A. F. IOFFE. Physics of Crystals. State Publishing House. Moscow—Leningrad, 1929.
Pp. 192. Price 4 rubles.

A. F. Ioffe’s book is an extremely compressed and far from complete account of the results of the work carried out by the author and his collaborators over the last 25 years. This work, fragmentary reports of which had only recently begun to appear in the specialized and general press, is here for the first time presented in the full breadth of its content. Even upon a person who, like myself, has had the opportunity to follow A. F. Ioffe’s investigations over the past 12 years, the abundance of results obtained in systematized form makes a deep impression. One hardly knows what is more astonishing: the wide scope and profound planning of these investigations, their pioneering character, the simplicity and clarity that they introduced into seemingly hopelessly confused questions, or, finally, the ingenuity and elegance of the methods employed.

The book under review is an almost exact translation of an English course of lectures delivered by A. F. Ioffe at the California university in 1927, without any substantial additions or changes. The first two lectures are of an introductory theoretical character. The remaining 15 lectures are devoted to an exposition of the experimental investigations of the author and his collaborators, as well as of foreign physicists working in the same field.

Of the 15 lectures mentioned, the first four are devoted to the mechanical properties of crystals, and the remaining 11 to electrical properties. It is curious that between these two, at first glance quite different, fields a number of analogies clearly emerges. Thus, for example, the apparent deviations from Hooke’s law in the phenomena of elastic deformation and elastic after-effect correspond to the apparent deviations from Ohm’s law when electricity passes through crystals. Plastic deformations and strength correspond to the electrical breakdown of dielectrics and their destruction in sufficiently strong electric fields. Further, interesting analogies are found also in the method of explaining certain mechanical and electrical anomalies. Thus, for example, in order to distinguish plastic deformation from rupture, A. F. Ioffe made use of the fact that the former requires a certain time, whereas the latter occurs practically instantaneously. In this way, a sufficiently rapid increase in load made it possible to determine the limit of strength, which under ordinary conditions is masked by the elastic limit. In an analogous manner, the determination of the change in current strength in a crystal under a rapid change of the applied ...

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the potential difference made it possible to determine the true resistance of the crystal, excluding the influence of the comparatively slowly changing electromotive force of polarization. Finally, the removal of conditions that reduce the mechanical and electrical strength of crystals (surface cracks in the first case; the elimination of thermal and ionization breakdown by lowering the temperature and reducing the thickness in the second) made it possible to reach the strength limit indicated by the electrical theory of crystals.

Turning to a systematic review of the contents, I shall dwell in somewhat greater detail on the second half of the book, devoted to the electrical properties of crystals. As for the chapters devoted to mechanical properties, they were printed in full in the pages of this journal (see A. F. Ioffe, Mechanical Properties of Crystals, UFN, Vol. VIII, p. 441, 1928), and therefore I shall confine myself to a simple listing of them: Chapter III. Elastic aftereffect. IV. Limit of elasticity. V. Mechanism of plastic deformation. VI. Strength.

The principal results established by the author and his collaborators concerning the electrical properties of crystals reduce to the following:

1. (Lecture VII. The passage of electricity through crystals.) When a constant potential difference is applied to a dielectric crystal, the current gradually decreases. This decrease, as Ioffe showed, depends on the appearance of a high-voltage polarization e.m.f. If the latter is allowed for by direct measurement, or else by sufficiently rapid variation of the applied e.m.f. (which the polarization cannot keep up with), it turns out that the passage of electricity through crystals strictly obeys Ohm’s law.

2. (Lecture VIII. Specific electrical conductivity.) The resistance of various specimens of one and the same crystal can be brought, by repeated purification (recrystallization), to a definite standard value depending only on the temperature \(T\), according to the law \(\sigma = Ae^{-q/T}\). The electrical conductivity of crystals has the same symmetry as thermal conductivity, but expressed much more sharply.

3. (Lecture IX. Electrolysis of crystals.) Experiments by collaborators of A. F. Ioffe (Lukirsky, Shukarev) showed that the mechanism of electrical conductivity in heteropolar crystals is the same as in liquid electrolytes. The passage of current is connected with the motion of ions, which are deposited at the electrode in full agreement with Faraday’s laws. In this process usually only ions of one sign move (Tubandt, Lorenz). Criticizing the views of Hvosha and Smekal, Ioffe shows that only dissociated (i.e., detached from lattice sites) ions take a direct part in electrical conductivity, and that crushing the crystal, for example under plastic deformation (Czachowitzer), has no effect on electrical conductivity.

