Bibliography

V. D. Kuznetsov. Crystals and Crystallization. State Publishing House of Technical and Theoretical Literature, Moscow, 1954, 411 pp., price 19 rubles.

In various fields of science and technology, the problems of crystal growth have acquired great importance over the last two decades. One of the main reasons for the increased interest in them is the multitude of important technical applications found during these years for artificially grown single crystals: piezo- and ferroelectrics, ferromagnetics, semiconductors, optical, superhard, and other materials.

At present, the study of crystallization processes and work on improving the properties of polycrystalline materials (metals, alloys, ceramics), chemical purification and the extraction of useful impurities, improvement of ingot quality, the problem of artificial precipitation, and many other important questions are very closely connected.

The present state of knowledge of crystal-growth processes is characterized by a large gap between theory and the data of real crystal formation. Works have not yet been published that would contain even the most approximate, but general, theory of the growth processes of real crystals, and from this standpoint the explanation of real crystal growth is still in an initial state.

In addition, the enormous number of experimental works on crystal growth, distributed over 150 years in numerous periodical publications—chemical, physical, physicochemical, and technical—is very diverse and often contradictory. All this makes it difficult to create monographs on crystal growth, and they are extremely few in number.

V. D. Kuznetsov’s book Crystals and Crystallization is a significantly revised and expanded edition of the well-known readers’ monograph by the same author, Physics of the Solid State, vol. I, published in 1937 and the first comparatively complete literary survey in world literature on crystal growth. It was preceded by only one original, likewise Soviet, book covering the problem of crystal growth as a whole—How Crystals Grow by A. V. Shubnikov (1935).

V. D. Kuznetsov’s monograph consists of six chapters: 1. Nucleation of crystals. 2. Growth and dissolution of crystals. 3. Real crystals. 4. The role of surface energy and impurities in crystallization. 5. Allotropy, polymorphism, and isomorphism. 6. Artificial growth of crystals.

Let us consider the contents of these chapters separately.

In Chapter “Nucleation of crystals” (pp. 9–84), a large amount of material is collected, chiefly on the nucleation of crystals from melts. The works of Tammann and his school on spontaneous nucleation are described in detail, together with their criticism (according to Fuchs’s work); the capacity for crystallization and cases of various relations between the curves of the rate of linear crystallization and the rate of formation of nuclei are considered; the structure of polycrystalline formations is defined. Experimental works by Meyers, Pfaff, Richards, and many other authors on investigating the influence of insoluble impurities on crystal nucleation are set forth. In a special paragraph, a large body of factual material is presented in detail on the little-known question of the supercooling of metals. The results of a large number of works by Soviet authors are discussed, beginning with Kondyurin and ending with Kapustin, devoted to the question of the influence of radiation, electric and magnetic fields, and ultrasound on crystal nucleation. The works of V. I. Danilov and his school on crystallization (according to the 1948 review), of Bezborodov, Ponomarev, and others on the study of glass devitrification are presented separately. In the section “Crystallization kinetics,” the work of Stark, Mirkin, and Romanskii, who analytically studied the process of overgrowth of polycrystalline material, is described in detail.

the area of the melt on which nuclei arise and grow. The exposition is accompanied by a large number of diagrams, schemes, and drawings, and gives a sufficiently complete idea of the material.

The theoretical side of the problem of nucleation is presented in the section “Theories of crystal nucleation,” where the views of Koppe and Tammann, the Gibbs–Volmer theory of nucleation, and the role of interface surfaces in nucleation processes are set forth in historical sequence; the work of Stranski and Kaishev is briefly described, in which, on the basis of the concept of the average work of detachment of surface atoms of a crystal, the equilibrium between a solution and two- and three-dimensional nuclei is considered.

