ON THE PROBLEM OF CRYSTAL NUCLEATION

V. Ya. Altberg, Leningrad

Phenomena involving changes in the states of aggregation are widespread in nature (the formation of fog, clouds, snow, ice, the evaporation of water, the precipitation of salts in salt lakes, etc.). It is therefore of great interest to study the conditions for the transformation of one phase into another, in particular of a liquid phase into a solid one.

The first investigators made the process of crystallization depend solely on changes in temperature conditions. At the present time, however, it has become known that the latter are necessary, but still insufficient, conditions. It is widely known that supercooling occurs, reaching, for some melts, 100° and more. Such a supercooled melt is most easily obtained if it is cooled while being protected from dust from the air and from strong shocks (Ostwald).

The supercooled state may in one way or another be disturbed, which indicates its instability; moreover, such a disturbance may sometimes occur spontaneously. The disturbance of the supercooled state is closely and inseparably connected with the onset of crystallization.

The emergence of crystallization has long been connected with the action of a solid body of the same or of a foreign substance. Ostwald tried to give this action an explanation from the kinetic point of view. He notes the accelerating action on crystallization of an impurity of traces of a solid phase, as well as the role of the motion of the liquid, its stirring. According to Ostwald, a supercooled liquid in contact with a part of its solid phase cannot remain in equilibrium, since it itself also solidifies.

A quarter of a century later, Tammann made resonance, induction, and the action of inoculation (Impfwirkung) the basis of this action.

The question of crystallization was subsequently taken up in greater detail, both from the experimental and from the theoretical side, in the closest connection with the study of the properties and features of nuclei as the inevitable and only agents of crystallization, its germs.

Ostwald’s idea that “a piece of the solid phase in a supercooled melt deposits solid substance upon itself from the surrounding medium” is transformed, in Möller’s work, into the proposition that “in front of the growing crystal there are always crystalline germs that promote crystallization.”

In Tammann and Buchner, the corresponding proposition is formulated as follows: “In dilute solutions, at the boundary of crystallization, a higher concentration of molecules forming ice is observed than in pure water.” From the fact that nuclei can be removed from a liquid by centrifugation, Bilman and Clint conclude that the nuclei have a density substantially different from that of the liquid. Consequently, the formation of nuclei is due to dust particles. The action of the latter manifests itself in a definite orientation of the adsorbed molecules. To each degree of supercooling there corresponds a size of dust particle sufficient to bring about immediate crystallization.

V. Ya. Altberg

Meyer and Pfaff\(^2\), on the basis of their investigations, also speak of the decisive role of dust particles. Dust particles are stimulators of crystallization and the cause of the disturbance of supercooling. They express similar ideas also with regard to water, which served them, among other things, as an object of investigation.

Wegener had already long ago pointed out that sand grains are especially favorable nucleus formers. It is not for nothing that a dust particle was usually found at the center of every snowflake.

In full agreement with these data are also direct observations of the floating up of deposits carried along above the river bottom (during the period of formation of underwater ice). The fact that sand floats up more readily than water particles is partly due to their icing and the consequent decrease in their overall density.

Observations on many rivers have established that this phenomenon is widely distributed in nature and occurs annually and regularly on silt-bearing rivers. The results of a questionnaire on underwater ice showed that this phenomenon is more often observed on sandy rivers and that sand is the most frequent kind of inclusion in bottom ice.

It was precisely by the method of crystallization on dust particles that Meyer and Pfaff were able most reliably to cleanse a liquid of the last traces of the finest dust.

Analogous purification of water from turbidity occurs in rivers after the period of silt carrying, when the water becomes especially clear. When bottom ice floats up, however, the water becomes, on the contrary, especially turbid because it is stirred up by the bottom ice saturated with silt and sand.

Our laboratory experiments showed that sand grains thrown into supercooled water (not cooled) may serve as an inoculation and as nucleus formers, becoming covered with a thin shell of ice (under experimental conditions guaranteeing the impossibility that hoarfrost or, in general, particles of the solid phase of water could enter the supercooled water).

The most complete data on nuclei and the laws of their development are given in Meller’s work.

