Glasses and the Glass Transition E-Book

Jürn W. P. Schmelzer

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 847

Veröffentlichungsjahr: 2011

Beschreibung

Written by renowned researchers in the field, this up-to-date treatise fills the gap for a high-level work discussing current materials and processes. It covers all the steps involved, from vitrification, relaxation and viscosity, right up to the prediction of glass properties, paving the way for improved methods and applications. For solid state physicists and chemists, materials scientists, and those working in the ceramics industry. With a preface by L. David Pye and a foreword by Edgar D. Zanotto

Leseprobe

Contents

Cover

Title page

Copyright page

Foreword

Preface

Contributors

Chapter 1: Introduction

Chapter 2: Basic Properties and the Nature of Glasses: an Overview

2.1 Glasses: First Attempts at a Classification

2.2 Basic Thermodynamics

2.3 Crystallization, Glass Transition and Devitrification of Glass-Forming Melts: an Overview of Experimental Results

2.4 The Viscosity of Glass-Forming Melts

2.5 Thermodynamic Properties of Glass-Forming Melts and Glasses: Overview on Experimental Results

2.6 Thermodynamic Nature of the Glassy State

2.7 Concluding Remarks

Chapter 3: Generic Theory of Vitrification of Glass-Forming Melts

3.1 Introduction

3.2 Basic Ideas and Equations of the Thermodynamics of Irreversible Processes and Application to Vitrification and Devitrification Processes

3.3 Properties of Glass-Forming Melts: Basic Model Assumptions

3.4 Kinetics of Nonisothermal Relaxation as a Model of the Glass Transition: Change of the Thermodynamic Functions in Cyclic Cooling-Heating Processes

3.5 The Prigogine–Defay Ratio

3.6 Fictive (Internal) Pressure and Fictive Temperature as Structural Order Parameters

3.7 On the Behavior of the Viscosity and Relaxation Time at Glass Transition

3.8 On the Intensity of Thermal Fluctuations in Cooling and Heating of Glass-Forming Systems

3.9 Results and Discussion

Chapter 4: Generic Approach to the Viscosity and the Relaxation Behavior of Glass-Forming Melts

4.1 Introduction

4.2 Pressure Dependence of the Viscosity

4.3 Relaxation Laws and Structural Order Parameter Approach

Chapter 5: Thermodynamics of Amorphous Solids, Glasses, and Disordered Crystals

5.1 Introduction

5.2 Experimental Evidence on Specific Heats and Change of Caloric Properties in Glasses and in Disordered Solids: Simon’s Approximations

5.3 Consequences of Simon’s Classical Approximation: the ΔG(T) Course

5.4 Change of Kinetic Properties at Tg and the Course of the Vitrification Kinetics

5.5 The Frenkel–Kobeko Postulate in Terms of the Generic Phenomenological Approach and the Derivation of Kinetic and Thermodynamic Invariants

5.6 Glass Transitions in Liquid Crystals and Frozen-in Orientational Modes in Crystals

5.7 Spectroscopic Determination of Zero-Point Entropies in Molecular Disordered Crystals

5.8 Entropy of Mixing in Disordered Crystals, in Spin Glasses and in Simple Oxide Glasses

5.9 Generalized Experimental Evidence on the Caloric Properties of Typical Glass-Forming Systems

5.10 General Conclusions

Chapter 6: Principles and Methods of Collection of Glass Property Data and Analysis of Data Reliability

6.1 Introduction

6.2 Principles of Data Collection and Presentation

6.3 Analysis of Existing Data

6.4 About the Reliability of the Authors of Publications

6.5 General Conclusion

Chapter 7: Methods of Prediction of Glass Properties from Chemical Compositions

7.1 Introduction: 120 Years in Search of a Silver Bullet

7.2 Principle of Additivity of Glass Properties

7.3 First Attempts of Simulation of Nonlinear Effects

7.4 Structural and Chemical Approaches

7.5 Simulation of Viscosity of Oxide Glass-Forming Melts in the Twentieth Century

7.6 Simulation of Concentration Dependencies of Glass and Melt Properties at the Beginning of the Twenty-First Century

7.7 Simulation of Concentration Dependencies of Glass Properties in Nonoxide Systems

7.8 Summary: Which Models Were Successful in the Past?

7.9 Instead of a Conclusion: How to Catch a Bluebird

Chapter 8: Glasses as Accumulators of Free Energy and Other Unusual Applications of Glasses

8.1 Introduction

8.2 Ways to Describe the Glass Transition, the Properties of Glasses and of Defect Crystals: a Recapitulation

8.3 Simon’s Approximation, the Thermodynamic Structural Factor, the Kinetic Fragility of Liquids and the Thermodynamic Properties of Defect Crystals

8.4 The Energy, Accumulated in Glasses and Defect Crystals: Simple Geometric Estimates of Frozen-in Entropy and Enthalpy

8.5 Three Direct Ways to Liberate the Energy, Frozen-in in Glasses: Crystallization, Dissolution and Chemical Reactions

8.6 The Fourth Possibility to Release the Energy of Glass: the Glass/Crystal Galvanic Cell

8.7 Thermoelectric Driving Force at Metallic Glass/Crystal Contacts: the Seebeck and the Peltier Effects

8.8 Unusual Methods of Formation of Glasses in Nature and Their Technical Significance

8.9 Some Conclusions and a Discussion of Results and Possibilities

Chapter 9: Glasses and the Third Law of Thermodynamics

9.1 Introduction

9.2 A Brief Historical Recollection

9.3 The Classical Thermodynamic Approach

9.4 Nonequilibrium States and Classical Thermodynamic Treatment

9.5 Zero-Point Entropy of Glasses and Defect Crystals: Calculations and Structural Dependence

9.6 Thermodynamic and Kinetic Invariants of the Glass Transition

9.7 Experimental Verification of the Existence of Frozen-in Entropies

9.8 Principle of Thermodynamic Correspondence and Zero-Point Entropy Calculations

9.9 A Recapitulation: the Third Principle of Thermodynamics in Nonequilibrium States

Chapter 10: On the Etymology of the Word “Glass” in European Languages and Some Final Remarks

10.1 Introductory Remarks

10.2 “Sirsu”, “Shvistras”, “Hyalos”,“Vitrum”, “Glaes”, “Staklo”, “Cam”

10.3 “Vitreous”, “Glassy” and “Glasartig”, “Vitro-crystalline”

