MASS CRYSTALLIZATION.

I. CRYSTALLIZATION FROM SUPERSATURATED SOLUTIONS AT MANY LEVELS UNDER RAPID COOLING¹

A. M. KUZMIN

Experimental investigations of the phenomena of mass crystallization have as their aim the obtaining of data for the solution of both theoretical and practical problems. In the present article the author very briefly sets forth his experimental material on simultaneous crystallization from supersaturated solutions at many levels, practically resolves the question of the stratification of solutions, and draws a number of theoretical conclusions following from the experiments.

The change of density (stratification) of solutions with height was studied by P. A. Zemyatchensky (1914). He proved the reality of this phenomenon both by crystallizing salts suspended at different levels and by directly determining the density of the solution at different levels. The validity of P. A. Zemyatchensky’s conclusions was at first questioned by A. V. Shubnikov (1918), who explained the stratification of solutions by temperature fluctuations, and then by V. I. Mikheev (1930) and A. K. Boldyrev (1934), who explained the same phenomenon by the role of concentration streams rising above crystals that had fallen to the bottom of the crystallizer.

It was precisely this contradiction in the interpretation of the causes of the stratification of solutions that prompted us as well to take up this extremely interesting phenomenon in crystallization; to understand it, the following path was chosen. Experiments on simultaneous mass crystallization at many levels from solutions saturated at 40–50° and heated to 80–100° were carried out under rapid cooling: the crystallizer with the solution, cooled to 60°, was lowered into a tank with water at 20°. Into the still-hot solution a rack with glass shelves was lowered; the number of shelves in different experiments was equal to 3, 4, and 9 (Fig. 1). Glass shelves measuring \(9 \times 12\) cm were arranged in the rack at equal distances from one another (17 mm in racks with 9 shelves and 20 mm with 3 and 4 shelves). From above, the rack was covered with a glass plate, which took upon itself all the crystals that fell out from the overlying layer.

The rack was removed from the solutions in each individual case after 5—12—18 and 24 hours from the moment the crystallizer was immersed in the tank with water. After air drying, the shelves with the crystals deposited on them

the shelves with crystals were weighed, and from the difference in weights the quantity of crystals that had precipitated on each shelf was determined.

A portion of the experiments from 41 crystallization experiments in crystallizers with racks of three, four, and nine shelves—levels—is given in the table below.

Fig. 1a. Diagram of a crystallizer for crystallization at many (4 working) levels.

Fig. 1b. Diagram of a crystallizer for crystallization at many (9 working) levels.

From examination of the experimental data one may draw a number of the following conclusions:

1. Experimental studies of mass crystallization at many levels from the listed solutions showed that the total quantity of crystals, in grams, precipitated on the shelves of the rack, as a rule, increases from top to bottom; this is indisputably indicated by the main body of the experiments carried out. Experiments I, V, X, XVI, XV, XXVII, XXXIX, XI, XIX, and XLI only confirm the conclusion drawn.

However, several experiments showed various kinds of deviations from the general rule. Thus, in experiment XX, at the lower (third) level, instead of an increase in the total quantity of potassium dichromate crystals in comparison with the second level, we see, on the contrary, a decrease in the total weight of the crystals. Similar facts occur in a few other experiments, for example, in XII, XIII, and XXIII, in which at the lower—fourth—horizon, instead of an increase, we likewise have a decrease in the weight of the precipitated crystals. Such a decrease in weight contrary to the rule should be explained by the fact that a large mass of crystals at the bottom of the crystallizer (for example, in experiment XX, crystals with a total amount of 46.88 g precipitated on the shelves, whereas on the bottom around the rack—65.22 g), drawing from the solution the substance supersaturating it, creates in part an unstable state in the region of the lower horizon of the rack. This disturbed equilibrium leads to the crystals on the shelf of the lower horizon of the rack partially dissolving. In experiment XXIX, which lasted 48 hours, up to and including the 6th level there is a regular increase in the weight of crystals from shelf to shelf, but from the 7th level the total weight of crystals on the shelves decreases with depth. The reason for this phenomenon is presumably the same as in experiments XX, XII, and XXIII.

