Die Begrenzung des Erweichungsintervalles der Gläser und die abnorme Änderung der spezifischen Wärme und des Volumens im Erweichungsgebiet

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

On the theoretical determination of the Prigogine-Defay ratio in glass transition

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.