target="_blank" rel="nofollow" href="#ulink_52fbf1c6-c893-5786-b9d0-ec9fd313df00">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 vibrational/configurational split can be simply illustrated by a schematic one‐dimensional representation of interatomic potentials (Figure 18). Contrary to crystals, where these potentials have a long‐range symmetry, glasses have essentially a short‐range order because the bond angles and distances between next‐nearest neighbor atoms are not constant but spread over a range of values. The minima of potential energy, which determine the glass configuration, are separated by barriers with varying heights and shapes [43]. When thermal energy is delivered to the glass, the subsequent temperature rise is associated only with increasing amplitudes of vibration of atoms within their potential energy wells. Like for any solid, the heat capacity of the glass is, therefore, only vibrational in nature.
Figure 18 One‐dimensional schematic representation of interatomic potentials. Inset: potential‐energy landscape for a strong and a fragile liquid
(Source: After [42]).
C: crystal; IG: ideal glass; MC: metastable crystal.
At sufficiently high temperature, thermal energy increases to the point that atoms can overcome the barriers that separate their own from the neighboring potential energy wells (Figure 18). This onset of atomic mobility signals structural relaxation. If the relaxation time is longer than the experimental timescale, however, only the vibrational heat capacity is measured. If the temperature is increased further, or if time is sufficient for the new equilibrium configuration to be attained during the measurement, then the configurational heat capacity is also measured. When integrated over all atoms, the configurational
