Stereoscopic Observations of Skeletal and Dendritic Forms of Crystal Growth

D. D. Saratovkin, V. A. Kulikov, P. I. Kaushanskaya

(Presented by Professor Doctor A. A. Vorob’ev)

There is a large body of work devoted to studies of crystallization using monocular microscopes without a stereoscopic attachment. However, all these works have a substantial drawback. Crystals grow in space; they have three dimensions, whereas in the microscope they are visible as flat figures. Without the ability to judge the mutual arrangement of the details of the object under study, the investigator sometimes takes an edge of a crystal for an angle, and a face for an edge. Measuring angles on planes obliquely situated with respect to the plane of the specimen loses all meaning.

The very first observations of the crystallization processes of ammonium chloride with the aid of the MBS-2 stereoscopic microscope showed that very important details had not been discovered in the investigations carried out earlier. In connection with this, it was decided to repeat some of the investigations described by D. D. Saratovkin [1, 2].

We used the MBS-2 stereoscopic microscope together with the MFN-1, “Exacta,” and “Photocor” cameras. An AU-12 stereo attachment with a biological microscope was also tried. The stereo effect here is much worse, but larger magnifications can be obtained.

As for the preparation of specimens, the method described by D. D. Saratovkin [2] was used for the most part; however, in order to achieve greater volume between the slide and the cover glass, threads or fragments of cover glasses were always placed along the edges.

Necessary Information on the Optical-Physical Foundations of Stereoscopy

Stereoscopic photographs are usually viewed with the aid of a stereoscope. However, a stereoscope may not always be at hand, and therefore it is useful to know how to manage without one.

There are two ways of viewing stereophotographs without a stereoscope. One of them is called the method of “parallel axes,” and the other the method of “crossed axes.” We shall describe here the method of parallel axes as the simplest and most suitable for viewing the appended stereomicrophotographs. This description has been borrowed by us from the book by S. P. Ivanov [3]. A reminder of the optical-physical foundations of stereoscopy will help the reader understand and master this method.

If a point of the object being viewed by the eye is located not far from it (Fig. 1), the bundle of light rays falling on the crystalline lens is perceived by the eye not as parallel, but as diverging, in the form of a cone with its vertex at point \(O\). The angle of divergence of the rays from point \(O\), denoted by the letter \(\alpha\), is called the angle of accommodation. By the automatic action of the ciliary muscle, the crystalline lens accommodates, i.e., acquires such a convexity that the bundle of rays is brought to a focus \(O'\) on the surface of the retina. A person senses the degree of effort of the ciliary muscle required for accommodation of the crystalline lens, and on this basis judges the distance of the observed object. However, this is possible only when the object under consideration is no more than five meters away. To judge distances extending to more remote objects, it is necessary to take into account the interaction of both eyes, which is characterized by the angle of convergence. In Fig. 2 this angle is denoted by the letter \(\beta\).

Fig. 1. Path of rays when viewing with one eye.

Fig. 2. Path of rays when viewing with two eyes.

In practical activity, the vertex of the angle of accommodation \(\alpha\) and the vertex of the angle of convergence \(\beta\) always turn out to be at one and the same point, which the eyes are viewing at the given moment. However, accommodation and convergence can be artificially separated, and after some training one can learn to use them separately. How this is achieved is shown in Fig. 3.

On a sheet of paper we paste two photographs taken from the positions of the right and left eyes. Let \(a_1\) and \(a_2\) be two points corresponding to one point of the photographed object. If an opaque partition \(CD\) is placed between the eyes, then each eye will see only one of the two images (the distance to the pair of photographs is best taken as 30–40 cm). At first these images will be perceived as separate, but after

Fig. 3. Superposition of a stereo pair by the method of parallel axes

two or three minutes, and sometimes sooner, they will merge into one. This will occur when the eyes are converged on point \(a\), located behind the pair of photographs. For some time the image will be blurred, because out of habit the crystalline lenses will be accommodated to this same point; however, very soon it will become sharp, clear, and somewhat larger in size than the actual one. The sharpness of the image obtained as a result of the separate perception of two images indicates that a rupture of accommodation and convergence has occurred. In Fig. 3 it is seen that the vertices of the cones characterizing the accommodation of both eyes have remained at points \(a_1\) and \(a_2\), whereas the intersection of the axes of the eye lenses occurs at point \(a\).