The last three chapters of this work are the most interesting: on the origin of nuclei ahead of the growing surface of a crystal, the manifestation of spontaneously formed nuclei, and the explanation of the observed phenomena of crystallization.

At the beginning of the article the author describes his experiments and those carried out jointly with Gross, which led them to the necessity of admitting the constant and continuous replenishment of the melt by variously oriented nuclei ahead of the growing surface of the crystal. Subsequent experiments clarified two paths of nucleation: first, spontaneous, and second, by the splitting off of nuclei from the crystal, which in turn act as inoculating (impfend) agents upon the melt.

According to Meller’s experiments, a formed nucleus, generally speaking, cannot grow immediately, but it “manifests itself” when crystallization reaches the immediate location of the nucleus.

Gross and Meller see the reason for the constant presence of nuclei ahead of the crystal in the constant splitting off of nuclei from the crystal, which in turn act as inoculation, and in the manifestation (near the crystal) of latent nuclei that had existed earlier. Splitting off, moreover, prevents the process of monocrystallization, since it leads to the development of many crystals. By the presence of the process of manifestation of previously existing latent nuclei, the authors easily explain the phenomena they observed.

Most latent nuclei, from the point of view of these investigators, degrade and are destroyed over time. Thus, for example, at \(t = -25^\circ\), during 3 min, 70 nuclei were manifested, while at \(0^\circ\) not a single nucleus was. At very large supercoolings, both overall crystallization and the growth of nuclei are practically equal to zero. The results of Meller’s investigation are shown in Fig. 1, where \(v\) is the rate of crystallization,

$w$ — the rate of development of a nucleus — the number of nuclei formed spontaneously per unit time and unit volume.

Nacken3 showed experimentally that the temperature inside the crystal, and also in the layer of melt immediately surrounding the crystal, is below the melting point. Thus he refuted the views of Tammann, who had asserted that crystallization takes place at a temperature equal to the melting point. In addition, Nacken directly observed the formation of nuclei on the surface of a slowly growing crystal face.

Fig. 1. Dependence of the rate of crystallization
and the number of nuclei on the degree of supercooling

In crystallization according to Tross,4 large molecular complexes are deposited on the surface of the crystal, owing to which the rate of growth of the crystal is accelerated. “Therefore,” says Meller, “it is impossible to preserve a supercooled liquid in such a state for an arbitrarily long time.”

Meller represents the development of a nucleus or, conversely, its degradation as a state of mobile equilibrium between two mutually opposite processes: the deposition of molecular groups and, conversely, their dissolution by the liquid.

The tendency of the crystal to give up molecules to the liquid depends on the supercooling. Therefore, at small supercoolings the growth of the nucleus proceeds extremely slowly.

The picture of the development of nuclei drawn by Meller is based both on his own experiments and on the experiments of Nacken and Gross, taking into account the latter’s hypothesis on the presence in front of the crystal of an accumulation of nuclei (Keimschar) that are at various stages of growth.

A more detailed picture of the development and degradation of nuclei has not been given by any of the investigators either before or after Meller.

Bilman and Klit1 established experimentally the fact that the number of nuclei formed depends on the duration for which the solution is kept at the temperature of nucleus formation. The authors ascribe the decrease in the number of nuclei with increasing temperature to the gradual destruction of nuclei as a result of the effect of thermal scattering of molecules adsorbed on the particle. The adsorption of molecules assumed by them indicates the possible stability of nucleus-forming agents even at a temperature higher than the phase-transformation temperature.1)

In the authors’ opinion, during the solidification process a speck may, but need not, become a nucleus, which they explain by the fact that samples “for determining the conditions of the experiment” may “grow old”; this means that reproducible results can be obtained only when, prior to the onset of—

1) This conclusion of Bilman and Klit is confirmed in recent experiments by Danilov and Neimark, which prove the presence of crystallization nuclei above the melting point.