In addition to the features of mass crystallization just indicated, second-order regularities are emerging within the general regularity. Thus, in experiment XXVIII we have, as it were, two layers, from horizons 1 to 4 and from 5 to 9, within which the total weight of potassium dichromate crystals increases from top to bottom and, at the same time, there is an overall increase in weight:

crystals from top to bottom. In experiments XXX and XXXI we have the same picture. The general regularity of an increase in the total weight of crystals along the horizon from top to bottom is maintained in this case as well. More complex relations are found in experiment XXXV, where it is necessary to distinguish five finer layers, which are also characterized by a regularity of the second order.

In experiments I, V, X—XII, XV—XVII, XXVII, and XXXIX potassium dichromate crystallized; in XX and XXIII—aluminum alum; in XII, XXX, XL, and XLI—chromium alum; in XXXIII—copper sulfate.

1. Thus, the experimental material presented on mass crystallization at many levels gives firm grounds for asserting that the density of a solution located in the field of terrestrial gravitation has time, even before crystallization begins, to become established and increases from top to bottom. Therefore the experiments of P. A. Zemyatchensky and his conclusions on the stratification of solutions, made with allowance for the force of gravity, are in complete agreement with our data. The general stratification of solutions is necessarily characteristic of solutions of any concentrations and does not depend on their composition and nature.

This conclusion is confirmed by the fact that solutions and melts, left to themselves as formations located in the field of terrestrial

gravitational attraction, obey the law of gravity and its particular expression—the hypsometric law of Halley–Laplace, which can be expressed by the formula:

\[ h=\frac{RT\ln \dfrac{p_0}{p_h}}{Mg} \quad \text{or} \quad h=\frac{RT\ln \dfrac{C_h}{C_0}}{Mg} = \frac{RT\ln \dfrac{n_0}{n_h}}{Mg}. \]

This law makes it possible to relate the magnitude of the pressure, where \(p_0\) is the pressure at a given level, \(p_h\) is the pressure at height \(h\) above the given level, \(M\) is the molecular weight of the substance, \(T\) the absolute temperature, \(R\) the universal gas constant, and the concentrations \(C_0\) and \(C_h\) to the numbers of particles \(n_0\) and \(n_h\) of the substance per unit volume at the corresponding levels.

The validity of the fact that the density of a solution decreases with height was also demonstrated in a graphic way by the physicist Perrin using the example of the distribution of gamboge suspensions, and, in the first half of the nineteenth century, by Gouy and Chaperon.

From what has just been said it naturally follows that the density of a solution decreases regularly from bottom to top and obeys the hypsometric law, while the regular decrease from bottom to top in the number of crystals precipitated of one substance or another in our experiments and in the experiments of P. A. Zemyatchensky is a consequence of the regular distribution of the substance in the equilibrated solution.

1. The process of crystallization in our experiments proceeded over a comparatively short time and lasted no more than 24 hours. During this time, owing to rapid cooling, at first convective motions, and then, with the appearance of crystals, the motion of concentration currents, were unable to eliminate in the solution the regular distribution of the dissolved substance and its regular precipitation at levels during crystallization. Therefore there is no basis, as A. K. Boldyrev did, for ascribing to concentration streams the principal factor in the stratification of solutions.

2. A study of crystallization at different levels at the very first stages of the formation of visible nuclei shows that, in the space between the glass plates, for example, very small and elongated crystals of \(K_2Cr_2O_7\) precipitate. They are formed at some point of the solution between the shelves, as seed crystals, which at first are held for some time in suspension by the forces of adhesion arising between the crystal and the solution. The seed crystals increase in size and, having reached a certain magnitude, as though projecting themselves, fall onto the surface of the shelf of the stand. At the places where the crystals fall, one can observe the formation of small clustered aggregates of small crystals (sometimes up to 20 in number), piled together in disorder. The piling up of crystals into clusters indicates that at each point of the solution, as at a node, seed crystals arise successively, one after another, each of which is held at the point of its birth for some rather long time. The disorderly distribution of clusters on the surface of the plate indicates that similar nodes of crystal nuclei also arise in disorder. Experimental investigations of crystallization carried out at many levels indicate that the number of such crystallization nodes increases numerically together with the increase in the density of the solutions in the same direction.