10.4 Glasses in Byzantium, in Western Europe, in Venice, in the Balkans and Several Other Issues

10.5 Concluding Remarks

References

Index

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The Authors

Dr. habil. Jürn W.P. SchmelzerInstitut für Physik Universität Rostock Rostock, Germany

Prof. Ivan S. GutzowBulgarian Academy of Sciences Institute of Physical Chemistry Sofia, Bulgaria

Prof. Oleg V. MazurinThermexSt. Petersburg, Russian Federation

Dr. Snejana V. TodorovaBulgarian Academy of Sciences Geophysical Institute Sofia, Bulgarien

Dr. Boris B. PetroffBulgarian Academy of Sciences Institute of Solid State Physics Sofia, Bulgarien

Prof. Alexander I. PrivenThermexSt. Petersburg, Russian Federation Cover

The cover-picture shows a sample of diopside glass heat-treated at 870– C for about one hour. In the bulk of the sample, one can observe a spherulite of a wollastonite-like phase having a composition similar to that of the diopside glass. The crystalline dendrites below appeared on the surface of a crack (by courtesy of Prof. Vladimir M. Fokin, St. Petersburg, Russia).

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Foreword

First I would like to stress that the main authors of this monograph – Jürn W.P. Schmelzer and Ivan Gutzow – are renowned experts on properties of glasses, relaxation and phase formation processes in glasses that include glass transition, liquid—liquid phase separation, crystal nucleation, crystal growth and overall crystallization processes. In the present book, their attention is concentrated on the description of glasses and glass transition. In analyzing this circle of problems, of special relevance is their strong background on thermodynamics; they always bring their research projects into a solid thermodynamic framework. Their new monograph Glasses and the Glass Transition is no exception; it could be also be named, for instance, Thermodynamics of the Vitreous State. In this book, they review, organize and summarize – within a historical perspective and discussing alternative approaches – the results of their own publications on different thermodynamic aspects of the vitreous state performed after the publication of their book, The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization published by Springer in 1995.

After the introduction, in Chapter 2, Schmelzer and Gutzow disclose their ideas on the nature of glasses through an overview of the basic laws of classical thermodynamics, the description of nonequilibrium states, phase transitions, crystallization, viscosity of glass-forming systems, thermodynamic properties of glass-forming melts, glass transition, and on the overall thermodynamic nature of the glassy state. Most of the presented concepts are discussed within a thermodynamic perspective.

In Chapter 3, they present and discuss in detail a “generic theory of vitrification of liquids” and explain the application of thermodynamics of irreversible processes to vitrification. Then, the authors review relaxation of glass-forming melts, define the glass transition, comment on the entropy at very low temperatures, the Kauzmann paradox, the Prigogine–Defay ratio – including several quantitative estimates of this parameter – the concept of fictive temperature as a structural order parameter, the viscosity and relaxation time at Tg, and finally frozen-in thermodynamic fluctuations. Once more, all these important characteristics of the vitreous state are discussed within thermodynamic insights. These concepts are developed in more detail in the application to relaxation and the pressure dependence of the viscosity in Chapter 4, and an analysis of systems with a glass-like behavior in Chapter 5.

In order to apply thermodynamic methods, in general, and to glasses and glass transition, in particular, the thermodynamic properties of the respective systems, such as the equations of state, must be known. In order to give an overview on the present state in this direction, the book also comprises two special chapters: Chapter 6, authored by Oleg Mazurin on the collection and analysis of glass property data; and Chapter 7, written by Alexander Priven, discusses the available models to correlate certain glass properties to their chemical composition.

Mazurin was the head of the famous Laboratory of Glass Properties of the Grebenshchikov Institute of Silicate Chemistry of the Russian Academy of Sciences in the former USSR, for almost 40 years. Then he retired and dedicated his efforts to his present passion: collection and critical analysis of glass property data. He worked intensively and published numerous papers on many types of glass properties, and perhaps most importantly, from the early stages he started to collect property data from his own group and from published literature to finally mastermind the assembly of an impressive and most useful glass database – SciGlass – which currently contains the properties of more than 350 000 glass compositions. In my opinion this database is a must in the library of any active glass research group in the world. I am particularly proud to say that my students and I have been using the SciGlass database for several years from its very beginning. In this chapter, Mazurin discusses the power of SciGlass, which is regularly updated on an annual basis, and its multiple utilities. The author emphasizes how one can and should use SciGlass to compare the values of properties measured by any author against all the available data. He also stresses a nasty and frequent problem; that is, the poor quality of data published by some research groups.

Having at one’s disposal such a comprehensive overview on existing experimental data on glass properties, the next question arises whether it is possible to theoretically predict – based on such knowledge – some properties of glass-forming systems, for which experimental data are not available. This task is reviewed in the chapter written by Priven. It is probably fair to say that Priven dedicated almost his entire career to this very important scientific and technological theme: development and testing of models to predict the compositional dependence of important glass properties, such as density, thermal expansion coefficient, refractive index, liquidus and viscosity, to their chemical composition. Priven has been involved in the arduous and complex quest of what he calls the “silver bullet.” Although I never carried out any specific research on this particular subject, I have always been a keen user of Appen’s model, and lately of Priven’s model, to calculate glass properties from chemical composition for the development of new glasses and glass-ceramics (which always have a residual glass matrix). Priven discusses the strengths and weaknesses of several available models, for example, Winkelman and Schott’s, Gelhoff and Thomas’s, Gilard and Dubrul’s, Huggins and Sun’s, Appen’s, Demkina’s, Mazurin’s, Fuxi’s, Lakatos’s and of his own model. He also discusses the numerous difficulties to develop an accurate model due to the nonexistence of data for many compositions and nonlinear effects, such as the anomalous effects of boron and alumina, which fortunately have been already solved by some of these models. At present one can use Priven’s model and some others for surprisingly

good predictions (say within 5–10%) of several properties of glasses containing up to 30 elements. But the “silver bullet” – to accurately predict the properties of all possible glasses with combinations of all the 80 “friendly” elements of the periodical table – is far from being found (please check the Zanotto paper on this topic published in the Journal of Non-Crystalline Solids, 347 (2004) 285–288).