From our point of view, a shortcoming of this chapter is the absence of a characterization of the state of the medium (gaseous and liquid) before crystallization. One gets the impression that, according to the author, it consists of unaggregated individual atoms or molecules. Therefore, he cites the old data of Wegener, who showed that for the formation of an equilibrium droplet during the condensation of water vapor the simultaneous collision of no fewer than 50,000 molecules is necessary. From this he draws the conclusion of the practical impossibility of spontaneous condensation. At present such a view may be considered refuted. Theoretical works (for example, the work of Meier) and experimental investigations (for example, the experiments of Nikandrov on the propagation of ultrasonic waves in moist air) have established that in a real gas (and still more in a liquid) there is a significant fraction of aggregated molecules. Even in saturated water vapor, according to Frenkel, there is a considerable number of aggregates containing more than 1000 molecules (an excellent summary of this question is given in the monograph by Vukalovich and Novikov, The Equation of State of a Real Gas, 1948). Investigations by Lengmuir and Schaefer showed that, in Wilson’s chamber, even at low concentrations of water vapor and in the absence of ions and dust particles, at temperatures below \(-39^\circ\)C its spontaneous crystallization begins. Theoretically, the presence in the medium of crystallites smaller than a nucleus (pre-nuclei) was also considered by Stranski.

Spontaneous nucleation does exist, but crystallization arises much more often on solid particles of isomorphous or epitaxial substances. In this connection it should also be pointed out that the author overestimated the significance of the old, pre-X-ray-period work of Koster (1903) on the “primitive crystallite,” having the size of the elementary cell and determining the limit of metastability. Undoubtedly, even in the supersaturated melt there are crystallites (pre-nuclei) considerably exceeding the size of the elementary cell.

Instead of the Thomson–Gibbs equation, which has fundamental importance for crystallization, the Thomson equation relating to vapor condensation is given, and without derivation. The Gibbs formula determining the work of formation of a nucleus is likewise given without derivation. The works of Stranski and Kaishev on nucleation are considered very schematically.

Finally, it is difficult to agree with the author that the terms “crystalline nucleus,” “center of crystallization,” and “seed” need not be distinguished.

A “nucleus” is a precise concept, introduced by Gibbs to denote a crystallite that is in strict equilibrium with a supersaturated or supercooled phase. The work of its formation \(\left(A=\dfrac{1}{3}\sigma s\right)\) is an important indicator of the stability of a metastable system. Aggregates smaller than nuclei are “pre-nuclei.” Aggregates larger than the nucleus are capable of growth and are centers of crystallization. As for a seed, proceeding from the work of T. Lowitz, who introduced seeding (1795) as an artificial method of inducing crystallization of supersaturated solutions, this term should be understood to mean a crystalline formation, large or small, which it is technically possible to introduce into the medium in a single number in order to induce crystallization in it.

Chapter II of the book is devoted to the growth and dissolution of crystals. It begins with an exposition, as the basic law of crystal growth and dissolution, of the experimental generalization by I. I. Andreev (1908) of Nernst’s proposition, according to which the rate of crystal growth is determined by the rate of diffusion. In the section “The mechanism of growth and dissolution of heteropolar crystals,” data from the works of Kossel and Stranski on the theory of crystal growth and O. M. Ansheles’s observations on the growth process are set forth. On the basis of the works of Bravais, Wulff, Weiber, Shubnikov, and Fedorov, questions concerning the growth rates of different crystal faces are discussed. The influence of viscosity on the rate of growth of potassium alum crystals is discussed in detail.

On the basis of the works of Shubnikov and Friedländer with Vysochki, the question of crystallization force is set forth. The solubility of crystals is considered in an analogous order. First the question of the rate of dissolution of crystal faces is considered, then etch figures and their use for orienting crystals; next, the dependence of solubility on surface energy, heat of fusion, and other physical

properties and, finally, the influence of the degree of comminution of crystals on solubility.

This chapter gives rise to a number of comments.