3. A similar phenomenon of microheterogeneity in supersaturated solutions is the cause of the formation of nodes with the greatest concentration

substances, which are the site of origin of crystal nuclei. The fluctuational centers of crystallization are retained for some time in the bulk of the solution, and here, one after another, there arise successively the second, third, fourth, etc., crystal nuclei, which, having overcome adhesion to the liquid, fall downward one after another.

1. After the first stage of crystallization, in the heaped cluster formations of crystallites—nuclei—there follows recrystallization of the clustered accumulations. This recrystallization leads to the formation, in place of the heap, of one or two relatively large crystals. The study of such single crystals shows that they constitute a clear example, according to M. V. Erofeev, of aggregate crystals, or crystals of clustering.

In Figs. 2a and 2b, which are photographs of chromium-alum crystals that precipitated on the upper and lower levels of the rack in experiment XL, it is clearly seen that such large and small crystals are distributed over the surface of the plates at random. The character of the distribution of crystals on one level does not repeat the character of the distribution of crystals on the neighboring one.

Fig. 2a. Example of the distribution of chromium-alum crystals in experiment XL on the first (upper) level

From the figures under consideration it is distinctly evident that the sizes of the crystals at the different levels generally increase from top to bottom. Comparisons of the figures showing the distribution of crystals on the same plates in different experiments show that the forms obtained for the distribution and clustering of crystals on the plates of the rack are not repeated.

1. From the moment when relatively large crystals form on the shelves of the rack, the latter grow at the expense of the substance of the solution. Simultaneously with the process of transformation of clustered accumulations of very small crystals into relatively large ones and with their growth, the process of formation of new crystal nuclei in the space between the shelves continues, and from time to time they fall from the suspended state onto the po—

surface of the shelves; the newly formed nuclei grow and increase in size.

1. Finally, the study of the distribution of crystals on the surface of the plates leads to the conclusion that individual crystals, being under the most favorable growth conditions, become relatively large and are often surrounded by ambiguously oriented and relatively small crystals.

Fig. 26. Example of the distribution of crystals of chrome alum in experiment XL at the third (lower) level.

Thus, the factual material presented above has made it possible to draw a number of extremely important conclusions, which were theoretically expected on the basis of all our knowledge about solutions and crystallization processes and were well confirmed by experiments.

Differentiation of solutions by density is an obligatory property for them and obeys the law of terrestrial gravitation and molecular (Brownian) motions; otherwise the dissolved particles would “fall” to the bottom of the crystallizer. At the same time, the experiments made it possible to reveal in detail certain aspects of the course of crystallization as mass crystallization.

LITERATURE

1. Boldyrev A. K. Crystallography. Moscow—Leningrad, 1934.

2. Erofeev M. V. Crystallographic and crystallo-optical studies of tourmalines. St. Petersburg, 1870.

3. Zemyatchenskii P. A. Studies on crystallogenesis. IV. Dissolution of supersaturated solutions. — Proceedings of the Academy of Sciences, Series VIII, Physico-Mathematical Section, Vol. XXXIII, No. 5, 1914.

4. Mikheev V. I. Causes of the dissolution of supersaturated solutions. Proceedings of the Mineralogical Society, General Part 59, 1930.

5. Shubnikov A. V. The influence of temperature fluctuations on crystals. Journal of the Russian Physico-Chemical Society, Physical Section, Issues 1–3, 1918.

1. Report read at the scientific conference on dielectrics and semiconductors on February 6, 1958, in the city of Tomsk. ↩