4. (Lecture X. Dissociation in quartz.) Investigating the dissociation and polarization of various crystals, Ioffe established two types, represented—

... of which are quartz and calcite. In quartz, dissociation equilibrium is established, at ordinary temperatures, very slowly. When an electric current passes, volume charges distributed throughout the entire thickness therefore appear. With rapid cooling of the crystal the number of ions remains unchanged, but their mobility decreases. This circumstance makes it possible to determine experimentally the degree of dissociation in quartz and the mobility of individual ions (since both obey the same law of variation with temperature).

1. (Lecture XI. High-voltage polarization in calcite.) In crystals of the calcite type, dissociative equilibrium is established practically instantaneously. Volume charges are absent, or rather are concentrated in an extremely thin layer (about \(1\ \mu\) thick) at the cathode. In this layer the polarization electromotive force is also produced. It proves possible to check the distribution of the potential in it. The immediate cause of its occurrence is evidently the departure of negative ions of an impurity and the appearance of an excess of positive ions that are not discharged at the electrode.

2. (Lecture XII. Electronic conductivity.) Under normal conditions electronic conductivity is apparently absent in dielectric crystals such as NaCl. It appears, however, under the influence of light after preliminary illumination of the crystal by X-rays. The latter apparently cause the separation of submicroscopic particles of metal. The subsequent action of light then reduces to the “internal photoelectric effect,” i.e. to the tearing of electrons from these particles into the surrounding dielectric.

3. (Lecture XIV. Dielectric losses.) The apparent non-observance of Joule’s law in dielectrics when determining their heating by the formula

\[ W=\int \frac{V^{2}}{K}\,dt \]

(\(V\)—potential difference, \(R\)—resistance) is explained by the author as: a) incorrect determination, b) failure to take into account the electromotive force of polarization. An exact calculation (connected, however, with a somewhat, in my opinion, doubtful principle of superposition) leads to an exhaustive quantitative explanation of dielectric losses in their dependence on the frequency of oscillations and on temperature. The results of the calculation have been verified by special experiments of L. K. Walter.

1. (Lecture XV. Thermal breakdown.) Wagner’s theory of thermal breakdown is set forth (an increase of electrical conductivity as a result of Joule heating), then its more exact form, given by Semenov and Fock, and the experiments of A. F. Walter and L. Inge, which brilliantly confirm it. At the same time, however, it turns out that the thermal theory of breakdown is justified only in the region of high temperatures.

2. (Lecture XVI. Ionization breakdown.) In the region of ordinary and low temperatures, breakdown of dielectrics is effected by impact ionization, occurring in very strong electric fields. A theory of such ionization (analogous to Townsend’s theory of ion...

gas protection), developed by A. F. Ioffe, is splendidly confirmed by experiment. An especially important consequence of it is the increase in breakdown voltage on passing to very thin layers. The electrical strength of such layers (with a thickness of about 1 μ and less) proves to be tens and even hundreds of times greater than that of layers of ordinary thickness. This circumstance is verified on the polarization layer in dielectrics of the calcite type.

1. (Lecture XVII. The limiting electric field.) When the field is increased beyond one and a half million volts per 1 cm, breakdown occurs in layers of any thickness. This last type of breakdown is conditioned by the destruction of the crystal lattice, i.e., by the tearing of ions from their positions. Such tearing is explained by the fact that such limiting electric fields have the same intensity as the electric fields that act on each ion of the lattice from neighboring ions.

I cannot dwell on a survey of the theoretical and technical prospects that follow from the results set forth in the book and are briefly outlined in the final lecture by the author himself.

Not a little has been written about these prospects in the general press in connection with “high-voltage accumulators,” not yet realized, and with a new system of insulation that is in the stage of technical implementation in Germany and America. This implementation is the best proof of the practical usefulness of the disinterested service to science to which A. F. Ioffe has devoted more than half of his life.

Ya. Frenkel.