First of all, concerning the work of I. I. Andreev. From our point of view, V. D. Kuznetsov rightly paid attention to it. We believe that it constitutes one of the parts of Soviet work on high-speed methods of growing crystals. The history of Andreev’s work is as follows. Noyes and Whitney (1897) found that the rate of dissolution of solid substances is proportional to the difference between the concentration of the solution and the saturation concentration

\[ \left(\frac{dx}{dt}=A(C-C_0)\right). \]

Nernst (1904) extended this proposition to heterogeneous reactions in general, and in particular to the growth of crystals. He assumed that, with good stirring, the crystal is surrounded by a thin layer of saturated solution, in which diffusion alone takes place, and considered the rate of attachment of substance to the crystal to be infinitely large compared with the rate of diffusion, believing that the latter determines the rate of the process. Nernst’s proposition required experimental verification, which Andreev undertook. He showed by careful experiments that the rate of growth and dissolution is indeed proportional to supersaturation and depends on the intensity of stirring, which confirmed the path of diffusion. He showed, although this has remained in the literature subsequently, that one can choose such a concentration of the solution at which, for a short time, one face will dissolve while another will grow *). To explain the different growth rates of faces and the monohedral form of crystals, Andreev proposed that the saturation concentration is different for different faces.

Numerous works by other investigators, especially Marc, showed that a number of Andreev’s conclusions are valid only under the limited conditions of his experiments, and that in general the intrinsic rate of attachment of substance to the crystal cannot be neglected. The rate of crystallization is strongly affected by impurities; isomorphous crystals have different growth rates; the rates of growth and dissolution for one and the same crystal are different. Therefore one cannot ascribe to the Nernst–Andreev proposition the significance of a fundamental law of the growth and dissolution of crystals. It is nothing more than a law of diffusion, in which the process of growth itself is ignored. It may be useful for a purely external description of growth and only under limited conditions. Incidentally, this proposition has nowhere to this day been formulated as a basic law of growth.

Little space is given to the works of Kossel and Stranski, the authors of the molecular-kinetic theory of crystal growth (1927–1928). Mainly the first work of Kossel is presented. Meanwhile, the numerous works of these authors constituted an important stage in the theoretical understanding of the processes of crystal growth.

Nor can one regard as correct the opposition of undoubtedly very interesting but purely descriptive works by O. M. Ansheles and the conclusion drawn from this opposition, that “the rate of growth of a crystal is determined exclusively by the rate of influx of nutrient substance, and not by the rate of deposition of particles on the faces of the crystal.” It is difficult to agree with this assertion also because the very rate of influx of nutrient substance is a function of several arguments, among them the rate of deposition of substance on the faces of the crystal. Thus, a crystal with a crack grows considerably faster than a homogeneous crystal located next to it.

In the section “Crystallization Force” only the experiments of A. V. Shubnikov and the data of Fridländer and Vysockaya are described, demonstrating its very small values. The question of the magnitude of the crystallization force has not been sufficiently studied, and for completeness of the picture it would be necessary also to cite the results of those experiments (for example, by Correns) in which large values of the crystallization force were obtained.

In the section dealing with the dissolution of crystals and etch figures, much valuable material is collected. On the rates of dissolution of faces, contradictory material is presented, from which no definite conclusion is drawn—whether the rate of dissolution changes in general with direction. It seems to us that a definite conclusion can nevertheless be made. It amounts to the fact that the rate of dissolution changes with direction in those cases when dissolution proceeds slowly. Otherwise, large and irregular pieces separate off, and the difference in dissolution is leveled out.

The third chapter of the monograph is devoted to real crystals. It assembles extensive and varied material on inclusions of mother liquor in crystals. Especially detailed accounts are given of the works of O. M. Ansheles and V. B. Tatarskii on mosaicity, the influence on form, and partly on the growth of crystals, of such factors as con—

*) At the present time, it has been established that there is not only different solubility, but also a different melting temperature of faces (Folmer and Schmidt).

centrational and convection currents, the degree of supersaturation or supercooling, and temperature (the works of Wulff and Shubnikov). Special forms of crystal growth are considered: boats floating on the surface of a solution, tablets and needles, dendrites and skeletons, spherulites, rhythmic structures, aggregates, and twins. The distribution of an impurity in crystals, radiant crystals of Berthollet’s salt, columnar crystallization, and orthotropism are considered. In this chapter, extensive material has been collected, especially valuable for persons engaged in growing crystals.