Similar experiments with the same samples had already been carried out many times before the experiment. Bilman and Klitt confirm the fact observed in Tammann’s latest works that the rate of formation of nuclei can be very strongly reduced by simple preliminary heating of the liquid to a temperature considerably exceeding its melting temperature. The explanation of this fact may perhaps lie in the presence of cybotactic groups (Stewart).

According to this theory, a liquid is not a homogeneous medium, since at every given moment a certain number of molecules gather into groups resembling a crystalline structure and called cybotactic groups. Thus the entire thickness of the liquid proves to be permeated by a whole network of correctly constructed molecular aggregates of pseudo-crystalline structure. The presence of such aggregates can to a considerable degree facilitate the nucleation and formation of crystalline embryos when other favorable conditions are also present, for example the presence of dust particles—carriers of already existing surfaces of separation between the liquid and solid phases, so important for the primary formation of a two-dimensional embryo.

It has already been noted above that the experiments of Meyer and Pfaff confirm the decisive role of dust particles as stimulators of nucleation. Their final conclusion amounts to the fact that, in order to excite crystallization in supercooled melts, crystalline embryos are always necessary, i.e. particles of a solid phase either of the same substance or of a completely different one (dust particles). In particular, in their opinion water contains an unusually large number of solid particles playing the role of nuclei.

Turning to the important question of the crystallization properties of water, it is first necessary to dwell on the work of R. Köppen^6, which appeared after the works of Bilman and Meyer with their collaborators on the same subject. Köppen studied the crystallization of a solution of chloroacetic acid, counting nuclei by Tammann’s method. A linear dependence of the number of nuclei on time was found, but only within the limits of a single minute, which by no means can be regarded as confirmation of the linear dependence required by Tammann’s theory, supposedly existing throughout the whole process of nucleation. Tammann’s linear dependence was completely refuted by Ginshelwood and Hartley^7, and also by Meller’s experiments.

Köppen discovered a great influence of the motion of the liquid on the character of crystallization. Whereas in a solution that was in an immobile state no new nuclei arose, after the solution was set in motion a multitude of crystals immediately appeared; thus, introducing a seed into an immobile solution of weak supersaturation caused only the growth of the seed itself, while in a mobile solution new nuclei arose under conditions of supersaturation and time under which in other cases the formation of new nuclei proved impossible. Thus Köppen’s findings emphasize two essential features in the process of crystallization: the presence of a seed and the mobile state of the solution.

In the light of the investigations of Meller and Gross, Köppen’s result is explained by the fact that nuclei formed in the presence of a seed not only in a moving liquid, but also in an immobile one, with the only difference that in the latter the nuclei, because of their low growth rate, remained in a latent state and therefore were not detected by the eye.

In analyzing the experimental results of Meller, Gross, and Köppen, it should be borne in mind that, according to theoretical considerations, at small supercoolings the formation of nuclei proceeds extremely slowly, and this rate increases very rapidly as the degree of supercooling increases (Volmer and Weber^8, Farkas^9, Stranski and Kaischew^10).

Let us now turn to the important question of the crystallization properties of water. Concerning the latter, according to Tammann, we are allegedly little informed—

ON THE PROBLEM OF CRYSTAL NUCLEATION

This field, in his opinion, has scarcely even been touched upon. In fact, however, the situation is somewhat better. First of all, the properties of water were studied by Meier and Pfaff, who found that water (unpurified) contains an unusually large number of such nuclei (dust particles), liberation from which, in order to obtain water that does not crystallize (with the aid of the aforementioned nuclei crystallizing out in the form of pure melts), proved exceedingly difficult. Nevertheless, Meier and Pfaff succeeded in purifying water from nuclei to such an extent that it did not crystallize even at large supercoolings (down to −33°).

Such properties of unpurified water indicated that, apparently, it is much easier to study nuclei in it than in other liquids and melts. Our experiments confirmed this. However, unfortunately, there was no possibility at the time of reporting properly the results of our work to foreign physical chemists, and in the foreign literature to this day there prevails another view, in our deep conviction, based on numerous experiments, an incorrect one.

According to Tamman, since one tries to study water nuclei, the latter possess so great a rate of crystallization that, allegedly, there is no possibility of studying them, and therefore water with respect to nuclei has remained completely unstudied.

