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The definition of the glass transition in terms of the standard glass transition derived from the viscosity–temperature relationship, η(T), is not thermodynamic, but operational [8]. As determined from changes in second‐order derivatives of thermodynamic variables, the glass transition takes place at viscosities in the range 10⁸–10¹³ Pa s depending on the cooling rate. In view of the very steep temperature dependence of viscosity, a great difference in this parameter results in only small variations of the operational T_g.

Table 1 Critical cooling rate for some glasses, K/s.

Source: After [9].

Material	Nucleation mechanism
Homogeneous	Heterogeneous θ = 100°	Heterogeneous θ = 60°	Heterogeneous θ = 40°
SiO2	9 × 10−6	10−5	8 × 10−3	2 × 10−1
GeO2	3 × 10−3	3 × 10−3	1	20
Na2O 2 SiO2	6 × 10−3	8 × 10−3	10	3 × 102
Salol [C13H10O3]	10
Water	107
Ag	1010

As has long been recognized, glass formation is therefore easier in eutectic regions because freezing‐point depressions enable lower temperatures and higher viscosities to be reached [11]. However, viscosity at the liquidus is not a single scaling parameter for assessing glass‐forming ability. The temperature dependence of the viscosity below T_m must also be considered because vitrification takes place much below the liquidus [6, 8].

Viscous flow in glass‐forming liquids is characterized by deviations from Arrhenius laws with an activation energy Q that decreases from a high Q_H near the glass transition to a low Q_L at superliquidus temperatures. As a fragility index characterizing the temperature dependence of viscosity, Doremus [12] has proposed the ratio:

(6)

Short (or fragile) and long (or strong) glass melts are, therefore, characterized by R_D values higher and lower than 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 Q_L and Q_H 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(−S_m/R), B = H_m, C = exp(−S_d/R) and D = H_d, 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, H_d the enthalpy, S_d the entropy of formation, and H_m and S_m 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(Q_H/RT) at T << T_g, and η(T) ~ exp(Q_L/RT) at T >> T_g, where Q_H = H_d + H_m and Q_L = H_m. Obviously, the activation energy of viscosity reduces to a low value equal to H_m 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 Q_H = H_d + H_m.