Preface

At some point in time, I got intrigued by the fact that attention for transitions between phases is more limited than for transformations within one phase. For example, in many books on the chemistry, physics, or thermodynamics of solids, melting is mentioned in passing, often merely stating the rather large change in properties between solids and liquids accompanying this discontinuous transition. This interest led to the present book. Discussing phase transitions requires knowledge of the phases themselves as well as various other disciplines. The physical chemistry, or chemical physics, of phases of matter and their transitions is wide, and therefore choices had to be made. This is always a difficult process, considering the interests of both readers and the author, coherency of the material covered, and size of the book.

As I always felt that a book, as far as is reasonably possible, should be more or less self-contained, the text is divided into three parts. Extending the metaphor of "stones" and "house" by Poincaré1 (1854-1912), the first part (Chapters 2-7) deals with the various disciplines involved, the "tools" or Basics, supported by some further background (Appendices A-E). In the second part (Chapters 8-11), we discuss the "stones," mostly "bricks" nowadays, or the Phases themselves. These parts are necessarily compact and selective. In the third part (Chapters 12-19), the "houses" or the Transitions are dealt with. In the same vein, the houses are part of the "city" of materials science, many cities form the "country" of natural science, what used to be called natural philosophy, and many countries constitute the "world" of science(s). Clearly, some of the same types of bricks are used for different houses, meaning that some topics could be considered to belong to either gases, liquids, or solids. The choice is evidently somewhat arbitrary. The topic at hand is also inevitably connected with some mathematics, and, contrary to present popular approaches, the mathematics required is presented concisely in Appendix A. This choice attempts to avoid entangling physical and mathematical issues and to make the more general use of these mathematical topics clear, quite apart from where they are really used in this book. Evidently, these "bricks" are all imported from the "city" of mathematics.

Given the "three-fold way," it is still clear that not all aspects of each of the three ways can be discussed, not even superficially. Making these choices is a matter of personal choice as well as one of what is of broad interest. The contents section makes the choices made clear: the focus is on thermodynamics and properties of dielectric behavior. Although the book focuses on phase transitions (i.e. changes from one phase to another), reviewers of the content outline pointed out that the inclusion of some aspects of phase transformations (i.e. structural changes within one phase) would be desirable. To remain in line with the focus on dielectric behavior, the phase transformation part deals with ferroelectrics and liquid crystals, as these are the most closely related to dielectric behavior (and, for ferroelectrics, within my primary interest). What to choose to discuss for liquids is particularly precarious, and I opted to include, what I now call, structural models. No apology is offered for that, as I am convinced that these models are there to stay for quite some time.

Another difficult choice is how to present the matter. There are essentially two ways to go. The first option, which may be more Anglo-Saxon in style, is to demonstrate concepts through examples of applications and thereafter generalize, that is, use an inductive approach. The second option, which may be more Franco-Roman in style, is to postulate concepts and thereafter specialize in specific examples of application, that is, use a deductive style. In view of the "Zeitgeist," the spirit of times, most books nowadays use the former approach. Nevertheless, I have chosen the second approach, as that is closer to my heart. To alleviate possible concerns, I also opted to include examples at many stages of the formal development to keep readers connected to practical issues. Nevertheless, it is important to keep in mind, as I learned already during my scientific education from Inorganic Chemistry by Phillips and Williams, that it is necessary "to distinguish quite clearly between the usefulness of a model in predicting or correlating certain types of experimental observation and the general validity of the picture that this model seems to convey. Usefulness and validity often go hand in hand, but they do not always do so". For several topics, different approaches, not necessarily compatible but all describing the facts reasonably well, exist, indicating that neither all is clear nor that all authors agree. Wherever appropriate, I pointed to that. As illustration, I refer for thermodynamics to Maugin, who jokingly (but I think not 100%) quoted, what he called a faked true common citation: Some many thermodynamicists, some many thermodynamics. For glasses, a field recognized to be loaded with uncertainty, Weitz has even joked that: There are more theories of the glass transition than there are theorists who propose them. This clearly suffices to underline that not all is certain.

In many cases, the relevant derivations are given in some detail, so that readers need not retrieve the original source right away if they are trying to follow the road towards the result instead of looking only for the results. This is another, at least partial, explanation for the inclusion of what I called Basics (Chapters 2-7, Appendices A-E).

Each chapter contains at the end a section on Further Reading with a list of books recommended. For each of them, I made a small comment, hopefully helping readers assess what they can expect. The fact that a book is on the list implies that I like that book, and most of the time I refrain from further recommendations.

To some, the Basics as described in Chapters 2-7 may seem, to quote Pippard (1920-2008) in the introduction of his Classical Thermodynamics, to be "concentrated too much on the dry bones and too little on the flesh." He continued with, "but I would ask such critics to concede at least that the bones have an austere beauty of themselves." I cannot agree more. On a more personal note, I remember that as a youngster of about 22 years, I was highly impressed by The Principles of Quantum Mechanics by Dirac (1902-1984), not only because of the clarity but also because of the conciseness and beauty of presentation.

Not all of the text is completely new, as I used some, generally heavily rewritten, parts of my earlier books. Still, the content is essentially new, with a focus on what the title promises. The concept of justification vignettes for dealing with more detailed or advanced arguments, as used before, is retained, as is the concept of examples, these being essentially solved problems. As I know from experience (in lecturing and when studying new topics), full answers to problems invite the reader, after a short time, to accept the implicit invitation to have a look at these solutions. Therefore, as a compromise, I provided in an appendix the final answers to selected problems and sometimes their full solutions.

On a somewhat different tone, Kuhn (1921-1996) has advocated that scientific progress is made by large leaps. Sometimes it is even advocated that a single person is mainly responsible for a certain topic, in one sense or another. Sometimes that seems true; for example, for the theory of special relativity, it is often stated that it was largely single-handedly created by Einstein (1879-1955). Actually, many of the relevant ingredients were already there, but Darrignol made clear that Einstein was most likely the first to take the principle of relativity and the constancy of the speed of light at face value. To quote another example, classical mechanics is often said to be based on the three laws formulated by Newton (1642-1727), implying that they were the result of his effort only, but in reality, many predecessors and successors contributed: Galilei (1564-1642), Huygens (1629-1695), Borelli (1608-1679), and so on. In fact, what is now known as Newton's first law, the principle of inertia, was formulated first by Galilei and reformulated by Huygens. The second law started with Galilei, was reformulated by Huygens and Newton, while the form f = ma as we know it now was first given by Euler (1750), as made clear by Maltese and Maronne and Panza. Another example is d'Alembert's principle (1743), first formulated in the form we know it by Lagrange (1788). For the history of mechanics, I refer to Dugas (1897-1957) and Dijksterhuis (1892-1965), while a critical assessment of the basis of mechanics was given by Mach (1838-1916). Highly readable in this connection is also the chapter on classical mechanics in the book by Lindsay and Margenau, which contains quite relevant parts on other parts of physics. For a brief review of energy and inertia, admittedly from a physicist's point of view, see a paper by von Laue and the highly relevant papers by Hecht referred to in the Introduction.

For those who...