However, in view of the role that water plays both in nature as a liquid and in the solid phase, one cannot be reconciled to the complete lack of study of water nuclei. All the more so since there is sufficient experimental material available.

In confirmation of what has been said, one may cite Tamman’s own curve of the dependence of the rate of crystallization of water on the degree of its supercooling (Fig. 2). From the curve presented it is evident: first, that with decreasing supercooling the rate of crystallization invariably falls, approaching zero in the absence of supercooling; second, that Tamman did not carry out experiments at very small supercoolings, the most favorable for experiments with nuclei, the rate of whose growth in this case is small.

Fig. 2. Dependence of the rate of crystallization of water on supercooling

Tamman and Büchner did not see that optimum of conditions within which it is easiest to study nuclei and not be confronted with the colossal difficulties to which they themselves pointed.

Long before the publication of the curve of Tamman and Büchner, guided by other considerations, we worked predominantly within the range of the optimum conditions for the study of nuclei, and therefore easily obtained the latter and studied them.

In addition, our recent experiments (1938), together with N. P. Polevoi, showed that sand thrown into supercooled water (not cooled) can cause, after agitation of the water, the formation of nuclei; in this process the grains of sand themselves prove to be clothed with a thin layer of ice and, owing to the consequent reduced density of the particles, float to the surface of the water. The conditions of the experiment were such that the entry of particles of ice from outside was absolutely excluded.

These experiments and our investigations of the so-called bottom ice showed that the latter is nothing other than nuclei-

ice. Therefore, the study of embryonic ice is of great practical importance.

Further, we experimentally refuted the erroneous assertion of V. Chernysh1 that “no mechanical shocks have any influence on the crystallization of supercooled water.” By striking a glass rod against the bottom of the vessel or by forcing a piece of metal located in the water to fall with height to the bottom, we could always induce crystallization. By the impact method, Young and Van Sicklen even showed that water does not possess a metastable zone: it crystallized from impact even at an insignificant supercooling of \(-0.02^\circ\). This fact is of great fundamental significance.

Observing more closely the process of the onset of crystallization, we could see how, in the water near the point of impact, a multitude of the finest elements of ice appeared in the form of a cloud, which then expanded more and more, rising higher and higher (Fig. 3 a, b, c).

We succeeded experimentally in establishing the following propositions:

1. It is possible to ascertain experimentally the presence of nuclei in supercooled water, which may be invisible and exist in a latent state, from which they can, by one means or another, be brought into the state of grown, manifested objects visible to the eye, with a definite structure and with a definite rate of crystallization, depending on the degree of supercooling1.

2. A nonlinear dependence of the number of nuclei on the degree of supercooling has been established, which is also confirmed by theory.

LITERATURE

1. Billman u. Klitt, Chem. Centralbl., 1568, 1933.
2. Meyer u. Pfaff, Z. anorg. Chem., 217, 257, 1934.
3. R. Nacken, N. Jahrb. Min., 11, 131, 1915.
4. H. Gross, Vortrag Naturf., u. Artze, Leipzig, 1922.
5. Tammann u. Röth, Z. anorg. Chem., 183, 388, 1930; Tammann u. Othmer, Ibid., 91, 207, 1915.
6. R. Köppen, Z. anorg. Chem., 228, 169, 1936.
7. Hinschelwood, a. Hartley, Phil. Mag., 43, 78, 1922.
8. Volmer u. Weber, Z. physik. Chem., 119, 277, 1926.
9. Farkas, Z. physik. Chem., 125, 236, 1927.
10. Stranski, u. Kaischew, Z. physik. Chem., B 26, 100, 1934.
11. V. Chernysh, Met. i gidrol. No. 4–5, 120, 1937.

To the article by V. Ya. Altberg

Fig. 3. Cloud of ice elements arising after a glass rod strikes the bottom of the vessel: a) first stage, b) second stage, and c) third stage.

1. Some investigators to this day stubbornly deny any possibility of the formation of nuclei in water and assert that such nuclei enter the water exclusively from outside (snowflakes). ↩↩