After completion of the general task, that is, the thermodynamic description of glasses and the glass transition, the overview on existing data on glasses and the methods of prediction of glass properties, Schmelzer and Gutzow go over to a more detailed discussion of some peculiar properties of glasses and glass-like systems and their possible technological applications. Chapter 8 deals with “glasses as accumulators of free energy, of increased reactivity and as materials with unusual applications,” whereas Chapter 9 is devoted to the third law of thermodynamics and its application to the vitreous state. It is usually stated that the third law is not applicable to glasses as they never reach equilibrium for temperatures tending to zero. Therefore, their entropy has to be larger than zero for T → 0. The authors present a detailed historical development, describe the application of thermodynamics to nonequilibrium states, show some thermodynamic and kinetic invariants at Tg and give an extended discussion on the current controversial issue of zero-point entropy of glasses. The book is completed by an interesting analysis of the etymology of the word “glass.”

Summarizing, the present book presents a thorough discussion about the nature of glass, with a rich historical background (a characteristic of Ivan Gutzow) on the most basic properties of glasses including vitrification kinetics, relaxation and glass transition. It cites more than 650 articles. This book will certainly be a very useful reference for experienced researchers as well as for post-graduate students who are interested in understanding the nature of glass and the application of the laws of thermodynamics to nonequilibrium materials such as glasses.

Edgar D. Zanotto

August 2010

Head of the Vitreous Materials LaboratoryFederal University of São Carlos, BrazilMember of the Brazilian Academy of SciencesMember of the World Academy of CeramicsFellow of the British Society of Glass Technology

Preface

Nearly all authors of modern science-based books aspire to write the definitive summary of a chosen subject, a field of inquiry, or the history or future of an emerging discipline. Books such as the Theory of Metals and Alloys by N. Mott and H. Jones, Introduction to Solid State Physics by C. Kittel, and The Nature of the Chemical Bond by L. Pauling readily come to mind in this regard. This book, more correctly a treatise, by Jürn W.P. Schmelzer and Ivan S. Gutzow, with collaboration by Oleg V. Mazurin, Alexander I. Priven, Snejana V. Todorova, and Boris P. Petroff, rises to this level in its comprehensive summary of the field of glass science. Drawing heavily on thermodynamics, kinetic theory, and the physical sciences, virtually all aspects of the material glass including the transition of an undercooled melt to the glassy state, are summarized in an authoritative, scholarly, and convincing manner. Not only is the scope and volume of material examined for this treatise impressive, so is the way in which it was compiled. That is, the compilation was made through an exhaustive, comprehensive review and evaluation of the major literature on this subject from the present day contributions back to the beginning of the last century.

The authors were aided immeasurably by a facility to read articles as they appeared in their original language thereby helping to gain special and even essential historical insight into the value and scientific correctness of the material being reviewed. This in turn allowed a more global approach in direct support of producing an authoritative discourse on glass and the glass transition. Worthy of exceptional praise is their discussion of glass and third law of thermodynamics found in Chapter 9. It gives credence to accepting glass science as a major field in its own right and the need for nearly all theorists to understand what glass is.

The completion of this task is, in fact, a life-long labor of love for these authors, one which could only be undertaken by a handful of scientists across the globe who have shared a similar devotion to this subject throughout their professional lives. In short, they have accomplished their intended purpose in preparing this treatise: writing the definitive description of glass and the glass transition. It holds potential to be recognized as a remarkable milestone.

And what might be the expected outcomes of this Herculean task? As a university professor, I use to make sure my students understood that the penultimate essence of science is to predict – to predict facts that are known and can be measured, to predict those that are unknown, and make sure the predictions are quantitative.

That is, science must be quantified through mathematical treatment. Through the authors’ mathematical description of the material of glass and its properties including the glass transition, practicing glass scientists and engineers will find this book invaluable in helping them understand and predict the behavior of glass in a wide range of settings and applications. It will no doubt be a springboard to the development of advanced and possibly even more mathematically rigorous theories of the vitreous state as new observations are recorded, and their meaning explored.

Additionally, it will be difficult to prepare a manuscript or professional presentation on glass or the glass transition without understanding or referencing this contribution to the scientific literature. In a similar way, countless students engaged in thesis work on glass will surely become familiar with this treatise, if their academic work involves fabrication, characterization, or application.

For all of these reasons, it is confidently predicted this treatise will gain international recognition – not only across the entire materials spectrum – but also in the broader fields of physics and chemistry. And for this potential, the authors and their collaborators should take a well-deserved bow.

L. David Pye

August 2010

Professor of Glass Science, Emeritus, Alfred University, USAPast President of the International Commission on GlassPast President of the American Ceramic SocietyHonorary Member of the German Society of Glass TechnologyHonorary Fellow, the British Society of Glass Technology

Contributors

Oleg V. Mazurin, Thermex, St. Petersburg, Russia, [email protected], Ph.D. (1953); D.Sc. (1962). Head of the Laboratory of Glass Properties (Grebenshchikov Institute of Silicate Chemistry of the Academy of Sciences of the USSR) from 1963 to 1999. Editor of the Journal Glass Physics and Chemistry from 1990 to 2000. Regional editor of the Journal of Non-Crystalline Solids from 1983 to 1990. Author and co-author of more than 400 papers, 14 books in Russian (including one hand-book in 9 volumes) and 3 books in English (including one hand-book in 5 volumes). Leading author of the scientific database for the Glass Property Information System SciGlass. Awarded by the Morey Award “for outstanding achievements in glass science” from the American Ceramic Society, Columbus (1994) and by the President’s award from the International Commission on Glass (2001). Field of expertise: studies of electrical conductivity, viscosity, thermal expansion, relaxation characteristics of inorganic glasses and melts, glass transition phenomenon, phase separation in glasses, collection and analysis of published data on properties of inorganic glasses.

Alexander I. Priven, ITC Inc., St Petersburg, Russia, [email protected], Ph.D. (1998), D.Sc. (2003). Author of methods for prediction of various physical properties of glasses and glass-forming melts in wide composition and temperature ranges. The dominant area of interest is simulation of the dependencies of physical properties of glasses and glass-forming melts on concentration, temperature and thermal history. Took part in the development of SciGlass Information System and other material property databases. Worked as a consultant for Samsung Corning Precision Glass Co. (South Korea), Corning Inc. (USA),

Snejana V. Todorova, Geophysical Institute, Bulgarian Academy of Sciences, Sofia, Bulgaria, [email protected], Associate Professor in geophysics at BAS and specialist of cloud microphysics, Dr. Todorova came to the problems of glass transition from joint investigations with I. Gutzow and J. Schmelzer on the kinetics of nucleation. Of particular significance in writing the present book was also her interest in processes of planetary and cosmic formation of vitreous ice and in the possible existence of intermediate amorphous stages in vapor condensation.

