Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов

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.

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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