Journal Browser

Journal Browser

Structural Relaxation in Glass Transition and Crystallization Thermodynamics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (15 May 2024) | Viewed by 1226

Special Issue Editor

E-Mail Website
Guest Editor
Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23–25, 18059 Rostock, Germany
Interests: glass and the glass transition, thermodynamics, structure, rheology, relaxation, and crystallization kinetics; thermodynamics and kinetics of first-order phase transitions, theory and applications; crystal nucleation and interplay of crystallization and glass transition
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • 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

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:


35 pages, 6220 KiB  
Effects of Structural Relaxation of Glass-Forming Melts on the Overall Crystallization Kinetics in Cooling and Heating
by Jürn W. P. Schmelzer, Timur V. Tropin and Christoph Schick
Entropy 2023, 25(11), 1485; https://doi.org/10.3390/e25111485 - 26 Oct 2023
Cited by 1 | Viewed by 812
In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to [...] Read more.
In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to the current values of pressure and temperature. However, near and below the glass transition temperature, Tg, this condition is commonly not fulfilled. In such cases, in the treatment of crystallization, deviations in the state of the liquid from the respective metastable equilibrium state have to be accounted for when determining the kinetic coefficients governing the crystallization kinetics, the thermodynamic driving force of crystallization, and the surface tension of the aggregates of the newly evolving crystal phase including the surface tension of critical clusters considerably affecting the crystal nucleation rate. These factors may greatly influence the course of the overall crystallization process. A theoretical analysis of the resulting effects is given in the present paper by numerical solutions of the J(ohnson)–M(ehl)–A(vrami)–K(olmogorov) equation employed as the tool to model the overall crystallization kinetics and by analytical estimates of the crystallization peak temperatures in terms of the dependence on cooling and heating rates. The results are shown to be in good agreement with the experimental data. Possible extensions of the theory are anticipated and will be explored in future analysis. Full article
Show Figures

Figure 1

Back to TopTop