized above their T g.
The glass transition is not a true phase change. It is not generally characterized by a clear change in material structure. Rather than an abrupt discontinuous change in properties, the glass transition is a smooth change over the temperature range. For the glass–liquid transition, the viscosity of the material can smoothly change with temperature.
During a heating cycle, the glass transition can also refer to a devitrification – an amorphous to crystalline transition. The T g may represent the temperature range over which nucleation and crystal growth starts to occur from an amorphous material. The T g is always lower than the melting temperature, T m, of the crystalline phase. The amorphous phase in question is not necessarily a thermodynamically stable state and the history of the material is critical to predict structure and properties. For example, an amorphous state that was initially achieved by quenching a disordered state (e.g. an amorphous metal) may devitrify upon heating to the T g, but the transition is not reversible. It will not vitrify, i.e. will not become amorphous again, upon cooling.
2.4.2 Structure of Real Glass
As discussed in Section 2.2.2, in materials science, amorphous solids are synonymous with glasses and include oxide glasses, amorphous polymers, and metallic glasses. In this section, we focus on the colloquial usage of the term “standard oxide glasses.”
The big question during the first half of the twentieth century was, “What is the structure of glass?” Two types of amorphous structural states, named as the glassy state, were proposed and debated vigorously during the second quarter of the last century. One was the irregular Zachariasen's (1932) model and the other was Lebedev's (1940) crystallite theory. Lebedev (1912, 1926) proposed the basic principles of his crystallite theory and influenced many scientists in Soviet Russia, as described by Evstropyev (1953). It should be noted that the word “crystallite” was coined by Lebedev; this term will be clarified later.
Based solely on the analysis of rather diffused X‐ray scattering results in silicate glasses and interpreted by the Fourier analysis method, Zachariasen (1932) concluded that the structural network of glass is irregular. Consider, for example, the structure of crystalline quartz. It is built of silicon–oxygen (SiO4) tetrahedrons arranged in a regular fashion in the form of a continuous network with atoms (or ions), or atomic groups at its junctions. Very similar to the structure of crystalline quartz, the structure of quartz glass is also built of SiO4 tetrahedrons; however, in the network of the glassy state, the degree of regularity in the orientation does not extend further than the neighboring tetrahedron. As the distance increases from a given tetrahedron, the regularity of orientation diminishes gradually and tetrahedrons at greater distances are randomly distributed. Quartz glass is the prototypical material for the continuous random‐network model described above.
Lebedev (1940) studied the physicochemical transformations in glass in the region of T g, which depends on chemical composition and thermal history. He demonstrated that the toughened state of silicate glasses is not only characterized by the existence of internal stress, but is also distinguished by its structure. According to him, the difference between the refractive indices of toughened and annealed glasses could not be attributed only to the existence of internal stresses in thermally tempered glass. Lebedev observed (Evstropyev 1953, p. 10) that the refractive index (n) of a silicate glass increases linearly with the increase in temperature (T) up to about 500 °C and then decreases rapidly between 520 and 590 °C. He also noticed that the linear section of the n–T plot (i.e. below 500 °C) was “rapidly” reversible and thus purely a thermal effect. However, if the glass is heated to high temperatures (say 600 °C) and then cooled, the descending branch of the n–T curve is not “rapidly” reversible, meaning – if not soaked for very long times at each step of cooling. This means refractive index of glass and hence the structure of glass depends on thermal history.
After considering the limitations of X‐ray analysis and techniques available at that time, Lebedev (1940) concluded that it was necessary to combine the X‐ray structural analysis with other methods, both physical and chemical, unlike the approach taken by Zachariasen (1932) and supported by Warren (1940) entirely on the basis of X‐ray analysis. In those days, of course, the modern techniques such as small‐angle X‐ray scattering and wide‐angle X‐ray scattering, nuclear magnetic resonance, X‐ray absorption fine structure, and neutron scattering were not available.
Chemically, quartz is SiO2, but the crystals exist in two crystalline forms, α‐quartz at normal temperatures and β‐quartz at high temperatures. The transformation from α‐quartz to β‐quartz takes place at about 573 °C (846 K). This transformation is accompanied by significant changes in volume, and hence density and other physical properties. Because of this α–β transition in crystalline quartz, Lebedev (1940) postulated that the sharp decrease in the refractive index of a silicate glass in the range 520–590 °C, mentioned above, is associated with the α–β transition in quartz and thus the microcrystalline formations, one form of which consists of quartz microcrystals. Real silicate glass may be regarded as a conglomeration of “sub‐microcrystalline” formations of various types of silicates and silica, the chemical nature of which depends on the chemical composition of the glass. The term “sub‐microcrystalline” is used to distinguish them from fragments of microcrystals with a perfect regular lattice. A new name was coined: “crystallites.” The greatest regularity in the lattice structure is thought to be in the central regions of the crystallites. The deviation of the crystal lattice occurs as the periphery of the crystallites is approached. The crystallites are separated by a mass of amorphous medium in which the degree of disorder in the atomic arrangements increases with increasing distance from the crystalline