Equilibrium Between Phases of Matter: Phenomenology and Thermodynamics , H. A. J. Oonk and M. T. Calvet

Springer, Dordrecht, the Netherlands, 2008. $109.00 (404 pp.). ISBN 978-1-4020-6123-3

Harry A. J. Oonk and M. Teresa Calvet’s *Equilibrium Between Phases of Matter: Phenomenology and Thermodynamics * is a welcome addition to the literature. The text will be useful to advanced undergraduates and first-year graduates who have had a solid course in physical chemistry and who want to extend their knowledge of phase diagrams and how those diagrams connect to thermodynamics. It will also be of value to more experienced practitioners who want to broaden their perspective. I have taught and done research on the thermodynamics and statistical mechanics of phase transitions and critical phenomena for more than 40 years; yet in reading through Oonk and Calvet’s text, I have learned new things and relearned others that I had once known “in principle” but had not taught over the years.

The authors divide the book into three parts. The first presents a phenomenological overview of phase equilibria with a minimum of thermodynamic analysis. Results are introduced simply as facts. The second deals with formal thermodynamics and its application to phase diagrams in which the properties of solutions, particularly non-ideal solutions, do not play a significant role. The third part covers the thermodynamics of solutions and is developed in some detail. The authors consider partial molar quantities and composition dependence of chemical potentials, and they explore the consequences of those concepts for phase diagrams. Extensive problems and their detailed solutions are a solid asset. I worked through several and found them well-posed and instructive.

The authors’ use of simple model free energies to explicate a variety of phase behavior is a strong point of the text. For example, they employ linear free energies to illustrate the distinction between monotrophism and enantiomorphism (pages 156 and 157). But I think that more care is needed to qualify the conclusions: If both the α → γ and α → β transitions were sufficiently slow, it would seem that the transition α → δ shown in figure 110.8b could sensibly take place reversibly Another strength of the text is that the authors approach the problem of understanding phase equilibrium from several different directions. In addition to employing simple model equations of state, they use geometric reasoning about the general shape of free energies as functions of mole fraction, temperature, and pressure as well as the numerical solution of nonlinear equilibrium equations. As a result, readers learn to think about a problem in phase equilibrium from various perspectives and determine which approach works best.

I have, however, serious concerns about the notation in the second part of the text. The authors use Δ*Q* and Δ*W* to represent the integral heat absorbed by and the work done on a system in a finite process. Their choice is unfortunate from a pedagogical viewpoint because the notation strongly suggests that those are changes in something—namely a state function—rather than simply the amounts of heat and work absorbed along a path. I can see no advantage to their notation over the simpler choice of *Q* and *W.*

Another problem for students—for most US students at least—is the use of *q* and *w* to denote differential heat and work absorbed in an infinitesimal process. That choice leads to such equations as ∫ *g* + ∫ *w* = Δ*U* and *q* + *w* = *dU*. In their differential notation, though, the authors are on more solid, theoretical ground; they have at their disposal both the impressive precedent of Edward Guggenheim’s classic * Thermodynamics: An Advanced Treatment for Chemists and Physicists * (North-Holland, 1949) and the mathematicians’ and mathematical physicists’ notation denoting general differential forms, of which differential heat and work are specific “1-form” examples.

They also have the compelling argument that *dq* and *dw*—commonly used in the US if not elsewhere—are easily mistaken for exact rather than inexact differentials. Other authors have used δ*q* or *đq* to emphasize that the differential quantity in question is an inexact differential, and those notations seem to me preferable as representations of an infinitesimal quantity. Nevertheless, the authors might reply in their defense, to paraphrase Humpty Dumpty that when they use a symbol, it means just what they choose it to mean—neither more nor less. Oonk and Calvet define their symbols and clearly know how to use them correctly, but I suspect that the mismatch between their notation and that commonly used in physical chemistry and thermodynamics textbooks in the US will limit their book’s adoption for classroom instruction.

In section 2 of the first part of the text, the authors use a simple model free energy to extract the dilute-solution laws. Although that model is an elegant and efficient way to extract the properties, I was disappointed that they did not emphasize more strongly that those are general laws of nature for nondissociating and nonassociating solutes that follow from the molecularity of the solute in dilute solution. Their powerful thermodynamic analysis of phase diagrams near the pure solvent depends on the generality of those laws.

I was pleased to see the authors’ treatment of the 180° rule and other rules concerning the placement of phase boundaries in phase diagrams—both in the early phenomenological section where the rules were simply proclaimed and in later sections where they were argued for in terms of the behavior of free energies. However, I was disappointed that they did not show the reader that those are rigorous theorems of thermodynamics under mild assumptions about the nature of the triple point and that the assumptions are necessary for the theorems to hold.

The text does have the kinds of typos and errors to be expected in any first edition. I was impressed, however, at how few I found. In problem 202.6 on page 189, the last datum for ρ is almost surely in error. The value 0.1972 agrees much better both with other data in the text and with literature values than the 1.772 that the authors give. An amusing faux pas occurs on pages 54–55. On page 55, the authors scrutinize the quality of phase diagrams in other textbooks, noting that some “drawn in a freehand manner” can lead to error; but on page 54 they provide—inadvertently, I assume—an example. The tie lines in their three-component phase diagram are essentially parallel, which leads to a contradiction at one side of the diagram. The authors, who are not native English speakers, request that the reader “enjoy the science and wink at the linguistic shortcomings.” Those shortcomings are numerous, and occasionally distracting, but nowhere did I find them a serious impediment to understanding the text.

Despite such quibbles, I heartily recommend *Equilibrium Between Phases of Matter* if you want to enrich your knowledge of phase equilibrium and phase diagrams and their relation to thermodynamics. You are remarkably knowledgeable about the subject if you do not learn something from this book.