The distance between points \(a_1\) and \(a_2\) is called the base of the stereo pair. It is quite obvious that the described effect can occur only if this base is no greater than the distance between the optical centers of the eye lenses. The described method of combining stereo pairs is called the “parallel-axes” method, because at the maximum base, i.e., one equal to the distance between the centers of the lenses, the optical axes are arranged parallel to one another.

For nearsighted persons, achievement of the described effect is facilitated by viewing without spectacles, and for persons with normal vision by the use of spectacles with an optical power of from \(+1\) to \(+5\) diopters.

It should be noted that abroad there already exist books supplied with such illustrations, which must be viewed by the method described. As an example we may cite the two-volume work by Morse and Feshbach, Methods of Theoretical Physics [4].

Skeletal Crystals

In the literature on crystallography, mineralogy, and physical metallurgy one constantly encounters two terms that are applied by different authors to the same crystals. These are skeletal and dendritic crystals. Crystallographers often call skeletal those crystals which metallurgists classify as dendritic. Conversely, metallurgists call dendrites those crystals which in mineralogy are classed as skeletal.

Such confusion in terminology can be explained by two circumstances. First, the cause of the formation of skeletal and dendritic forms is one and the same. These forms are obtained during the rapid growth of a crystal, when in the space surrounding the crystal there are foreign particles (molecules, atoms, ions) that are not removed by convection or diffusion. Second, even if we introduce the strictest distinction between these two forms, we shall encounter crystals that are difficult to assign to one form or the other. They will be transitional from one form to the other.

Characteristic of dendritic forms of crystals is the presence of branches attached to one another. Metallurgists usually call them axes of different orders ([5], p. 335). However, even such halogen salts as sodium chloride, potassium bromide, potassium iodide, etc., in many cases give well-expressed cubes with a complete set of angles and edges; but instead of faces they have deep, terraced depressions. From the side, especially when observed with one eye in a microscope, such crystals resemble sectorial ones. However, their “growth pyramids” turn out not to be filled with the substance of the crystal, but empty. Here there are both angles and edges, but no faces. In the stereomicrophotograph (Fig. 4) such a crystal is clearly visible, surrounded by others of more bizarre shape, but likewise hollow inside and without any branches.

V. A. Mokievskii and S. N. Semenyuk [6], touching on this same question, described similar forms of alum crystals and presented a drawing of skeletal crystals of cuprite and gold, where there are likewise the angles and edges of an octahedron, but no faces; in their place are pits extending almost to the center of the crystal. Of course, such crystals cannot be called dendritic, since they have no branches.

Fig. 4. Skeletal crystals of potassium iodide formed from a solution in water; ×14.

The further development of similar crystals gives very diverse forms, which should nevertheless be regarded as skeletal, since here too there are no branches. As an example we give Fig. 5. But here, under the same crystallization conditions, with further growth the crystals begin to branch distinctly, and they can already be assigned to the dendritic forms, although they only weakly resemble ordinary dendrites (Fig. 6).

Fig. 5. Skeletal crystals of potassium iodide. View in the direction \([111]\); ×14.

Thus, between skeletal and dendritic forms of crystals there is the following distinction: for skeletal forms, retardation of the growth of faces is characteristic, while at the same time there is the possibility of the formation of more or less developed edges typical of crystals of the given substance. This leads to the fact that, as a rule, no branches are formed. Dendritic forms, however, are characterized by retardation not only of faces but also of edges, which leads to the formation, at the corners of the crystals, of branches or “axes” of dendrites.

