Advanced textbook on inorganic glasses suitable for both undergraduates and researchers.
* Engaging style to facilitate understanding
* Suitable for senior undergraduates, postgraduates and researchers entering material science, engineering, physics, chemistry, optics and photonics fields
* Discusses new techniques in optics and photonics including updates on diagnostic techniques
* Comprehensive and logically structured
1.1 Definition of Glassy States
A "glassy or vitreous" state is classified as a state of condensed matter in which there is a clear absence of a three-dimensional periodic structure. The periodicity is defined by the repetition of point groups (e.g. atoms or ions) occupying sites in the structure, following a crystallographic symmetry, namely, the mirror, inversion and rotation. A glass is a condensed matter exhibiting elasticity below a phase transition temperature, known as the glass transition temperature, which is designated in this text as (Tg). By comparison, an "amorphous" state, as in the "vitreous" state, has an all-pervasive lack of three-dimensional periodicity; it is more comparable with a liquid rather than a solid. An amorphous structure lacks elasticity and has a propensity to flow under its own weight more readily than a solid-like vitreous state does below Tg. An amorphous inorganic film also has a glass transition temperature and elastic behaviour, which varies with that of the corresponding vitreous state of the same material. The recognition of apparent differences in the properties of "vitreous" and "amorphous" structures, will be discussed in subsequent chapters on fabrication and processing and such comparative characterizations are essential in developing a deeper understanding of a structure-optical and spectroscopic properties of transparent "inorganic glasses as photonic materials" for guiding photons and their interactions with the medium. Such differences in structural and thermal properties between a glassy or amorphous and a crystalline state explain why the disordered materials demonstrate unique physical, thermo-mechanical, optical and spectroscopic properties, facilitating light confinement and propagation for long-haul distances better than any other condensed matter.
1.2 The Glassy State and Glass Transition Temperature (Tg)
The liquid-to-solid phase transition at the melting point (Tf) of a solid, for example, is characterized as a thermodynamically reversible or an equilibrium transition point, at which both the liquid and solid phases co-exist. Since at the melting point both phases are in equilibrium, the resulting Gibbs energy change (?Gf), as shown in Equation 1.1, of the phase transition is zero, which then helps in defining the net entropy change associated with the phase change at Tf: (1.1)
In Equation 1.1, ?Hf and ?Sf are the enthalpy and entropy changes at the melting point. Since ?Gf equates to a zero value at Tf, from Equation 1.1, the entropy change at Tf consequently is equal to: (1.2a)
From Equation 1.2a, for pure solids the magnitude of entropic disorder can thus be determined at the melting point by measuring the enthalpy of fusion. This characteristic of a solid-liquid transition will become quite relevant in the examination of glass-formation in multicomponent systems. In Figure 1.1, the liquid-to-crystal and liquid-to-glass transitions are shown by identifying the Tf and a range of transition temperatures, , and , respectively. These glass transition temperatures are dependent on the quenching paths AA1E, AA2F and AA3G, which differ from the equilibrium route ABCD for liquid-crystal transition at Tf.
Figure 1.1 Plot of the entropy change (?Sf in J mol-1 K-1) in a solid-liquid and liquid-glassy state transitions, shown schematically to illustrate the respective apparent change in the value of entropy end point, as a result of various quench rates applied, which are designated by the paths AA1E, AA2F, and AA3G.
In Figure 1.1, the glass experiencing the fastest quenching rate (Q3) has the corresponding transition temperature at , whereas the quenching rates Q2 and Q1 yield glasses having transition temperature at and , respectively. The end entropic points thus relate to the thermal history of each glass. The slowest cooling rate yields the lowest temperature, as the supercooled liquid state below Tf attains a metastable thermodynamic state, which is still higher in Gibbs energy than the equilibrium crystalline state designated by line CD in Figure 1.1. When the fastest quenching rate path, AA3G, is followed the liquid has little time to achieve the thermodynamic equilibrium, as reflected by the transition temperature , which is closest to the melting point.
The annealing of the fastest quenched glass in Figure 1.1, having a transition temperature at , provides the driving force for structural relaxation to lower energy states progressively. With a prolonged isothermal annealing, the end point entropy state might eventually reach much closer to the equilibrium crystalline state (line CD in Figure 1.1). As the annealing allows the quenched glass to dissipate most of the energy in a metastable quenched state, the end point entropy never approaches the line CD, which is consistent with the theory proposed by Boltzmann in the context of the second law of thermodynamics. This condition mathematically limits the value of viscosity approaching infinity, an impossible value. Considering the thermodynamic state properties, e.g. the molar volume (V) and entropy (S), and their dependence on pressure (P) and temperature (T), any change in the entropy of a state corresponds to a proportional change in the molar volume, which follows from the differentials in Equations 1.2b-d, shown below. It is for this reason that in Figure 1.1 the discontinuity in fractional change in molar free volume (vf), which is dependent on V, is shown along with the entropy change: (1.2b) (1.2c) (1.2d)
The implication of thermodynamic state analysis in Equations 1.2b-d is that the discontinuities in glassy states are also observed when their state properties, such as the enthalpy (H), specific heats at constant pressure (Cp) and volume (Cv), thermal expansion coefficient (aV) and isothermal compressibility (ßT), are plotted against temperature. Discontinuities in the thermodynamic state properties for several glass-forming liquids are compared and discussed by Paul  and Wong and Angell  in publications that readers may find helpful.
From Figure 1.1, the glass transition temperature is represented by the presence of a discontinuity, which is dependent on the quenching rate (Qi), and the points representing Tgs are not sharp or abrupt, as shown in the liquid-to-crystal transition. The range of Tgs in Figure 1.1 is characterized as the "fictive glass temperature" and their position is dependent on the quenching history. Several text books designate the fictive temperature as Tf, and readers should cautiously interpret this temperature along with the quench rate and associated thermal history, because unlike Tf, the Tgs are not fixed phase transition points. A major discrepancy in the property characterization might arise if experiments are not carefully designed to study the sub-Tg and above-Tg structural relaxation phenomena, which are discussed in great detail by Varsheneya [3a] in his text book. Elliott  explains the exponential relationship between quenching rate and Tg in Equation 1.3, showing that the corresponding relaxation time (which is the inverse of the quenching rate) is likely to be imperceptibly long, since a glass is annealed to achieve a new metastable equilibrium state above a crystalline phase, corresponding to line CD in Figure 1.1: (1.3)
In Equation 1.3, the value of Qo for different glasses differs, as observed by Owen , and was found to be of the order of 1023 and 104 K s-1 between Se and As2S3 glasses. The constant B was found to be of the order of 3 × 10-5 K. An analysis of quenching rate and glass transition temperature implies that near Tg, there is an Arrhenius type activation energy barrier, which is path dependent and can be reached in numerous ways by following different thermal histories, which is discussed extensively by Varsheneya [3b]. Based on path dependence analysis and the associated changes in the first order thermodynamic properties, namely the enthalpy of glass transition, the phase transition is a "first-order" transition and, unlike the Curie temperature in a magnetic metallic glass, the glass transition is not a second-order transition. The Curie temperature is a fixed point, dependent upon the electronic-spin relaxation, the time-scale for which is of the order of 10-15 (femto to sub-femto) seconds, which is six orders of magnitude faster than the molecular relaxation characterized by an Arrhenius type of energy barrier. From reaction rate theory, the pre-exponential in the rate equation is equal to kBT/h, where kB and h are the Boltzmann constant and Planck's constant, respectively and T is the absolute temperature. Applying the reaction rate theory for quenching of a glass, the minimum and maximum values therefore may vary between 10-7 and...