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Among all the properties of a glass‐forming substance, the viscosity–temperature relationship is by far the most important practically in glass making. Referring to Chapter 4.1 for an in‐depth review of this topic, here we will consider it from a simpler technological point of view. The main feature then is that the viscosity of a glass‐forming liquid extends over a range of 12–14 orders of magnitude, which thus involves large rheology changes in the temperature range relevant to glass manufacturing (Table 2). Conventionally, technologists do not report viscosities in terms of values found at given temperatures, but rather in terms of temperatures at which given viscosity values are obtained. Thus, T(n.n), the isokom temperature, denotes the temperature in °C at which the melt assumes a value log η = n.n in poise CGS units (1 P = 0.1 Pa·s so that all values compiled in Table 1 have to be decreased by 1 if one retains instead the Pa·s SI unit used in many recent publications). The importance of reporting temperatures instead of viscosities rests on the facts that the (Newtonian) rheological response of all substances is by definition the same at the same viscosity and that only the temperature of a glass – not its viscosity – can be operationally regulated during the various forming, tempering, annealing, or cooling steps of glass making.

Table 2 Viscosity ranges of industrially manufactured glasses.

Viscosity as log η,η in dPa·s	Process range, technological meaninga
	Melting
2.0	Typical of a soda‐lime silicate glass melt at 1450 °C
3.0	Transfer to forming area Volume relaxation time is <1 s Fixpoint T(3.0) = gob temperature Bushing tip temperature for fiber productionb
	Forming
4.0.	Upper limit of mechanical working range Fixpoint TWP = T(4.0) = working point
6.0	Lower limit of mechanical working range The difference T(4.0) – T(6.0) is termed the “length” of a glass
	Tempering, annealing, and cooling
7.6	Upper limit of macroscopic shape stability Fixpoint TL = T(7.6) = Littleton softening point
11.0c	Dilatometric softening point TD Above TD, temperature gradients in a glass object no longer cause thermal stresses A related temperature level is Td = T(11.5) = deformation point Glass objects deform under own weight at rates of a few μm/h
13.0	Technical definition of the glass transition Fixpoint Tg = T(13.0) = annealing point Volume strain relaxation time is 60 s
14.5	Technical definition of ultimate transition to a rigid state Fixpoint T(14.5) = strain point Volume strain relaxation time is 30 min

^a In the earlier days of mechanical forming, empirical indicators were in use. They remain worth to be consulted as empirical guidelines when the complex feature of “workability” is to be kept constant under a compositional change; these indicators read: gob temperature, GT = 2.63·(T_L – T_g) + T_L; working range index WRI = T_L – T_g; RMS = relative machine speed = (T_L – 450)/(WRI + 80); DI = devitrification index = WRI – 160.

^b Some stonewool processes use T(1.5) as fibrization temperature.

^c Approximation, the exact value depending on the load applied by the dilatometer.

Viscosity–temperature relationships do vary much with chemical composition: as illustrated in Figure 3 by the data for a soda‐lime float glass, a stonewool and silica glass, and those for a bulk metallic glass and pure Ag and Fe liquids. The fixed points of Table 1 are pinpointed for each glass melt and read in this graph, as just explained, starting from its Y axis. The complete viscosity curves can be reproduced by Vogel–Fulcher–Tamman (VFT) equations,

Figure 3 Viscosity–temperature relationship of different glass‐forming systems; pure metallic melts of Ag and Fe are displayed for comparison.

(2)

where A, B, and T₀ are empirical fit constants and T is expressed here in °C. The float glass DGG‐1 included in Figure 3 is a certified viscosity standard whose VFT equation has been derived from 44 measurement points. These are reproduced with the parameters A = −1.601, B = 4330.9, and T₀ = 246.1 (η in dPa·s) with a standard deviation of δlog η = ± 0.16, illustrating that the VFT equation is a valuable tool for any technological purpose.

