Structural Relaxation in Glass Transition and Crystallization Thermodynamics

Dear Colleagues,

In the application of classical nucleation theory to the theoretical description of crystallization of liquids and glasses, it is assumed as a rule that the nucleation and subsequent growth of the crystal phase proceed only after the supercooled liquid or the glass have completed structural relaxation processes towards the given values of pressure and temperature corresponding to a metastable equilibrium state. Only by employing such an assumption can the thermodynamic driving force of crystallization and the surface tension be determined in the way it is commonly. However, as shown in detail in the first Special Issue on “Crystallization Thermodynamics”, Entropy 2020, 22, 1098, a different situation is observed as a rule near and below the glass transition temperature. In this temperature range, these processes proceed concomitantly with structural relaxation. As a consequence, nucleation and growth rates depend not only on temperature but also on the current state of the relaxing melt. A similar behavior is expected to occur if the glass transition is governed by variations in pressure or other external control parameters.

To treat the nucleation kinetics theoretically for such cases, adequate expressions of the thermodynamic driving force and the surface tension are required which can account for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. Utilizing the approach developed by de Donder, these deviations may be expressed via deviations in a set or appropriately chosen structural order parameters from their equilibrium values. Relaxation processes result in changes in the structural order parameters with time. As a consequence, the thermodynamic driving force and the surface tension, and other basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, as well as the rates of growth, also become time-dependent. The correct description of relaxation of the structural order parameters is consequently a prerequisite of a correct treatment of nucleation and growth in such cases. As shown in the paper cited above paper and in Acta Materialia 2021, 203, 116472, based on the analysis of experimentally observed nucleation rate data, the liquid may be trapped temporarily in this relaxation process in local minima of the potential energy landscape, resulting in a step-wise change in the work of critical cluster formation and the steady-state nucleation rate.

The scenario described above scenario of nucleation and growth is realized if diffusion (or other appropriate kinetic mechanisms controlling nucleation and growth) and viscosity (responsible widely for the α-relaxation process in the liquid) are decoupled. At such conditions, elastic stresses evolving in nucleation and growth may also significantly affect the crystallization kinetics. Consequently, a comprehensive theoretical description of crystal nucleation and growth near and below the glass transition range has to account appropriately for the effects of deviations of the liquid from the metastable states and of their relaxation on crystal nucleation and the growth of crystals in glass-forming liquids and on the effects caused by simultaneous stress evolution and stress relaxation.

These theoretical concepts have been successfully applied to the interpretation of experimental data on nucleation as shown, e.g., in J. Chem, Phys. 2023, 158, 064501. They also allow for the development of new approaches to the understanding of hysteresis effects in crystallization in cooling and heating, as discussed in detail in Int J Appl Glass Sci. 2022; 13:171–198. To obtain a more comprehensive description of the highly complex crystallization behavior near and below the glass transition, scholars are invited to submit papers to the Special Issue that deal with (i) the determination of the thermodynamic driving force of crystallization and the surface tension as in dependence on the conventional set of thermodynamic state parameters but including also the dependence on a set of appropriately chosen structural order parameters; (ii) methods of description of relaxation of structural order parameters allowing, in particular, researchers to explain step-wise relaxation; (iii) theoretical approaches to the description of stress evolution and relaxation in crystallization accounting for the effect of elastic stresses, both on the thermodynamic driving force of crystallization and on the surface tension; (iv) theoretical description of the effect of deviations from metastable equilibrium and elastic stresses on the kinetic coefficients determining crystallization; (v) experimental methods of analysis of relaxation of structural order parameters and (vi) the application of these approaches to the interpretation of experimental data on the glass transition and the crystallization kinetics of glass-forming melts and glasses.

Dr. Jürn W.P. Schmelzer
Guest Editor

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• crystal nucleation
• crystal growth
• general theory of phase transition
• prediction of properties of glass-forming melts
• glass and glass transition
• thermodynamics of nucleation and growth
• surface thermodynamics
• description of relaxation in deeply undercooled liquids and glasses
• interplay of elastic stress evolution and relaxation on crystallization