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Special Issue "Crystallization Thermodynamics"

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

Deadline for manuscript submissions: 31 August 2019.

Special Issue Editor

Guest Editor
Dr. habil. Jürn W.P. Schmelzer

Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23–25, 18059 Rostock, Germany
Website | E-Mail
Phone: +49 381 4986889
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 Issue Information

Dear colleagues,

The theoretical description of crystallization processes has a long history. Nevertheless, it remains an actively developing area of research with a variety of unresolved and newly evolving problems and a wide spectrum of applications. The classical theory of nucleation and growth processes assumes that crystallization proceeds via the formation of small crystallites, with properties being essentially the same as those of the finally evolving macroscopic phases. This assumption allows one to describe theoretically nucleation and growth processes in a qualitatively adequate way but leads to significant problems in reconciling theory and experiment quantitatively. New theoretical developments and advanced experimental analysis are required to fill this gap, which is the topic proposed for this Special Issue. Particular problems in this direction are, for example, (i) the further elaboration of methods to determine the thermodynamic driving force of crystallization by advancing the knowledge of phase diagrams of multi-component systems and the methods of theoretical predictions of the properties of the melts, (ii) the further development of methods of specification of the curvature dependence of the surface tension in the classical theory of nucleation and growth and its generalizations, (iii) the specification of both bulk and surface properties of critical crystallites in dependence on the degree of deviation from equilibrium, (iv) the interplay of crystal nucleation and glass transition in cooling processes, (v) the qualitative change of the response of the ambient phase on crystallization near to the glass transition temperature, (vi) crystallization and growth in inhomogeneous media, and (vii) new methods of specification of the crystallization activity of heterogeneous nucleation cores. In the present Special Issue, it is proposed to concentrate on thermodynamic aspects being one of the essential ingredients of the theory of crystallization processes.

Dr. habil. Jürn W. P. Schmelzer
Guest Editor

Manuscript Submission Information

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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.

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Keywords

  • crystal nucleation
  • crystal growth
  • general theory of phase transition
  • phase diagrams
  • prediction of properties of glass-forming melts
  • glass and glass transition
  • thermodynamics of nucleation
  • surface thermodynamics
  • surface energies in surfaces and interfaces

Published Papers (3 papers)