Viscosities are in addition an indicator of crystallization tendency at the liquidus temperature T_liq, which is shown in Figure 3 on the viscosity curves. Melts with log η(T_liq) < 2.0 tend to crystallize quickly, thus requiring very high cooling rates, whereas melts with η(T_liq) > 4.0 may in contrast be vitrified at moderately low cooling rates.

Of great interest, therefore, is the possibility to predict the viscosity of a glass melt as a function of its temperature and chemical composition. From measurements performed for a variety of samples, sets of incremental factors have been empirically derived by regression analysis for this purpose. The left‐hand part of Table 3 presents such a widely used database [19] with which the effect of additions of individual oxides (by weight and molar amounts, respectively) have been calculated for a soda‐lime silicate. The temperature T(n.n) at which viscosity reaches 10^n.n dPa·s is thus calculated as

(3)

where y(j) is the weight fraction of oxide j.

Helpful guidelines for the design of the viscosity curve of a mass‐produced glass may be derived from the graphs of Figure 4. For example, replacement of 1 wt % SiO₂ by 1 wt % Li₂O to yield a glass 73 wt % SiO₂, 10 CaO, 16 Na₂O, 1 Li₂O lowers the temperature at log η = 4.0 and 13.0, relative to the base glass, by 45 and 29 K, respectively. Among the alkali oxides, lithia is the strongest liquidus flux; it significantly lowers viscosity at all levels. Boron oxide has a similarly strong effect, however, at high‐temperature only. So it reduces the working range (the “length”) of a glass. In the language of glass technologists, boron oxide makes a glass “short.” Lime strongly reduces viscosity at high temperatures; the effect is almost as strong as with soda. Thus, if viscosity needs to be lowered in this range, inexpensive limestone as a calcium carrier raw material may be used instead of expensive soda ash as a sodium carrier. Also note that lime, quite in contrast to magnesia, makes a glass “short.” One can thus extend the working range of a glass by manipulating its CaO/MgO ratio. Alumina makes at the same time a glass more viscous and “longer.” Although not giving any in‐depth scientific understanding, these empirical tools undoubtedly have their merits in glass technology.

Table 3 Empirical factors for the calculation of viscosities [19] and elastic properties [21, 22] (units revisited) from composition.

Oxide j	Viscosity	Elastic properties
	a(j) for	Validity range (wt %)	V(j) (cm3/mol)	U(j) (GPa)
T(2.0) (°C)	T(4.0) (°C)	T(6.0) (°C)
SiO2	1847.80	1249.70	962.90	60–77a	28.0	64.5
TiO2	−4.00	−4.00	−4.00	0–8b	29.2	86.7
ZrO2	8.65	7.96	8.16	0–8b	30.2	97.1
Al2O3	8.32	5.23	4.01	0–8a	42.8	134.0
B2O3	−21.62	−11.97	−6.42	0–14a	41.6	77.8
‐ “‐	0.5122	0.3182	0.1900	—c	—	—
MgO	−5.87	−0.12	0.91	0–6a	15.2	83.7
CaO	−11.27	−3.99	−0.74	4–13a	18.8	64.9
BaO	−5.67	−3.04	−1.88	0–17b	26.2	40.6
ZnO	−5.37	−1.99	−0.71	0–9b	15.8	41.5
PbO	−4.85	−3.17	−2.24	0–12b	23.4	17.6
Li2O	−35.54	−30.04	−26.45	0–3a	16.0	80.4
Na2O	−12.65	−9.19	−7.06	10–17a	22.4	37.3
K2O	−5.93	−4.17	−3.53	0–9a	37.6	23.4
Error	±4.7 K	±3.4 K	±3.2 K	—	n.s.	n.s.

^a Combinations of these oxides, plus one.

^b Oxide only, keep the error within the given ± range.

^c For boron oxide, the factors in the second row are square terms; thus, the sum for each T(n.n) has to be expanded by a term 10 000·a(B₂O₃)·[y(B₂O₃)/y(SiO₂)]².

Figure 4 Temperature change brought about by a replacement of 1% of SiO₂ by another oxide in the base glass composition 74SiO₂, 10CaO, 16Na₂O; left side: for oxide amounts by wt; right side: for molar amounts.