Ya. G. Dorfman and I. K. Kikoin, Physics of Metals. Electrical, Optical, and Magnetic Properties, 552 pp., GTTI, 1934, price 8 rubles.

This is the first fundamental book on the physics of metals. For that reason alone its appearance cannot fail to be welcomed. In Russian literature there are no sufficiently modern surveys of these questions. Recently, in the series “Advances in Physics,” two little books appeared: Metallophysics (a collection of articles) and C. Darrow’s Electron Theory of Metals.

The first of these books is metallurgical rather than physical in character. It is devoted primarily to the mechanical properties of metals. Ewald’s introductory physical article, “The Structure of Solids from the Atomistic Point of View,” does not go beyond Bohr’s theory. Containing a large amount of empirical material, this book does not at all reflect the modern—or, better, quantum—point of view on the structure of metals.

Darrow’s book, on the contrary, is an exposition of the modern quantum theory of metals. It is a brilliantly written essay, popular to the extent possible, and for that very reason in some places superficial and far from exhaustive of the subject. Darrow’s book does not go beyond the limits of quantum theory, which interests the author here more than metals themselves. The theory of metals serves here merely as an extensive illustration of quantum statistics.

These two books, wholly different in character, represent two currents existing in the science of metals. This bifurcation, for which there are no natural grounds, is very characteristic. In the science of metals there exist two paths, as yet very little connected: along one go physicists, along the other metallurgists. They speak different languages and often do not even understand one another. In the preface to Physics of Metals the authors point out that such a gap (like, for example, the notorious gap between physics and chemistry) makes further progress almost impossible.

Physics of Metals is distinguished by its tendency to unite these two directions. The physical character of the book is evident in its striving to provide a theoretical basis for the enormous empirical material accumulated by metallurgists. On the other hand, the authors constantly remain in the realm of real metals (or, in any case, constantly return to them), without restricting themselves to the ideal simplified scheme with which quantum theory operates. Very much space in the book is devoted to alloys. Several paragraphs are devoted to liquid metals.

Physics of Metals, however, does not exhaust all of the physics of metals. Phase transformations are touched upon only briefly. Mechanical and thermal properties are absent altogether. The book is devoted chiefly to electri-

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… and magnetic properties. Contents: general ideas on the structure of metals and on the bonding of electrons; optics of metals; electrical conductivity and thermal conductivity; thermoelectricity; superconductivity; magnetic properties of metals.

It is very regrettable that in this fundamental book wave mechanics is altogether ignored. This is all the more regrettable because The Physics of Metals claims not only to be an experimental survey, but also has the tendency to interpret theoretically the rich experimental material collected in it. The modern theory of metals is quantum theory. To expound the modern theory of metals without quantum mechanics is as thankless a task as to expound the modern theory of the atom without quantum mechanics. If one rejects the horror of quantum mechanics which some experimentalists still experience, then it seems completely incomprehensible why, in such a largely theoretical book as The Physics of Metals, it should have been found necessary to omit almost all the ideas connected with quantum-mechanical conceptions of the metal. This is all the more incomprehensible because quantum mechanics, as applied to the theory of metals, although it is associated with a very cumbersome mathematical apparatus (which can always be omitted), contains nothing essentially difficult in itself (from the theoretical point of view). In the preface the authors motivate this omission by their unwillingness to introduce a special chapter devoted to the general questions of wave mechanics. Nevertheless, the authors have devoted quite a few pages to questions of statistics in general (classical and quantum). This omission is felt throughout the whole book. It is felt especially acutely (as was to be expected) in the chapters devoted to the electrical conductivity and the optics of metals.

Sommerfeld’s theory of the electron gas is set forth rather fully. However, the authors barely touch on the theory of bound electrons. Half a page is devoted to Bloch’s theory. Bloch’s formula for the energy of an electron in a crystalline lattice is not given at all. The splitting of the discrete energy levels of an isolated atom when such atoms are combined into a lattice, the concept of energy “bands”—the essential result of Bloch’s theory—is set forth so carelessly and superficially that the reader will find quite incomprehensible those particular questions which are based on these ideas and are encountered in other places in the book. For example, Shubin’s idea in his work on superconductivity must remain incomprehensible. Incidentally, Fig. 65, illustrating the arrangement of electrons according to the energy levels of a metal, which is hardly explained in the text, also remains incomprehensible.

Without the concept of “bands,” of course, the optics of metals in its modern understanding is impossible. A free electron gas, as is known, is capable neither of absorbing nor of radiating. Quantum optics of metals appears only at the moment when electrons become bound. The chapter “Optics of Metals” is, however, predominantly theoretical in character. After some very general and thoroughly explained considerations that an electromagnetic wave must somehow influence the behavior of electrons in a metal, the authors present certain conclusions from the electron optics of metals, in which electrons were regarded as oscillators, and then, after a brief experimental survey, conclude this chapter with the remark that quantum optics has only very recently been developed quantitatively by Shubin. Thus the modern optics of metals is absent here. Meanwhile, the first quantitative work on the quantum optics of metals dates as far back as 1929 and belongs to Kronig, as do a number of subsequent works in this field. Kronig, however, is not even mentioned in the text.

Without the concept of energy “bands,” it is also impossible to give a sufficiently profound definition of the distinction between a dielectric and a conductor. The authors define metals as bodies possessing electronic conductivity, and dielectrics as bodies possessing ionic conductivity…

—whereas semiconductors are bodies possessing both properties. If this is characteristic, then in any case it cannot serve as a distinction, since, as is known, dielectrics under certain conditions can possess electronic conductivity while remaining dielectrics. Elsewhere the authors see the difference between metals and dielectrics in the fact that in the former the electrons are weakly bound to the atoms, while in the latter they are firmly attached to them. The degree of binding of the electrons in itself does not yet determine whether we have before us a metal or a dielectric. Indeed, one can imagine two crystal lattices with the same degree of electron binding, of which one will conduct and the other will not. The qualitative distinction between conductors and dielectrics ultimately has a quantitative nature and reduces to the question of the location of the “zones” in the energy spectrum of the metal plus the Pauli principle.

The exposition is rather uneven. In some places it is wearisomely elementary (for example, Maxwellian optics of metals); in other places, on the contrary, it is wearisome in its laconicism (for example, the Bloch theory). The parts based principally on empirical material are very important. Thus, for example, in the chapter on superconductivity (very interesting and rich in experimental material) it is difficult for the reader to grasp wherein, properly speaking, the difficulty in constructing a theory of superconductivity consists. ((For the information of the publishing editor: in this chapter, incidentally, the designations in Fig. 119 do not correspond to the designations in the text.) In the chapter on electrical conductivity the question of what causes resistance is expressed so indistinctly that the reader may get the impression that the very fact of the existence of a lattice (even in the absence of thermal motion of the ions) is the cause of resistance. In the chapter “Optics of Metals” it is said, among other things: “... for such wavelengths (lying in view of the light absorbed by the metal) electrons in the metal cannot be regarded as free.” In the present context this phrase cannot but give the reader false notions that the wavelength of the incident light affects the degree of binding of the electrons, which is thus determined not only by the nature of the metal but also by the light with which we illuminate it.

Despite the indicated shortcomings in illuminating the theoretical side of the question, Dorfman and Kikoin’s book is very useful and valuable, since it brings together for the first time extensive and varied experimental material. It can be very useful to the metallurgist, bringing him closer to physics. If it is not capable of bringing the experimentalist closer to the theory of metals, it nevertheless brings the theorist closer to experiment.

F. Volkenstein