Boris P. Petroff, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria, [email protected], As a theoretical physicist with excellent knowledge in many fields of solid state and intermediate liquid/solid forms of condensed matter and especially in liquid crystals, Boris Petroff provided for the present book the necessary links between typical glasses and other forms of systems with frozen-in defect structure.

Reflections of some of the discussions held over the course of preparation for the present monograph (Ivan S. Gutzow, Jürn W.P. Schmelzer, and Oleg V. Mazurin (from left to right))

Chapter 1

Introduction

Jürn W. P. Schmelzer and Ivan S. Gutzow

The present book is devoted to the ways of formation, to the analysis of the properties and to the theoretical description of matter in a very particular state: in the vitreous state. In such a state, as it is usually assumed, amorphous solids may exist with a kinetically frozen-in, rigid structure and correspondingly frozen-in thermodynamic and mechanical properties. In technical applications and in every-day life as materials, in solid state physics, in scientific literature and also in the title of the present book these amorphous solids are called glasses. Glasses are formed in a process, which is also very particular in its physics, in its kinetics and thermodynamics, in the process of glass transition or vitrification. The reverse process is denoted as devitrification, and is frequently but not always accompanied by crystallization processes. Definitions of both these notions are given in this book, accounting for present-day results of structural analysis, statistical physics and especially of thermodynamics of glasses, since thermodynamics is the science that decides over the states of matter.

It turns out that many solids, even with a partly crystalline structure, behave in their properties and thermodynamic state-like glasses: such solids with a frozen-in defect crystalline structure (e.g., defect molecular crystals) are sometimes called glass-like, or even glassy crystals. It is shown in one of the following chapters, that highly oriented liquids, so-called liquid crystals, also form glasses, corresponding to the particular structure of the precursor liquid. Another very particular class of solids with usually crystalline structure but with glass-like magnetic properties are the spin glasses.

The process of glass transition has general, characteristic and remarkable features, which are observed not only in the vitrification of glass-forming melts and in other processes of glass formation to be discussed in details in the present book (e.g., vapor quenching in the formation of amorphous layers or electrolytic deposition of metallic alloy glasses), but also, according to some authors, in quite different events, for example, in cosmic processes. There are also many models in statistical physics, the solution of which leads to virtual systems with glass-like thermodynamic or kinetic properties; or on the contrary, to solutions of the theory developed, which against the expectations of their authors, are far from the behavior of real (or “common, molecular or laboratory”) glasses.

Out of many possible real or imagined glassy or glass-like systems of different solids with amorphous or defect crystalline frozen-in structure, are the common glasses of every-day life, in particular the technical glasses, who give well-known and best studied examples of the process of glass transition and of the properties of vitreous states. Besides systems with inorganic composition (silicates, phosphates, halides, elemental glasses, etc.), what must also be included are the numerous representatives of organic chemistry (polymers, molecular glasses), aqueous solutions, metal alloys: practically representatives of any known structure and chemical composition. There are, as we have discussed in several publications, serious expectations, based on well-founded kinetic and structural criteria, that almost any substance could be vitrified at appropriately chosen conditions. These expectations are substantiated in our foregoing monograph [1] also devoted to the vitreous state.

However, the best known representatives of vitreous solids still remain the “common” inorganic glasses, which in their composition are oxides and especially silicates. The properties of these silicate, phosphate, borate, and so on, oxide glasses are summarized in a series of monographic reference books and the database organized by Mazurin and his collaborators [2, 3] discussed in detail in one of the chapters of the present book.

Silicate glasses belong with pottery, ceramics and bronze to the oldest materials employed by man. This early widespread application of glasses is in some respect also due to their broad distribution in nature. As an example, magmatic rocks can be mentioned, which to a large degree consists of vitreous silicates, or completely amorphous natural glasses such as obsidian or amber. It is well-known that the natural glass obsidian served as a material for the preparation of the first cutting tools of primitive men. Obsidian remained in the ancient cultures of Central America as the material for objects not only of art but also for the horrible ritual knives of the high priest of these Native American societies. Amber is most probably the first organic glass to be appreciated and used by mankind: impressive with both its beauty and for its unusual dielectric properties, known from ancient times in Greek natural philosophy.

The wide distribution of glasses in nature is not due to chance. The inner part of the Earth, characterized by very high values of pressure and temperature, is most probably itself an enormous reservoir of highly pressurized glass-like or glass-forming melts. Processes of crystallization and glass-formation connected with the eruption of volcanoes and the more or less abrupt cooling and even quenching processes of parts of this melt determine to a large degree the course of geological processes and the structure and properties of the lithosphere. Natural glasses are widespread not only on Earth but also on the Moon as it became evident from the investigation of samples of lunar rocks brought to Earth by the lunar expeditions in the mid-1970s.

Of particular interest is also the vitreous form of water. In this respect it is also worth mentioning that according to estimates made by some authors (see [4, 5]) water in the universe as a whole appears to be practically 99.9% in this vitreous form. In its vitreous form water is the main constituent of comets (of the comet “head”). At earth conditions, glassy water or aqueous solutions can be vitrified only by superfast quenching methods (described in its principle features in Chapter 2) or (as thin layers) by water vapor quenching on cold substrates (held below 120K). On the possible role of vitreous water in the dissemination of life in the universe (the panspermian hypothesis of Hellenistic philosophy) see the considerations given below and in Chapter 8 of the present book.

The first applications of natural glasses in primitive societies for a limited number of purposes were followed by the beginning of glass production in Mesopotamia, Egypt and ancient Rome, by medieval European and Middle East glass-making and then by a long evolution to the modern glass industries and to glass science. From the point of view of the variety of properties of glasses and of the spectrum of possible applications, the significance of the vitreous state in its different forms in present-day technology and the technical importance of different glasses can hardly be estimated. The validity of this statement becomes evident if one tries to imagine for a while things surrounding us in every day life without the components made of vitreous materials. Technical glasses (like chemically resistant glasses) or optical glasses are well-known to everyone. Imagine, for example, a chemical plant, a physical laboratory, a car or a dwelling house without glasses or let us think about the importance of silicate glasses and optical glasses (with their complex compositions) in general for optical devices, and in particular, in microscopy and astronomy.

