G. Buckley. Crystal Growth. 1951. Translated from English by M. A. Kulakov, edited by O. M. Ansheles and V. A. Frank-Kamenetskii. Foreign Literature Publishing House, Moscow, 1954, 406 pp.

G. Buckley’s monograph is the first detailed survey abroad of questions of crystal formation. Its author was apparently unaware of the work of V. D. Kuznetsov (Physics of the Solid State, vol. I, 1937), but with regard to A. V. Shubnikov’s book

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In How Crystals Grow (1935, 175 pp.) he stated directly in the preface: “The only work which, in its content, can be compared with the present book was published in Russian and belongs to the pen of the well-known Russian crystallographer A. V. Shubnikov.”

As a scientist, Buckley is known chiefly for many years of detailed investigations of the influence of impurities on the growth of crystals from solutions. Crystallization from solutions, the most thoroughly studied field of crystal growth, provided the principal material for his entire monograph, which is a summary of about 700 works. It should be noted that Russian and Soviet crystallographic works on crystal growth published in foreign languages are represented in it comparatively fully; some works published only in Russian are also represented.

The book contains the following 12 chapters: 1. Solution, solubility, normal solubility, supersaturation. 2. Artificial growth of crystals. 3. Curie’s theory of crystal growth. 4. On the so-called rate of growth of crystals. 5. Diffusion theories. 6. Modern theories of crystal growth. 7. Ideal and real crystals. 8. Various types of crystallization. 9. Dissolution of crystals. 10. The influence of impurities on the habit of crystals. 11. Relations between various substances during crystallization. 12. Peculiarities of crystal growth.

In addition, there is an appendix containing a summary of data on changes in the habit of crystals owing to the presence of impurities.

The first chapter presents information on the state of the medium before crystallization and, in part, on questions of crystal nucleation. On the basis of a large, chiefly experimental, body of material (52 sources), a characterization of solutions is given and the following are considered: solubility, supersaturation, the influence on solubility of the size of the particles being dissolved, and types of crystal nuclei. Solubility and supersaturation are set forth on the basis of the old fundamental works of Ostwald, Miers, Kopp, and Tammann. On extensive experimental material the author demonstrates the advisability of the concept of a metastable region, despite the dependence of its boundaries on many factors and especially on the presence of impurity particles.

The little-known quantitative investigations of Young and Berkeley, who caused crystallization of supersaturated and supercooled media by friction and impacts, are set forth in detail. The question of the relation between solubility and the sizes of the particles of a dissolving substance is examined theoretically. The connection between solubility and the surface energy of particles is discussed on the basis of formulae of Ostwald, Freundlich, and other authors.

The nuclei that induce crystallization are divided into particles of the crystallizing substance and particles of isomorphous and epitactic substances. The influence of impurities on nucleation is considered with a number of examples.

On the whole, the chapter is rich in valuable factual material and contains a thorough consideration of the questions touched upon.

From our point of view, among its shortcomings one should first of all include the absence of a rigorous discussion of crystal nucleation. Instead, the question of the boundaries of the metastable region and the relation between solubility and particle size are considered. Thus, in a monograph on crystal growth, there has been no special section on nucleation. The relevant works of Gibbs, Volmer, and Stranski have not been considered; the concept of a three-dimensional nucleus and the work of its formation, which could facilitate understanding of the factual material, have not been formulated. In discussing epitaxy, P. D. Dankov’s works on the principle of crystallochemical correspondence are not used; these works considerably deepened the concept of epitaxy. This greatly impoverished the discussion of the epitactic growth with which the author deals in the section on types of nuclei.

The second chapter describes the growth of crystals from solutions, melts, and by other methods. The description of methods of crystallization from solutions begins with the crystallizer, well known in the USSR, of G. V. Wulff (1895), rotating around a horizontal axis. Then there are described Johnson’s method (1915) of rotating a crystal around a vertical axis; apparatus for isothermal continuous crystallization by evaporation of a solvent according to Kroger and Finke, Valeton, Nacken, and the modern apparatus of this type of Walker and Comyn. For crystallization by cooling of a solution, the first works of Moure, the industrial installations of the Brush firm with rocking crystallizers, Becker’s thermostats—rooms, the growth of ammonium dihydrogen phosphate (ADP) crystals according to Holden with reversible rotation, are described. Industrial methods for the simultaneous production of large masses of not very large crystals and Bounds’s growth of unique single crystals of alumopotassium quartz (up to 110 kg in weight) are described. The synthesis of quartz is described from Schafhäutl’s first work to Walker and Bühler, who obtained crystals up to 150 g.

