Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
composition at least for oxide glass‐forming liquids [38, 39]. Compared with the tremendous variations of viscosity with temperature and composition, G∞ thus is almost constant. If the viscosity is known, structural relaxation times can be readily estimated from Eq. (7).
2.4 Configurational Properties
2.4.1 Equivalence of Relaxation Kinetics
It is usually more difficult to account for the kinetics of a reaction than for its thermodynamics. Relaxation in glass‐forming systems does not depart from this rule. Whereas a single‐order parameter such as the fictive temperature may be appropriate for characterizing the volume or enthalpy of a glass, relaxation kinetics requires models much too complex to be discussed here (see Chapter 3.7). One can nonetheless have a first look at the mechanisms involved in relaxation by examining whether their kinetics varies or not with the particular property considered.
As done for viscosity, the kinetics of volume equilibration can, for instance, be measured by isothermal dilatometry experiments. If samples with the same thermal history are studied, comparisons between the relaxation kinetics of different properties can be made in terms of normalized variables
(8)
where Yt, Y∞, and Y0 are the property Y at time t, initial time, and equilibrium, respectively. To within experimental errors, experiments on E glass, for example, show in this way the same kinetics for viscosity and volume (Figure 14).
Figure 14 Kinetics of equilibration for the viscosity and volume of E glass. Differences between the ascending branches mainly due to the uncertainties on the Y0 values caused by unrecorded relaxation during the initial thermal equilibration of the sample.
Source: Data from [28].
More general conclusions are readily derived from comparison between different glass‐transition temperatures even though these are not necessarily defined in the same way in different kinds of measurements. What is important is that they be defined consistently and refer to samples with the same thermal histories. For volume and enthalpy, the latter condition is fulfilled in dilatometry experiments and differential thermal analyses performed simultaneously, whose results can also be compared with standard glass‐transition temperatures (Figure 15). The close 1 : 1 correspondences found in this way for the three temperatures of silicates, calcium aluminosilicates, titanosilicates, and borosilicates over a 400 K interval thus confirm the equivalence of the relaxation kinetics for differing properties [28]. In other words, one must conclude that the same configurational changes are involved in enthalpy, volume, or viscosity relaxation at least in oxide systems, which illustrates their overall cooperative nature.
Figure 15 Equivalence of the relaxation kinetics for the enthalpy, volume, and viscosity illustrated by 1 : 1 correlations between the relevant glass‐transition temperatures determined by differential thermal analysis (DTA), dilatometry (dil), and viscometry (vis, i.e. standard Tg). BNC: sodium borosilicate; WG: window glass; E: E glass; Ab: NaAlSi3O8; Di: CaMgSi2O6; N:Na2O; S: SiO2; T: TiO2; Ca.xx.yy: xx mol % SiO2, yy % Al2O3.
Source: Data from [28].
2.4.2 Vibrational vs. Configurational Relaxation
The equivalence of relaxation kinetics allows an important distinction to be made between vibrational and configurational contributions to the properties of glass‐forming liquids. In preamble, one should note that relaxation in solids does not need to be specifically addressed, as long as macroscopic properties are concerned, because it takes place at the 10−14 –10−12 seconds timescale of atomic vibrations. This instantaneous vibrational response persists in liquids where it combines with the configurational response whose timescale markedly decreases with increasing temperatures (Figure 16). For volume, isothermal dilatometry experiments near the glass transition may yield these two contributions (Figure 17) whose relative magnitudes directly reflect the increase in thermal expansion at the glass transition [40]. For the compressibility, another approach may take advantage of experiments made at different timescales. As described above, in certain temperature ranges, ultrasonic measurements yield the equilibrium adiabatic compressibility whereas Brillouin scattering experiments probe only its vibrational part. The configurational compressibility is then given by the difference between these two results [32]. That such determinations are actually scarce is not too problematic for second‐order thermodynamic properties because, at least as a first approximation, one can assume that the vibrational contribution is represented by the glass property and the configurational one by the variations of these properties at the glass transition. In silicate systems, the configurational heat capacity can thus be written
Figure 16 Relative importance of configurational and vibrational relaxation with increasing temperatures for a given property Y (a) after instantaneous temperature jumps ∆T (b).
Source: Data from [40].
Figure 17 Vibrational and configurational contributions to the volume change of CaMgSi2O6 liquid after an abrupt temperature decrease from 982 to 972 K.
Source: Data from [40], cf. Chapter 3.5.
(9)
where the subscripts l and g refer to the liquid and glass phases, respectively, and a further simplification arises from the fact that Cpg(Tg) may be considered to be the Dulong–Petit harmonic limit of 3 R/g atom (R = gas constant) the isochoric heat capacity [41].
2.4.3 A Microscopic Picture
The