In addition to the classical oxide and particularly silicate glasses in the last decades of the twentieth century new structural and chemical classes of vitreous materials gained scientific and technical importance. They consist, as said at the beginning of this introduction, of substances of any class, or of mixtures and solutions of different substances, for which the possibility of existence in the vitreous state at these times was thought as being exotic or even impossible. One example in this respect are metallic glasses which are formed usually in processes, connected with hyper-quenching rates (e.g., in splat-cooling, to be discussed in Chapter 2) of metallic or metal-semi-metal alloy systems. Metallic glasses, first synthesized in the early 1960s, in a period of about ten to twenty years were transferred from a stage of exotic research to the stage of production and world-wide technological application. Similar examples are supplied by glassy polymers or vitreous carbon, glass-forming chalcogenide or glassy halide systems. The development of modern methods of information technology, for example, cable TV is also based on glass: on defect-free, extremely translucent glassy fibers with appropriate optical characteristics.

With the dramatic increase of the number of substances obtained in the vitreous state, the variety of properties and possible applications of glasses has also increased. Beyond the traditional applications in technology and science glassy materials are also used as substitutes for biological organs or tissues, for example, as prostheses (as vitreous carbon in heart transplants, as bio-glass ceramics in bone operations) and even in ophthalmology. Glass-forming aqueous solutions with biologically relevant compositions are used as a carrier medium for the freezing-in of biological tissues. Thus, it seems that even life can be frozen-in to a glass solving the problems of absolute anabiosis within the vitreous state. Life, frozen-in to a glass, supports the already mentioned idea of Hellenistic philosophy for the spreading of life from planet to planet. This ancient hypothesis, further developed at the beginning of the twentieth century by Arrhenius [6], was exploited not only in science fiction, but also in more or less, still fantastic proposals to guarantee immortality. The survival of animals (insects, reptilian, etc.) and of marine life at the polar regions of the Earth is also due to controlled crystallization or to the vitrification of cellular biological liquids [7–9]. Freezing-in of domestic animal sperms at liquid nitrogen temperatures to a glassy aqueous solution is for many years a known practice in present-day veterinary zoo-techniques. Porous silicate glasses are used to supply nutrient solutions to microbial populations and slowly soluble glasses containing exotic oxides are used as an ecologically compatible form of micro-element fertilization. These are only a few examples of the biological significance of vitreous materials.

Besides pure glasses, glass ceramics, like Pyroceram, Vitroceram, various sitals, that is, partially crystalline materials formed via the induced devitrification of glasses and glass-forming melts, are also gaining in importance in modern technology, architecture and in the immobilization of ecologically hazardous waste materials. A well-known example of the last mentioned application gives the vitrification of radioactive waste, originating from the nuclear fuel cycle and from nuclear weapons reprocessing. In this way dangerous radioactive materials are immobilized and stored as insoluble glasses, stable for millennia to come.

In glass-ceramic materials the transformation of the melt into the desired vitro-crystalline structure is initiated by a process of induced crystallization usually caused by the introduction of insoluble dopants (more or less active “crystallization cores”) or of appropriate surfactants into the melt. As a result heterogeneous materials are formed in which the properties of both glasses and crystals are combined. In this way, an astonishing variety of new products with extreme properties and unusual possibilities of application is obtained. Classical enamels of every-day cooking ware, the mentioned glass-ceramic materials and so-called glass ceramic enamels for high temperature applications give additional examples in this sense. The physics and the physical chemistry of these materials, the kinetics and the various methods of their formation and the employment of glass ceramics, only mentioned here, is described in detail in many books and review articles and also the previous monograph of Gutzow and Schmelzer [1].

The widespread application and development of different vitreous materials and their production was connected with a thorough study of related scientific and technological aspects, resulting in the publication of a number of monographs, devoted to special classes of vitreous materials or special technological processes like the technology of silicate glasses, glassy polymers, metallic glasses, and so on. In these books specific properties of various vitreous materials are not only discussed in detail, but the attempt is also made to point out the fundamental properties and features which are common to all glasses, independent of the substance from which they are formed and the way they are produced. Latter topic is the focus of the present book. Therefore, particular attention is directed to the specification of the thermodynamic nature of any glass, regardless of its composition or other specific properties. Special glasses or the particular technologies connected with their production are discussed here only so far as it is desirable as an illustration of general statements or conclusions.

We are interested in the present book mainly in finding and describing in an appropriate way the common, general features of glasses. This refers to any of the following chapters and especially to Chapters 2, 3 and 4. There we have tried to elucidate the main, the most characteristic properties of glass-forming substances, common to all or at least to all real, physical glass-forming systems as yet known. In Chapter 2 the thermodynamically significant experimentally known properties of glasses are summarized and compared with the properties of the other forms of existence of matter. Glass transition is paralleled with phase transitions and the similarities and differences are reviewed. In Chapter 3 an attempt is made to correlate in the framework of a generic and generalized phenomenological approach both the kinetics of glass transition and its thermodynamic description. In the same chapter, following the same general approach, developed mainly by its authors in collaboration with several colleagues [1, 10–12], the thermodynamic nature of glasses is analyzed and defined. In doing so the general formulations of the thermodynamics of irreversible processes are applied and developed in a form, first proposed by De Donder [13] and Prigogine [14, 15], convenient to treat glasses as representatives of nonequilibrium systems with frozen-in structure. In Chapter 4 the same approach is used to analyze from a thermodynamic point of view the main kinetic characteristics of glasses: their rheology and viscous flow in particular. Particular emphasis is given in both chapters on the description of viscosity of nonequilibrium systems: here again a proposal by Prigogine [16] is followed in a generic approach, developed by Gutzow, Schmelzer et al. in [1, 17], as it follows from the derivations of Chapters 3 and 4. It is shown in Chapter 5 that many of the common properties of typical glasses are repeated or mimicked in a particular way by many other solids with frozen-in defect structures: even by those, which are crystalline.

A detailed analysis of the experimental results and their initial phenomenological interpretation, given in Chapter 2, leads to the conclusion that from a thermodynamic point of view glasses are frozen-in nonequilibrium systems. The detailed thermodynamic description of such states and their specific thermodynamic and kinetic properties are outlined in Chapters 3,4 and 5. The respective discussion is based on the general postulates of thermodynamics of irreversible processes and, in particular, on the method of description of nonequilibrium states, developed by De Donder [13], Prigogine [14, 15], Glasstone, Laidler, and Eyring [18], Davies and Jones [19, 20] and many following authors as this is given in detail in Chapters 3, 4, 5, 8 and 9.