The shortcomings of this chapter are its weak use of works of recent years. Thus, in the description of whiskers, the questions of their spiral structure in many cases are passed over, a structure established, in particular, by the Soviet scientist G. G. Lemmlein as early as 1948. The discovery of the spiral structure of whiskers resolved in a new way the scientific disputes set forth in the monograph.

In general it should be noted that the book contains a complete absence of material on dislocations.

In the fourth chapter the role in crystallization processes of surface energy and of impurities affecting it is examined. The basic idea, pursued by the author, is identical with the idea of W. I. Vernadsky (1911), who regarded the crystal as a drop of a solid body. The author first gives the concept of surface energy, shows the scatter of its calculated as well as experimentally found values, and sets forth, in its historical development, the Gibbs—Curie—Wulff principle and data on the equilibrium form and the growth form of crystals.

In the section devoted to impurities, their influence on the form of crystals is considered. Experimental material is used mainly from Russian (Orlov, Zemyatchensky) and Soviet (Mokievsky) works. The mutually contradictory works of V. D. Kuznetsov and L. Yu. Gilmans are considered in detail. According to Kuznetsov, an impurity must not only be present in the solution and change its surface tension or viscosity, but must also act chemically on the crystallizing substance (NH₄Cl). This point of view is akin to the views of Orlov, Zemyatchensky, and Fedorov.

The influence on a crystal of impurities forming regular intergrowths with it is considered. The rule of Royer and the experimental works of Maksimov are set forth. Valuable material is presented on the question of modifiers in melts and solutions and the influence of surface-active substances on the crystallization of eutectics.

The following observations may be made on this section.

One cannot agree with the author’s basic proposition that further theoretical penetration into the mechanism of crystal growth is connected with the refinement of data on the surface energy of crystals. Surface energy, as Valeton showed as early as 1915, is of secondary importance for the processes of crystal growth. Moreover, Nossal’s reports showed that the concept of surface energy, borrowed by analogy from the theory of liquids, is also too summary for the analysis of the processes of crystal growth. Only the replacement of this concept by the concept of the energy of individual growth steps made it possible, within the framework of the molecular-kinetic theory, to reveal the distinctive character of crystal-growth processes. This important modern stage in the development of the theory is, in essence, not reflected in V. D. Kuznetsov’s monograph. In presenting the question of the equilibrium form of crystals, it makes no mention of the theoretical achievements in this field belonging to Stranski and his school, who determined equilibrium forms for a number of basic structures, well, and in some cases brilliantly, confirmed experimentally.

The Curie principle, not quite identical with the Gibbs principle, is explained not entirely successfully. The reader may understand it to mean that a macrocrystal having a nonequilibrium form, in a saturated solution, will spontaneously pass into the equilibrium form, which does not correspond to reality. One cannot agree that Wulff only modified the Gibbs—Curie principle. He generalized it to the phenomena of crystal growth and gave a method for the geometrical construction of equilibrium forms.

In the section “The Form of a Crystal of Cubic Syngony,” depending on the value of the surface energy of the faces, the desired results on the conditions under which a crystal has the form of a cube, octahedron, or cuboctahedron could have been obtained much more simply if, instead of surface energies, one considered the distances of the faces from the center of the crystal that are proportional to them.

The forms obtained by Lukirsky on spheres of rock salt cannot be considered equilibrium forms, since they are the result of the rearrangement only of thin surface layers of the crystallizing sphere and do not satisfy Gibbs’s condition $\sigma_i F_i = \min$ at $v = \mathrm{const}$. They can also be obtained on single-crystal bodies bounded by any curve, and not only by a spherical surface.