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Research

Open AccessArticle
Distinguishing between Clausius, Boltzmann and Pauling Entropies of Frozen Non-Equilibrium States
Entropy 2019, 21(8), 799; https://doi.org/10.3390/e21080799
Received: 13 June 2019 / Revised: 9 August 2019 / Accepted: 12 August 2019 / Published: 15 August 2019
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Abstract
In conventional textbook thermodynamics, entropy is a quantity that may be calculated by different methods, for example experimentally from heat capacities (following Clausius) or statistically from numbers of microscopic quantum states (following Boltzmann and Planck). It had turned out that these methods do [...] Read more.
In conventional textbook thermodynamics, entropy is a quantity that may be calculated by different methods, for example experimentally from heat capacities (following Clausius) or statistically from numbers of microscopic quantum states (following Boltzmann and Planck). It had turned out that these methods do not necessarily provide mutually consistent results, and for equilibrium systems their difference was explained by introducing a residual zero-point entropy (following Pauling), apparently violating the Nernst theorem. At finite temperatures, associated statistical entropies which count microstates that do not contribute to a body’s heat capacity, differ systematically from Clausius entropy, and are of particular relevance as measures for metastable, frozen-in non-equilibrium structures and for symbolic information processing (following Shannon). In this paper, it is suggested to consider Clausius, Boltzmann, Pauling and Shannon entropies as distinct, though related, physical quantities with different key properties, in order to avoid confusion by loosely speaking about just “entropy” while actually referring to different kinds of it. For instance, zero-point entropy exclusively belongs to Boltzmann rather than Clausius entropy, while the Nernst theorem holds rigorously for Clausius rather than Boltzmann entropy. The discussion of those terms is underpinned by a brief historical review of the emergence of corresponding fundamental thermodynamic concepts. Full article
(This article belongs to the Special Issue Crystallization Thermodynamics)
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Open AccessFeature PaperArticle
Heterogeneous Nucleation in Solutions on Rough Solid Surfaces: Generalized Gibbs Approach
Entropy 2019, 21(8), 782; https://doi.org/10.3390/e21080782
Received: 19 July 2019 / Revised: 6 August 2019 / Accepted: 7 August 2019 / Published: 9 August 2019
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Abstract
Heterogeneous nucleation of new phase clusters on a rough solid surface is studied. The ambient phase is considered to be a regular supersaturated solution. In contrast to existing studies of the same problem, the possible difference between the state parameters of the critical [...] Read more.
Heterogeneous nucleation of new phase clusters on a rough solid surface is studied. The ambient phase is considered to be a regular supersaturated solution. In contrast to existing studies of the same problem, the possible difference between the state parameters of the critical cluster and the corresponding parameters of a newly formed macroscopic phase is accounted for. This account is performed within the framework of the generalized Gibbs approach. Surface imperfections are chosen in the form of cones. The model allows us to simplify the analysis but also to obtain the basic results concerning the defect influence on the nucleation process. It is shown that the catalytic activity factor for nucleation of the cone depends both on the cone angle and the supersaturation in the solution determining the state parameters of the critical clusters. Both factors considerably affect the work of critical cluster formation. In addition, they may even lead to a shift of the spinodal curve. In particular, in the case of good wettability (macroscopic contact angle is less than 90°) the presence of surface imperfections results in a significant shifting of the spinodal towards lower values of the supersaturation as compared with heterogeneous nucleation on a planar solid surface. With the decrease of the cone pore angle, the heterogeneous spinodal is located nearer to the binodal, and the metastability range is narrowed, increasing the range of states where the solution is thermodynamically unstable. Full article
(This article belongs to the Special Issue Crystallization Thermodynamics)
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Open AccessArticle
Entropy and the Tolman Parameter in Nucleation Theory
Entropy 2019, 21(7), 670; https://doi.org/10.3390/e21070670
Received: 23 May 2019 / Revised: 26 June 2019 / Accepted: 5 July 2019 / Published: 9 July 2019
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Abstract
Thermodynamic aspects of the theory of nucleation are commonly considered employing Gibbs’ theory of interfacial phenomena and its generalizations. Utilizing Gibbs’ theory, the bulk parameters of the critical clusters governing nucleation can be uniquely determined for any metastable state of the ambient phase. [...] Read more.
Thermodynamic aspects of the theory of nucleation are commonly considered employing Gibbs’ theory of interfacial phenomena and its generalizations. Utilizing Gibbs’ theory, the bulk parameters of the critical clusters governing nucleation can be uniquely determined for any metastable state of the ambient phase. As a rule, they turn out in such treatment to be widely similar to the properties of the newly-evolving macroscopic phases. Consequently, the major tool to resolve problems concerning the accuracy of theoretical predictions of nucleation rates and related characteristics of the nucleation process consists of an approach with the introduction of the size or curvature dependence of the surface tension. In the description of crystallization, this quantity has been expressed frequently via changes of entropy (or enthalpy) in crystallization, i.e., via the latent heat of melting or crystallization. Such a correlation between the capillarity phenomena and entropy changes was originally advanced by Stefan considering condensation and evaporation. It is known in the application to crystal nucleation as the Skapski–Turnbull relation. This relation, by mentioned reasons more correctly denoted as the Stefan–Skapski–Turnbull rule, was expanded by some of us quite recently to the description of the surface tension not only for phase equilibrium at planar interfaces, but to the description of the surface tension of critical clusters and its size or curvature dependence. This dependence is frequently expressed by a relation derived by Tolman. As shown by us, the Tolman equation can be employed for the description of the surface tension not only for condensation and boiling in one-component systems caused by variations of pressure (analyzed by Gibbs and Tolman), but generally also for phase formation caused by variations of temperature. Beyond this particular application, it can be utilized for multi-component systems provided the composition of the ambient phase is kept constant and variations of either pressure or temperature do not result in variations of the composition of the critical clusters. The latter requirement is one of the basic assumptions of classical nucleation theory. For this reason, it is only natural to use it also for the specification of the size dependence of the surface tension. Our method, relying on the Stefan–Skapski–Turnbull rule, allows one to determine the dependence of the surface tension on pressure and temperature or, alternatively, the Tolman parameter in his equation. In the present paper, we expand this approach and compare it with alternative methods of the description of the size-dependence of the surface tension and, as far as it is possible to use the Tolman equation, of the specification of the Tolman parameter. Applying these ideas to condensation and boiling, we derive a relation for the curvature dependence of the surface tension covering the whole range of metastable initial states from the binodal curve to the spinodal curve. Full article
(This article belongs to the Special Issue Crystallization Thermodynamics)
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