In Chapters 6 and 7, O.V. Mazurin and A.I. Priven explain and elucidate another problem of present-day glass science: which are the most reliable and convenient ways to collect and preserve, to calculate and to predict the most significant properties of single and multi-component glasses using existing experimental data, summarized in current literature and databases, as it is given the already cited series of reference monographs devoted mainly to silicate and other oxide glass-forming systems.

In Chapter 8 an attempt is made to summarize results on properties of glasses which from the standpoint of every day users are unexpected: their vapor pressure, solubility and electrochemistry. These properties not only illustrate some of the most significant features connected with the thermodynamic nature of glasses, but also give some indications of new and unexpected applications of the different substances in vitreous form. These applications include the usage of glasses as accumulators of hidden potential, of energy, and increased reaction power and (very unusual but possible, e.g., with metallic glasses) as electrochemical power sources. In this chapter also the possibilities of glassy states as a medium of frozen-in life and as promising soluble micro-fertilizers are discussed together with possible employment of soluble glasses in solving some medical problems.

Finally, in Chapter 9 the properties of glasses at extremely low temperatures are considered in detail. In doing so the authors of this chapter were mainly interested in elucidating a very general thermodynamic problem: what would be the most appropriate formulation of the third principle of thermodynamics for nonequilibrium systems, transferred into the vicinity of absolute zero of temperatures. The respective considerations require an analysis of the classical, sometimes already forgotten, formulations of this law as developed by the greatest representatives of classical thermodynamics at the beginning of the twentieth century, like Nernst, Einstein and Planck. Thus, Chapter 9 shows how glass science in its general formulations can give new visions in treating nonequilibrium systems, in general. Glasses, it turns out, are simply the best known representatives of the great class of systems in nonequilibrium. With Chapters 8 and 9 opening new horizons of applications of the vitreous states, the present book deviates from most existing monographs on glass science, treating glasses mostly in their common uses and classical ways of theoretical analysis.

The transformation of more and more substances into the frozen-in, nonequilibrium state of a glass is connected also with a substantial change in the meaning of the word “glass.” Originally under the term glasses only amorphous (in the sense of nonstructured) frozen-in nonequilibrium systems were understood. At present every frozen-in nonequilibrium state (nonamorphous systems included) is denoted sometimes as a glass, for example, frozen-in crystals, crystalline materials with frozen-in magnetic disorder (spin glasses) and so on. The etymology of the word glass in its conventional use is given here in the concluding Chapter 10.

Despite its mentioned distinguishing features, the present book is in many respects a direct continuation and development of ideas formulated and exploited in several preceding books by the present authors which, to their satisfaction, were met with interest by the glass community. These publications are firstly the already mentioned collection of available data of Mazurin and colleagues on the properties of oxide glasses (and of silicate glasses in particular) [2, 3]. Secondly, the present book incorporates the concepts from the book by Gutzow and Schmelzer [1] in which the basic ideas on the phenomenology of glass transition, on simple glass models, on molecular statistics and on the crystallization of glass were summarized, corresponding to the state of knowledge at the time of its publication. In its phenomenological aspect this monograph by Gutzow and Schmelzer [1] is to a great extent based on an approximate way of treating the thermodynamics of glasses, proposed many years ago by Simon [21–23]. This fruitful but nevertheless approximate approach is brought in the mentioned monograph to its completion and many useful results are obtained in its framework. Moreover, ways are initiated there, based on the thermodynamics of irreversible processes, to develop a more general approach in the kinetics of glass transition and on the relaxation of glasses, which are developed here to a new level of understanding and application in Chapters 3 and 4. These new ideas are developed in the mentioned parts of the present book in the form of a new generic description on the kinetic processes, connected with glass formation and glass stabilization, as glass relaxation is also called. In doing so we have tried to take account of the whole development in this field of glass science, and especially in what was called in Russian literature the kinetic theory of glass transition; in fact, new thermodynamic foundations are given to this approach in both mentioned chapters of the present book. Moreover, out of it a full generic thermodynamic theory of glass transition is derived there in the frameworks of the thermodynamics of irreversible processes and the course of thermodynamic functions upon which glass transition is constructed. In treating technological problems in the already mentioned multi-volume monograph and reference book, compiled and edited by Mazurin et al. [2, 3], also opened are new, empirical and theoretical ways in predicting glass properties: by establishing connections, property vs. composition, to predict the properties of still not synthesized multi-component glasses out of their composition.

As it is seen from the above summary, the present book is directed towards the fundamental problems of glass science which are important for understanding the properties of glasses as a particular state of matter. In this discussion of the basic ideas concerning the vitreous state the historic course of their evolution is also briefly mentioned. In this discussion, a chronologically exact or comprehensive description is not attempted, but a characterization of the inner logics of the historical evolution, the interconnection of different ideas within it. This approach implies that in addition to the most fruitful concepts, which revealed themselves as real milestones in the evolution of glass science, proposals were also analyzed, which already at the time of their formulation or by the subsequent developments, were shown to be incorrect or even misleading, at least, as far as it is known today. It is the opinion of the authors that only by such an approach can a correct picture be given of the evolution of science as a struggle between different or even contradicting ideas. On the other hand, the detailed analysis of different proposals and the proof that some of them are not correct or even misleading is of an undoubted heuristic value. Such an approach can, the present authors hope, also prevent an over-enthusiasm with respect to insufficiently substantiated new or super-new hypotheses or to old, already refuted ideas presented in a modern form.

In the list of literature the interested reader may search for ideas and developments, results and interpretations, which could not be included in this volume. The present authors had to concentrate on those problems and solutions that formed the main roots of development of the knowledge of the vitreous state into a new well-founded science. As far as the present authors took an active part in this development, their results and publications are in many cases discussed in detail. In the theoretical interpretations in the present volume, as already mentioned, the phenomenological approach and the thorough comparison with experimental data is preferred: in this way, at least serious mistakes, common in the history of glass science will hopefully not be repeated. Where possible, as given in Chapters 6 and 7, a general survey of existing experimental data in glass science literature as a method of prediction and scientific prognosis and further development should be recommended. Several statistical model considerations are also introduced here in Chapters 3, 4, 8, and 9, and 9; although, from previous developments it is known that theoretical modeling can be sometimes dangerous. That is, in many cases it is not sufficiently evident, as to what extent inevitable approximations change the real picture of the systems investigated. In this sense phenomenology in many cases has been proven to be a more simple tool in glass science, especially when thermodynamics of irreversible processes is used: glasses are nonequilibrium systems and have to be treated accordingly, even classical thermodynamics may here also be misleading.

