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2.4.2 Vibrational vs. Configurational Relaxation
ОглавлениеThe 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].