Obviously, at some point it will be very difficult to decide to which form a given crystal should be assigned. However, this should not cause any misunderstanding. Certain forms of crystals will always be intermediate, no matter how carefully we separate skeletal crystals from dendritic ones.

Fig. 6. Potassium iodide. Transitional form from a skeletal crystal to a dendritic one; ×14

Octahedral and Cubic Forms of Dendritic Crystallization

Pure ammonium chloride, beginning to crystallize in the form of microscopic octahedral crystals, gives dendrites with branches forming at the angles of the octahedron. It is quite clear that these branches prove to be perpendicular to one another, since they must grow in directions parallel to the edges of the cube. Let us agree to call this form of dendritic crystallization octahedral. Figure 7 shows a stereo-microphotograph of typical dendrites of octahedral form.

Fig. 7. Octahedral dendrites of ammonium chloride; ×14

Here it is clearly seen that the difference between the dendrites consists only in their orientation relative to the plane of the preparation and depends on whether or not the slide and cover glass interfere with the branches’ growth. On the right we see two dendrites positioned with one of their branches parallel to the plane of the slide. Nothing prevents such a branch from growing straight…

mo, and it becomes very long. In a different position are the branches of the dendrite located in the left part. They all grow at an angle to the glass plates and cannot grow without limit. It is not difficult to understand that decreasing the distance between the glass plates should lead to a shortening of such branches. Examination of such a specimen under a microscope with one eye leads to the erroneous conclusion that there are dendrites of two fundamentally different types.

Thus, ammonium chloride, free from a sufficient quantity of impurities that enter into chemical interaction with it, crystallizes from an aqueous solution in octahedral form.

The situation is different when the solution contains an impurity capable of forming a complex compound with ammonium chloride. We used urea as such an impurity.

The cube faces on an octahedral crystal are absent because they grow faster than the octahedron faces. If a molecule of an impurity, appearing in small quantity in the space surrounding the crystal, forms a complex compound with the crystallizing substance, then around the crystal there appear, in addition to impurity molecules, molecules of this compound. When impurity molecules adhere selectively to the octahedron faces and do not adhere at all to the cube faces, then the octahedron faces capture them and are inhibited only by molecules of the complex compound, not counting solvent molecules; the cube faces, however, are inhibited both by molecules of this compound and by impurity molecules. This leads to a considerable decrease in the growth rate of the cube faces, and they appear on the crystal; the octahedron faces are displaced by them, and the crystal assumes the faceting of a cube. In the case of dendritic crystallization, the needles or branches of the dendrites must now appear at the corners of the cube and therefore grow parallel to the directions of the cube diagonals. The angle between the diagonals of a cube is \(70^\circ 24'\); therefore dendrites appear with angles between the branches of approximately \(70^\circ\) and with the angle supplementary to this to \(180^\circ\), i.e. \(110^\circ\). We shall call this form of dendritic crystallization cubic. Figure 8 gives a stereomicrophotograph of typical dendrites of cubic form.

Fig. 8. Cubic dendrites of ammonium chloride with an admixture of 8% urea; ×14.

We have established experimentally that, at small supersaturations of the solution, crystallization proceeds in octahedral form even in the presence of 6 molecules of urea per 100 molecules of ammonium chloride. An increase in supersaturation, however, leads to the cubic form of dendritic crystallization already at 2 molecules per 100 and less. Explanation

this, apparently, must be as follows: at low supersaturation the crystals grow slowly. Any impurities that impede the growth of their faces have time, to a more or less sufficient degree, to move away from these faces by diffusion. As a result, the crystals can assume their usual form. For ammonium chloride these will be octahedral dendrites. When the supersaturation is increased, the rate of crystal growth should increase, the interference from impurities should increase, and the form that should occur in the presence of these impurities appears.