The present book represents again an attempt to take up Tammann’s approach, made in his book Der Glaszustand [24] and repeated by two of the present authors in their preceding monograph [1]: to summarize the basic ideas of glass science, including the newest developments, remaining in the framework of only one volume. Many important topics, they initially wanted to include, could not be incorporated due to the lack of space. Other topics – new problems, theoretical approaches and complicated new attempts at a structural or general statistical description – seemed to us to be too complex to be included into one volume, directed not only to the well-established glass scientist, but also to the newcomers to a new and exponentially developing science. To simplify things, in many cases only reviews of new developments are given, in order to find a compromise. Hereby we tried to follow – hopefully successfully – the advice given by Einstein: “Everything should be done as simple as possible but not simpler.”

Chapter 2

Basic Properties and the Nature of Glasses: an Overview

Ivan S. Gutzow Jürn W. P. Schmelzer

2.1 Glasses: First Attempts at a Classification

From a molecular-kinetic point of view all substances can exist in three different states of matter: gases, liquids and solids. These three states of aggregation of matter (from the Latin word: aggrego – to unite, to aggregate) are distinguished qualitatively with respect to the degree of interaction of the smallest structural basic units of the corresponding substances (atoms, molecules) and, consequently, with respect to the structure and mobility of the system as a whole.

Gases are characterized, in general, by a relatively low spatial density of the molecules and a relatively independent motion of the particles over distances significantly exceeding their size. The average time intervals τf of free motion in gases are considerably larger than the times of strong interaction (collisions, bound states) in between two or more atoms or molecules. In a first approximation the free volume in a gas is equal to the volume occupied by the system. The molecules can be treated in such an approximation as mathematical points (perfect gases). However, in more sophisticated models, volume, shape and the interaction of the molecules have to be accounted for. Gases are compressible: with a decreasing volume of the gas its pressure increases as expressed, for example, for a perfect gas, by Boyle–Mariotte’s law.

Liquids have a significantly higher density than gases and a considerably reduced free volume. Thus, an independent translation of the building units of the liquid is impossible. The molecular motion in liquids and melts gets a cooperative character and the interaction between the particles determines to a large extent the properties of the system. Moreover, the compressibility is much smaller than for gases, simple liquids are practically incompressible.

According to a simple approximation due to Frenkel [25] liquids can be described in the following way. The motion of the building units of the particles in a liquid can be considered as oscillations around temporary average positions. The temporary centers of oscillations are changed after an average stay time, τR. The mean distance between two subsequently occupied centers of oscillation is comparable with the sizes of the molecules. Every displacement of the building units of the liquid requires thus a more or less distinct way of regrouping the particles and an appropriate configuration of neighboring molecules, for example, the formation of vacancies in terms of the “hole” theories of liquids to be discussed in Chapter 3. Though such a picture of the molecular motion in liquids can be considered only as a first approximation, it explains both the possibility of local order and the high mobility of the particles as a prerequisite for the viscous flow and the change of the shape of the liquids. New insights into the nature of the motion of the building units in glass-forming liquids were developed in a series of publications by Götze [26–28] at the beginning of the 1980s (see also the further work on these ideas cited in [29]).

A quantitative measure for the ability of a system to flow is its shear viscosity, η. According to Frenkel the shear viscosity, η, and the average stay time, τR, are directly connected. This connection, discussed further in Section 2.4.3, becomes evident by the following two equations (Frenkel [25]):

(2.1)

and

(2.2)

By U0 the activation energy of the viscous flow is denoted, kB is the Boltzmann constant and T the absolute temperature. More accurate expressions for the temperature dependence of η are given in Section 2.4.1. Nevertheless, Eqs. (2.1) and (2.2) already show in a qualitatively correct way the significant influence of temperature both on the viscosity η and on the relaxation time, τR.

Liquids like gases have no characteristic shape but acquire the shape of the vessel they are contained in. They are amorphous in the classical sense of the word, that is, a body without its own shape (from the Greek word morphe: shape; amorph: without shape). This classical meaning of the word amorphous is different from its modern interpretation. Today amorphous bodies are understood as condensed (i.e., liquid or solid) systems without long-range structural order being a characteristic property of crystals only.

Solids in classical molecular physics were identified initially with crystals. Their structure can be understood as a periodic repetition in space of a certain configuration of particles composing a certain elementary unit. In addition to the local (short-range) order found already in liquids, a long-range order is established in crystals, resulting in the well-known anisotropy of the properties of crystals. The motion of the atoms is, at least for a perfect crystal, an oscillation around time-independent average positions. This type of motion is connected with the absence of the ability to flow and the existence of a definite shape of crystalline solids.

The properties of gases and liquids are scalar characteristics, while the periodicity in the structure of the crystals determines their anisotropy and the vectorial nature of their properties. Liquids and solid crystals belong to the so-called condensed states of aggregation of matter. In condensed states the intermolecular forces cannot be neglected, in principle.

This classification is, of course, useful only as a first rough division between different states of aggregation of matter. It has its limitations. For example, it was shown that some gas mixtures may undergo decomposition processes, which are the result of the interaction of the particles. Liquids can be brought continuously into the gas phase (cf. van der Waals [30–32] or in a modern interpretation [33, 34]) and vice versa. Perfect, absolutely regular crystals do not exist in nature; moreover, under certain conditions crystals can also show some ability to flow, in particular, so-called plastic crystals. On the other hand, liquids are known (usually denoted as liquid crystals [35]) in which the optical properties of crystals are mimicked in a curious way (e.g., under flow). We will also come across cases where orientational disorder is frozen-in in crystals in the same way as in vitrified undercooled liquids and in other amorphous solids.

The elementary structural classifications given above employ criteria pertaining to the topological form of order (or disorder) exclusively (cf. [1]). Despite this limitation, one of the first questions discussed with the beginning of a scientific investigation of glasses was the analysis of the following problem: to which of the mentioned states of aggregation can glasses be assigned to. Experimental results indicated on one hand that glasses exhibit a practically infinite viscosity, a definite shape, and mechanical properties of solids. On the other hand, typical properties of liquids are also observed in glasses: the amorphous structure, that is, the absence of a long-range topological and orientational order, and the isotropy of its properties.