Crystallization from a melt begins with an exposition of Tammann’s method, the fundamental basis of the crystal-growth methods described further: Obreimov and Shubnikov, Bridgman and Kapitza. Then the methods of Czochralski are described—the pull-

Bibliography

crystallization from the melt, Nacken’s work on growing faceted crystals from the melt with the aid of a regulated heat sink, Kyropoulos, Stöber, and the work of Dittler and Simmens on the synthesis of mica.

In the section on other methods, works on obtaining single crystals are described: Carpenter’s—by recrystallization of deformed polycrystalline specimens; Finch’s—by recrystallization of polycrystalline wire drawn through a heating zone; Corefa and Van Arkel’s—by growth of single crystals in vapors; and Van Limpt’s—by obtaining single crystals by electrolysis.

At the end of the chapter, Verneuil’s synthesis of precious stones is characterized. For all methods, improvements introduced by later authors are described.

The material presented gives a sufficient idea of the development of work on crystal growth and of the state of the art today.

In the descriptions of some works there are inaccuracies. Thus, in Spezia’s experiments one cannot speak of quartz vapors. In Wooster’s work the autoclave is filled at room temperature with solution not to 30, but to 80%. In Verneuil’s method the Al₂O₃ melt on the surface of the corundum crystal is heated only slightly above the melting point and cannot boil. The review lacks important data on the synthesis of single crystals of semiconductors (the works of Teal, Teal and Little, Teal and Buehler, and others) and of a number of other important crystals.

Contemporary Soviet works on crystal growth, not published in foreign languages, are not reflected in Buckley’s review. Such are the works of Anshles, Tatarsky, and Shternberg (1945) on the rapid growth of crystals of Rochelle salt; the work of S. K. Popov on the creation of improved apparatus and a new method for the synthesis of ruby crystals, and others.

A reader familiar with Soviet work on crystal growth will not find substantially new material in Buckley’s review. For the growth of soluble crystals, Vitovsky’s room thermostats appeared in our country in 1941; at the same time, A. A. Shternberg’s method was used to obtain crystals of Rochelle salt weighing up to 4 kg. ADP crystals are obtained here of smaller size than abroad, but without the enormous cloudy seed inside. S. K. Popov’s apparatus for ruby synthesis is considerably superior to foreign apparatus. The original works of I. V. Stepanov and P. P. Feofilov on the synthesis of optical fluorite are also not inferior to the foreign level.

Chapter 4 is devoted to the rate of crystal growth. It considers only the normal rates of growth of faces. Tangential rates, as well as the rates of growth of the crystal as a whole—for example, as a function of stirring intensity—are not considered, although they are of great interest for growth processes.

Much space is devoted to the works of Russian crystallographers: G. V. Wulff—on growth rates and the surface energy of faces; A. V. Shubnikov—on the dependence of growth rates on supersaturation; D. N. Artem’ev—on the method of crystallization of spheres.

The geometrical relations of growth rates in the processes of expansion and wedging-out of faces and of the overgrowth of one another by crystals are considered. The connection between growth rate and the reticular density of faces, real and possible faces, crystal regeneration, and final forms of growth is discussed. The experimental material obtained by the method of crystallization of spheres on the growth rates of faces, published by Spangenberg and his school, is presented; Friedel and Erdély-Grúz present the work of L. Wulff, who established the dependence of the growth rate of crystals on homogeneity.

Chapter 9 is close in its content to Chapter 4. It is devoted to the dissolution of crystals.

It examines in detail: the question of the reciprocal nature of growth and dissolution; etching as a special case of dissolution, and especially etch figures—the conditions of their appearance, the causes of discontinuous arrangement, the nature of bounding surfaces, and their connection with symmetry and anomalies.

The monograph does not express a definite opinion as to whether growth and dissolution of crystals are reciprocal, although the reciprocity of the growth of a convex crystal and the dissolution of a concave crystal has been proved quite well in the literature. The repeated assertions that the ratio of reticular densities (which, naturally, do not reflect the crystallochemical properties of faces) determines the ratio of their growth rates seem somewhat superfluous. One cannot agree with Buckley’s assertions that the growth rate of a given face is independent of the presence of neighboring faces. The works of Neuhaus (1928) showed that the presence of secondary faces has a substantial influence on the growth rate of the principal faces, which in some cases do not grow at all until the secondary faces have disappeared.

Chapters 3, 5, and 6 are devoted to theories of growth.

Chapter 3 is entitled “Kossel’s Theory of Growth.” It is devoted to the work of Kossel and to the further development of his ideas by G. V. Wulff, Markov, Ritzel, and also to a thorough exposition of criticism of this line of thought by Berthoud and Valeton.

Here it should be noted that Curie himself did not propose any theory of growth. He put forward (1885), independently of Gibbs (1878), the idea of an equilibrium, or stable, form of crystals, distinguished from all others by its minimum surface energy for a given volume.