Concerning the mechanism of the influence of impurities on the form of crystals, the author asserts that in order to change it, not only is the presence of an impurity required that affects the surface tension or viscosity of the solution, but also its chemical action on the crystallizing substance. We would like to note the correctness, from our point of view, of this opinion. In a more general form, we believe that it may be said that the impurity capable of affecting the form of a crystal is one that enters into that

or another form into its composition, and it is not always necessary that it form a chemical compound with the substance of the crystal.

In the fifth chapter of the monograph, allotropy, polymorphism, and isomorphism are considered. At its end the crystallization of one substance at the boundaries of another is examined—a section devoted to an exposition of the works of P. D. Dankov. A large part of the material of this chapter does not relate to crystallization, but sets forth mainly crystallochemical material. It should be noted that, in presenting the works of P. D. Dankov, the author has unfortunately completely omitted his kinetic and energetic conclusions.

The monograph concludes with a large chapter, “Artificial Growth of Crystals.” In the introduction, after preliminary remarks on the chapter, the crystallization of a vaporous substance in chemical reactions, from solutions in a melt, and in polymorphic transformation is briefly considered. Then growth from solutions is examined in detail, and, separately, rapid growth and apparatus (thermostats and temperature regulators). Crystallization from melts is also considered in detail: the methods of Czochralski, Obreimov and Shubnikov, Bridgman, Kyropoulos, Stöber and Strong, Kapitsa and Shubnikov. The growing of corundum, quartz, the production of single crystals with a specified orientation, collecting crystallization, recrystallization of deformed crystals, and electrolysis are then examined.

The chapter contains valuable material which will undoubtedly help experimenters find their way in this field. In addition to the original method and its main idea, improvements introduced into the method by later authors are described, as well as a number of practical observations that must be taken into account in the work. However, general conclusions on the methodology of growing crystals are absent, and all the material is presented as the scattered experience of individual investigators.

The following comments may be made on this chapter.

In describing methods of growth, the author takes a somewhat uncritical attitude toward the literature. Thus, the method of V. B. Tatarskii is indicated as the most advanced method for growing crystals from solutions, although an attempt to apply it in industry yielded no positive results and it is not used in production, just like the planetary method. Much space is devoted to describing thermostats with gas heating that are no longer used, mercury-free temperature regulators, and Beneshevich and Vadillo devices for automatically lowering the temperature. But no good circuit is given for a relay and thermostat that could be recommended to investigators.

Good-quality crystals of synthetic corundum do not crumble into small fragments. Not all processing of corundum is done with diamond. In many operations it is replaced by carborundum. In this connection, throughout the world not 75–80% of the crystal is wasted, but not less than 90% (until recently about 97%).

The opinion of P. V. Grushvitskii and O. M. Ansheles on the origin of parasitic crystals from nuclei that arise near a growing crystal does not seem sufficiently well founded to us: it is much more likely that the parasites arise from pieces that break off from the growing crystal when it cracks and is struck by solid particles.

Turning to an assessment of the monograph as a whole, it may be noted that the experimental material in it predominates over the theoretical, and that the author does not put forward original theoretical ideas in it, with the possible exception of the idea of the mechanism of the influence of impurities on crystallization.

In the field of theory, the author is an adherent of the Nernst–Whitney diffusion theory and exaggerates the role of surface energy in the crystallization process. The theoretical works of the past decade are poorly covered by him.

The work, it seems to us, lacks unity in the presentation of the totality of the phenomena described. Not all questions are treated with entirely up-to-date material.

Despite these substantial shortcomings, the author has done an important and useful work. His survey, encompassing a very large body of material, like the work of previous years, helps disseminate knowledge about crystals and crystallization processes, promotes the development of work on the synthesis of single crystals, and propagates the significance of these works. The author’s great merit also lies in the fact that his books are the first comparatively complete compendia of information in this complex field.

N. Sheftal