As a solution to this problem, Parks [36], Parks and Huffman [37] and Berger [38] (see also Blumberg [39]) and subsequently other authors, proposed to define the vitreous state as the fourth state of aggregation in addition to gases, liquids and (crystalline) solids. In this connection we have to mention that similar proposals have also been developed (but never accepted generally) with respect to other systems with unusual structures and properties (liquid crystals, elastomers, gels, etc.) thus introducing the fourth, fifth and further states of aggregation of matter. Already the considerable increase of the number of states of aggregation, which would follow from the acceptance of such proposals, shows that the generalization obtained with the classical division of the states of aggregation would be lost. A considerably more powerful argument against such proposals is connected with the limits of existence, stable coexistence and the possible transformations between the different states of aggregation.

Sometimes the partially or totally ionized state of matter, the plasma state, is denoted as the fourth state of aggregation (compare Arcimovich [40] and Frank-Kamenetzki [41] for its definition and description). The details of the transition of matter into the plasma state cannot be discussed here. It is only to be mentioned that it is quite different in its very nature, when compared with the transformations between the different states of aggregation – gases, liquids and crystals – discussed so far. It seems also that, in attributing the term fourth state of matter to the plasma state, physicists are more or less emotionally influenced by the beautiful schemes of ancient Greek philosophy (e.g., by Anaxagoras and, especially, by Empedocles; see, e.g., Bernal [42]) and its four elemental forces constituting the Universe: air (= gas), water (= liquid), earth (= solid), and fire (= plasma).

It must also be mentioned in connection with further discussions of the structure of glasses that in the same Hellenistic philosophical schemes the five regular (Platonic) polyhedra were also mystically introduced (Figure 2.1) as representing the four elements: tetrahedron (= fire), cube (= earth), octahedron (= air), icosahedron (= water) and the dodecahedron (because of its 12 pentagonic faces, corresponding to the zodiacal signs) as representing the Universe (or the Aristotelian fifth element: the famous quinta essentia). In attributing such meaning to the Platonic bodies, ancient Greek and Medieval and Post-Medieval philosophy (e.g., Kepler) have correctly chosen the icosahedron as representing liquid structures, as proven in many present-day models of liquids and glasses [1] and the cube as giving the basic features of a crystalline solid. The octahedron gives, on the contrary, in the framework of these classical schemes an idea of free movement and thus of the vapor phase.

Figure 2.1 The five regular polyhedra (Platonic bodies): (a) tetrahedron; (b) cube; (c) octahedron; (d) dodecahedron; (e) icosahedron.

The modern concepts concerning the division of matter into different states of aggregation and the structural characteristics of these states stem from the molecular kinetic ideas of the eighteenth century. These ideas were supplemented in the nineteenth century by a simple but unambiguous thermodynamic analysis. Thermodynamics defines the states of aggregation as thermodynamic phases and the transitions in between them as particular cases of transformation between thermodynamic phases. This approach requires first an exact definition and thorough discussion of the significant thermodynamic attributes to the notion of thermodynamic phases and to their classification, to the kinetics and thermodynamics of phase transformations, as they are given in Section 2.2.3.

If we accept the point of view that the states of aggregation are thermodynamic phases, we could call glasses an additional (e.g., a fourth) state of aggregation only, if we could prove that glasses fulfill the requirements thermodynamics connects with the definition of thermodynamic phases. However, such a proof cannot be given, as it is shown in the subsequent analysis. On the contrary, it turns out that glasses are not thermodynamic systems in the classical sense of this statement: they are in fact an example of nonequilibrium states. Thus, in order to understand the nature of glasses first a knowledge of the essentials of classical thermodynamics is necessary: we have to know what thermodynamic phases are and what glasses are not. This is the reason why in Sections 2.2.1 and 2.2.2 basic thermodynamic ideas and principles are summarized and briefly discussed in their application to our field of interest. In this way, a more correct understanding of the states of aggregation and of thermodynamic phases and of transitions taking place between them becomes possible. A more general discussion on this subject is then given in Section 2.2.3 in terms of existing phenomenological approaches, formulated in the framework of classical thermodynamics.

However, in order to analyze glass formation and the nature of glasses – as a particular physical state of nonequilibrium, of frozen-in disorder – an additional knowledge of the basic principles of thermodynamics of irreversible processes is required. Thermodynamics of irreversible processes is in some respects the continuation of classical thermodynamics into the field of nonequilibrium states and processes. It is the science describing in a thermodynamically correct way frozen-in states, their stability and the changes, connected with the processes of relaxation, leading to stable or metastable equilibrium. In many respects, this approach is a more general formulation of thermodynamics. The discussion of these topics and its application to glass formation is given in detail in Chapter 3. This approach is unfortunately little known even among scientists seriously involved in the problems of the analysis of glassy states. Such knowledge is, however, a necessity for the formulation and understanding of these problems and most of the following discussions. Thus a minimum of knowledge of the foundations of the thermodynamics of irreversible processes, at least as they are required here, is outlined in the following discussion in a simplified manner for the reader’s help. A more detailed introduction into this rapidly developing branch of thermodynamic science may be found in the literature cited here, and especially in the books and monographs like [14, 15, 43–48].

Our subsequently performed discussion of existing experimental and theoretical evidence shows, as first outlined in a famous series of publications by Simon [21–23], that glasses are nonequilibrium (i.e., in classical terms: nonthermodynamic) systems and thus they cannot be described comprehensively in the framework of classical thermodynamics (or thermostatics, as this science is also denoted). However, we now also know that glasses and glass transitions give a classical example of systems and processes, which can and have to be analyzed by irreversible thermodynamics. Glasses are thus not “a hard knock to thermodynamics” and it is not true that “…their …thermodynamic description is in principle not possible” [49, 50] as it is sometimes stated even in serious journals by authors seemingly unaware of present-day irreversible thermodynamics. Glasses are on the contrary a brilliant case for illustrating the possibilities of thermodynamic analysis and of phenomenological treatment in general, however, only when thermodynamics is applied in its correspondingly enlarged formulations, appropriate for treating irreversible processes. It can be even stated that the treatment of frozen-in disorder and of nonequilibrium states, as this was demonstrated first on the example of several silicate and organic glasses (see Sections 2.5) and then of the vitreous state as a whole, determined to a great extent the development of thermodynamics of irreversible processes as a science.