He then developed the proposition that deformations of a liquid occurring without a change in volume are, for a crystal, equivalent to a change in its form, which could occur in a saturated solution through the dissolution of some parts and the deposition of the substance obtained on others. Finally, Curie indicated that it seems possible that a crystal which has no stable form in a saturated solution will transform into it, but that only experiment can answer whether such a possibility can be realized.

G. V. Wulff (1895) extended Curie’s ideas to the growth of crystals. He assumed that the growth rates of crystallographic faces, and consequently their central distances, are proportional to their surface energies, and indicated a method for constructing equilibrium forms.

Buckley treats with great doubt the fact of different solubilities of faces, although at the present time a difference has also been established in the melting temperature of faces (Folmer and Smit), and a theoretical interpretation of this phenomenon has been given (Stranks). Buckley gives no exposition at all of the important ideas of the equilibrium form.

Chapter 5 sets forth the diffusion theories in detail. The equations of Noyes—Whitney, Nernst, and Berthoud are analyzed, and Spangenberg’s criticism of them is presented. The results are described of many years of experimental work by Marc, who obtained rich material for testing the diffusion theory. Friedel’s works, applying the equations of the diffusion theory to processes of heat removal during the crystallization of metals, are presented.

We believe that, for the material of this chapter, it would have been essential to describe Spangenberg’s valuable experiments, in which he determined, by direct microscopic observation, the thickness of the supersaturated layer and established that it is considerably thinner than calculated. Mentioned, but unfortunately likewise not described, are Wenck’s works on the method of calculating the total surface of a growing crystal. Analogous works in the Soviet literature were carried out by A. Kukharenko (1923). These calculations are of interest for work on growing crystals.

Chapter 6 is devoted to modern theories of crystal growth. The adsorption-layer theories of Folmer, Folmer—Brandeis, the theories of Kossel and Stranski, and Burger’s theory of branching growth are set forth. Some information is presented on the works of Donnay and Harker and on Bunn’s views. In expounding the content of the theories, Buckley notes the difference between the works of Kossel and Stranski, compares the theories with experiment, and offers a number of important critical remarks. As the prehistory of modern growth theories, Bravais’s theory and its latest development by Niggli are presented.

In our opinion, the main shortcoming of this chapter is the absence of an account of the later works of Kossel and Stranski, and especially of works on the equilibrium form, the form of crystal growth, and the mechanism of crystal melting. The amount of information on Folmer’s works is also small. Therefore, although the outline of modern growth theories is, on the whole, undoubtedly successful and rich in valuable comparisons, it is nevertheless very incomplete. This is all the more so since in the remaining chapters the author makes little use of the concepts of these theories.

The remaining chapters of the book (7, 8, 10, 11, 12), which make up more than half of the monograph, concern the real crystal and real crystal formation. This section, containing very valuable and, in many respects, original material in its selection, is apparently especially close to the author of the monograph.

Let us briefly characterize the content of these chapters, and then make general comments on them.

In Chapter 7 (ideal and real crystals), after a discussion of the question of the possibility of the existence of a perfect crystal, the ideas of Smekal and Zwicky on the structure of a real crystal are briefly considered; they are supplemented by Burger’s ideas on branching structures. Balarev’s theory, which conceives of crystals as a colloidal-dispersed medium, is presented; the works of Traube and Beren, who observed that dissolution and crystal growth occur by submicrons, are presented; so are Herlinger’s views on defects and their induction, and the layer growth of crystals according to Straumanis’s works. The first works of Frank on the theory of dislocations are also mentioned very briefly. Finally, Fedorov’s views on growth at the expense of particles produced near a growing crystal are set forth. Shakolskaya’s and Shubnikov’s experiments on the accretion of crystallites to a growing crystal are described.

In Chapter 8 (various types of crystallization), the specific features of crystallization are considered: of magmas and metals from the melt, of metals from vapors in a vacuum, the formation of snow, the formation of precipitates in chemical reactions, the growth of crystals during electrolysis, recrystallization processes, crystallization of compressed powders, and polymorphic transformations. Some general ...

questions: the role of overheating and underheating at the crystal–melt boundary, geometrical selection, the role of impurities, and liquid inclusions.

Chapter 10 considers the influence of impurities on the habit of crystals and, in an appendix, gives a summary of known cases of this influence for more than 50 substances. Buckley considered the concept of “impurity” and showed that, in a broad sense, it should include both the solvent and the products of dissociation and association present in the solution. The standard habit of a crystal grown in the absence of an impurity affecting the habit is stated. Certain views on the mechanism by which impurities influence the habit of a crystal are set forth, and the concepts of the standard concentration of an impurity and of the effectiveness of its action are formulated.

