2, respectively.
Many equations have been proposed to express viscosity–temperature relationships (Chapter 4.1, [13–15]). Consistent with Doremus criterion, an exponential expression with activation energies QL and QH at low and high temperatures, respectively, [13] will be used here because it results from the configuron percolation theory (CPT), which accounts for viscous flow in terms of elementary excitations resulting from broken bonds named configurons [14, 16]. This equation (Sheffield model) is
(7)
where A1 = k/6πrD0, A2 = exp(−Sm/R), B = Hm, C = exp(−Sd/R) and D = Hd, R the gas constant, k Boltzmann constant, r the configuron radius D0 = fgλ 2 zp0 ν0, f the correlation factor, g a geometrical factor (~1/6), λ the average jump length, ν0 the configuron vibrational frequency or the frequency (with which the configuron attempts to surmount the energy barrier to jump into a neighboring site), z the number of nearest neighbors, p0 a configuration factor, Hd the enthalpy, Sd the entropy of formation, and Hm and Sm the enthalpy and entropy of motion of the configurons.
In practice, one finds that A2 exp(B/RT) > > 1, i.e. that four parameters usually suffice for Eq. (7) to be fitted to practically all available experimental viscosity data [17]. Comparison with other viscosity models and numerical calculations have confirmed the excellent description of the viscosity provided by Eq. (7) for simple and complex organic and inorganic compositions (e.g. [13]). This equation can be readily approximated within narrow temperature intervals by expressions derived from the well‐known Vogel‐Tammann‐Fulcher, Adam–Gibbs, Avramov–Milchev, or Sanditov models [14, 15, 17]. It can be used at all temperatures and gives the correct Arrhenius‐type asymptotes at high and low temperatures, namely η(T) ~ exp(QH/RT) at T << Tg, and η(T) ~ exp(QL/RT) at T >> Tg, where QH = Hd + Hm and QL = Hm. Obviously, the activation energy of viscosity reduces to a low value equal to Hm at high temperatures when temperature fluctuations create plenty of configurons. In contrast, some bonds need to be broken in the glassy state as temperature fluctuations do not create them effectively so that the activation energy then takes its full value QH = Hd + Hm.
5 Structural Factors
Apart from inhomogeneities and potential phase separation, glasses lack long‐range order but do possess short‐ and medium‐range ordering (Chapter 2.1). A number of models have aimed at revealing the most characteristic structural aspects of good glass formers. The most noted structural criterion for ready glass formation, i.e. at rates qc lower than 10 K/s, is based on Zachariasen theory in which the oxide glasses AmOn are assumed to be 3‐D networks obeying four rules: (i) the oxygen is linked to two atoms of A; (ii) the oxygen coordination number around A is three or four; (iii) the cation polyhedra share corners; and (iv) at least three corners are shared [18]. This theory is referred to as crystallochemical, but was applicable only to oxide glasses in its original form; it led to the so‐called 3‐D continuous random network (CRN) model (Chapter 2.1). With respect to a glass and its isochemical crystal, the basic postulates of CRN are that: (i) interatomic forces are similar in both phases; (ii) the glass is in a slightly higher energy state; (iii) nearest‐neighbor coordination polyhedra are similar; and (iv) the nature of interatomic bonds is also similar.
The strong points of Zachariasen's model are that it predicts the existence of the main oxide glass formers (SiO2, GeO2, B2O3, P2O5, etc.) and glass modifiers (Na2O, CaO, etc.) and makes room for the distinction between bridging (BO) and non‐bridging oxygens (NBO). Its main limitation is that it does not consider at all modified oxides or multicomponent systems, or even non‐oxide glasses. In addition, several exceptions to its rules are found as exemplified by alumina‐lime glasses and chain‐like glass structures (e.g. metaphosphate glasses).
Smekal [19] thus developed the concept of the mixing bond nature of (good) glass formers. He noted that pure covalent bonds are incompatible with a random arrangement in view of sharply defined bond lengths and angles. Purely ionic or metallic bonds lack any directional characteristics so that the presence of mixed chemical bonding is necessary for glass formation. Indeed, known glass formers obey this concept: (i) inorganic compounds like SiO2 or B2O3 where the A─O bonds are partly covalent and partly ionic; (ii) elements (S, Se) having chain structures with covalent bonds within the chain and van der Waal's forces between them (Chapter 6.5); and (iii) organic compounds containing large molecules with covalent internal bonds and van der Waals' forces between the molecules (Chapter 8.8).
Alternatively, Stanworth proposed a criterion for glass formation according to which the electronegativity of cations in oxide glasses falls within a certain range between 1.90 and 2.20 [20]. Although the electronegativity values of the constituent atoms can be used to predict the formation of many glasses, this criterion cannot account for systems when bond strength needs to be considered as a secondary criterion.
Sun developed the bond‐strength model on the assumption that, when a melt vitrifies, the stronger the metal–oxygen bond, the more difficult the structural rearrangements necessary for crystallization become and, hence, the easier is glass formation. Glass formation is then ensured by the connectivity of bridging bonds combined with strong bonding between atoms (ions) [21]. Sun thus classified oxides according to their bond strengths so that glass formers form strong bonds with oxygen to yield a rigid network, which results in a high viscosity. He defined modifiers as weakly bonding with oxygen in such a way that they disrupt and modify the network. Without producing glasses on their own, they do form intermediate bonds with oxygen and thus aid vitrification with other oxides.
In practical terms, Sun's energy criterion establishes a correlation between the glass‐forming tendency and the strength of the bond between the elements and the anion in the glass. The single bond strength Eb was defined as:
(8)
where CN is the coordination number and Ed the dissociation energy of oxides into their gaseous elements. For B2O3, SiO2, GeO2, P2O5, or Al2O5, the single bond strength of network formers with oxygen is higher than 330 kJ/mol. Values lower than 250 kJ/mol hold for network modifiers such as Li, Na, K, Mg, or Ca whereas intermediate cations such as Ti, Zn, and Pb are characterized by values intermediate between these two figures.
For both Zachariasen and Sun models Al+3 is a challenge. Although Al2O3 satisfies Zachariasen's criteria, it does not form a glass. Likewise, with Ed = 1320–1680