In Chapter 11 the question of the influence of impurities is, in substance, developed further. It considers the interactions of large quantities of one or more substances crystallizing together with the principal material. First of all, mixed crystals and double salts are considered, as are the crystallochemical prerequisites for their formation, the role of the rate of crystallization, and stability. Then there are considered such less closely connected forms of joint crystallization as parallel growth, hourglass-type inclusions, and accidental inclusions. Certain physical properties of crystals connected with inclusions are considered, such as, for example, the pleochroism and false cleavage caused by them, as well as the conditions for the formation of inclusions. Questions of adsorption of particles on the surface of a growing crystal are also considered.

In the last, Chapter 12, all possible deviations of crystals from the ideal form and the causes producing them are considered. This includes violation of the isometric habit depending on the position of the crystal in the solution, dendrites, acicular and platy growth—especially of cubic crystals—spherulites, hollow crystals, curved faces, and vicinal faces. Convection currents, the influence of temperature, viscosity, and surface tension are considered. The crystallization of melting is treated in detail.

Several particular remarks should be made on these chapters. In Chapter 8, the growth of a crystal in a bent tube is analyzed only under the condition of strict preservation of the single-crystal structure of the growing crystal at its turns. Meanwhile, a case is widespread and important in which a crystal, by means of the process of geometrical selection repeated at the bends of a tube, turns the direction of its highest growth rate so that it constantly remains parallel to its elongation (Gross and Müller, 1915).

Little space is devoted to geometrical selection in comparison with the Russian literature. It is illustrated only by examples of crystallization from the melt. No attention at all is paid to the formation of druses.

The description of the work on convection currents begun by Lovitz (1805) starts with the work of Gober (1902).

In the section concerning vicinal faces, nothing is said about their spiral structure, which gives this section a somewhat outdated character.

Turning to an evaluation of the monograph as a whole, it should be noted that it is a conscientious and, in its own way, consistent summary of literary material. Besides the 700 cited works, behind it stands a significantly larger number of works on which the material presented and the author’s generalizations are based.

One should note the progressive scientific positions, the author’s great personal experience, and his views—correct, from our point of view—on questions of real crystal formation, which are vividly reflected in his work.

Thus, together with E. S. Fedorov, A. V. Shubnikov, and O. M. Ansheles, Buckley pays great attention to the growth of crystals from crystallites. In doing so, he correctly indicates that confirmation of this fact is a strong argument in favor of the long-range action of a crystal.

If Buckley ignores the problem of a single equilibrium form, he nevertheless, though not quite distinctly, advances the idea of a “standard habit” of crystals determined by a lattice. His attitude toward surface energy as a secondary factor in crystal growth is correct, as is his high appraisal of the idea of a repeated course.

It is not stated sufficiently explicitly, but it is nevertheless distinctly evident, that Buckley adheres to the point of view that the mechanism by which impurities influence the form of a crystal is connected with their entry into the composition of the crystal.

Behind the extensive literary material one clearly senses Buckley’s general realistic conception, based on his great experience in real crystal formation. Much valuable material is given in the analysis of concrete forms of crystallization: magmas, metals, crystallization from the gas phase, and others. Especially much valuable material has been collected on the peculiarities of crystallization of individual substances.

Finally, one should emphasize the great attention devoted throughout the monograph to the works of Russian and Soviet crystallographers.

Buckley’s monograph also has a number of general shortcomings.

Little space is devoted to theories of crystal growth, and their presentation is poorly connected one with another. There is no general theoretical conception in the monograph. The molecular-kinetic theory is presented only on the basis of the earliest works. The material of the book is predominantly mineralogical, chemical, and metallurgical in character; the theoretical treatment of the processes is pushed into the background.

The book contains no single phenomenological conception. Crystal growth is not shown as a unified process, as the history of the development of a crystalline individual. The book does not clearly reveal the author’s point of view on many important questions, even on those in which he has considerable personal experience—for example, on the question of the influence of impurities on the habit of crystals. Therefore the abundance of material and opinions, not accompanied by definite conclusions, disputes, and a sequence of presentation, fatigues the reader.

The monographs of Buckley and Kuznetsov appeared at a turning point in the development of the science of crystal formation. New, delicate applications of single crystals, together with the improvement of methods for studying their surface and structure and with the development of theoretical work, led to the creation of the theory of dislocations (1949) and to the discovery of spiral growth of crystals (1950). Molecular-kinetic theory received a powerful impetus and development. It became possible to consider the real crystal and the mechanism of its formation in a new and deeper way. In recent years many works have been devoted to these questions, transforming old ideas. In the books under review this material is not reflected, and in this important respect they no longer correspond to the present state of the doctrine of crystal growth.

One may hope that in the coming years the problem of crystal growth will advance greatly and that, in particular, a more coherent theoretical basis will be created, one that will make it possible not only to explain the processes of crystal formation, but also to control them more consciously and successfully.

The monographs by G. Buckley and V. D. Kuznetsov, summing up what has been done, make a definitely useful contribution to the preparation of this work.

N. Sheftal’