Stereomicroscopic observations of the crystallization with 6 molecules of urea per 100 molecules of ammonium chloride, at a variable cooling rate entailing a change in supersaturation, make it possible to record the transition from the octahedral form to the cubic one.

Fig. 9. Diagram of the transition from the octahedral form of a dendrite to the cubic form.

Structures are obtained that correspond to the scheme of arrangement of dendrite branches shown in Fig. 9. Here, below, the octahedral form of branch arrangement is depicted; in the upper part, the transition of this dendrite to the cubic form is shown.

In the stereomicrophotograph of Fig. 10 one can see such a transition from the octahedral form to the cubic one.

An increase in the amount of impurities in such a case causes a slowing of the growth rate of the dendrites and, as a consequence, a clear manifestation of the faces of the cube. In essence, dendritic crystallization passes over into skeletal crystallization. Fig. 11 presents a stereomicrophotograph of the same transition from the octahedral form to the cubic form in the presence of 8.4 molecules of urea per 100 molecules of ammonium chloride. Both the branches of the octahedral form, perpendicular to the main trunk arranged horizontally, and the branches of the cubic form that appeared from the site where this trunk split—all of them are covered with cube faces.

A further increase in the concentration of the impurity transfers crystallization from dendritic to skeletal. Large crystals are obtained, having well-developed edges and portions of cube faces. Fig. 12 presents a stereomicrophotograph of such a skeletal crystal of ammonium chloride.

Fig. 10. Transition from the octahedral form of dendritic crystallization of ammonium chloride to the cubic form. Urea 6%; ×14.

Fig. 11. Same as in Fig. 10, but urea 8.6%; ×14.

Fig. 12. Skeletal crystal of ammonium chloride, with an admixture of urea 12.6%; ×14.

ammonia with an admixture of urea, 12.6 molecules per 100 molecules of ammonium chloride.

In his book Dendritic Crystallization, D. D. Saratovkin describes dendrites outwardly resembling honeycombs, and also considers the possible cause of the appearance of such structures. Stereomicroscopic observations of the growth of similar dendrites make it possible to detect details that are completely unnoticeable when observed in a monocular microscope with one eye. The cause of the appearance of such original structures turns out to be not only the impurity, which causes the appearance of the cubic form of dendritic crystallization. An essential role is played here by the circumstance that the cubic dendrite proves to be oriented in a strictly definite way and is clamped between two glass plates.

Specially designed experiments showed that these structures form predominantly under rapid cooling, i.e., when the supersaturation of the solution is greater. The center of crystallization is an ordinary octahedral crystallite, lying with an octahedron face on the object glass. Then the \([111]\) direction proves to be perpendicular to both glass plates. Rapid crystallization, on the one hand, leads to the appearance of needles of cubic form; on the other hand, it does not allow the crystal to turn and assume another orientation, since the needles growing upward quickly run into the cover glass.

Let us consider the growth of one needle, for example \([111]\) (Fig. 13). Since the \([111]\) direction proves to be perpendicular to the cover glass, and the angle between the directions \([111]\) and \([\bar{1}11]\) is \(70^\circ 24'\), the \([\bar{1}11]\) needle approaches

Fig. 13. Scheme of formation of honeycomb-like dendrites of cubic form.

the cover glass, making an angle of \(19^\circ 36'\) with it. If the \([\bar{1}11]\) needle runs into the cover glass at point \(A\), then from its end new needles can grow in the directions \([\bar{1}\bar{1}1]\), \([1\bar{1}1]\), and \([11\bar{1}]\), since the directions \([\bar{1}11]\), \([1\bar{1}1]\), and \([11\bar{1}]\) require emergence into the space above the cover glass. Of these three possible directions, the last two are the most favorable from the standpoint of moving the crystal away into the side where there is material for growth. In the \([\bar{1}\bar{1}1]\) direction the concentration of the solution is undoubtedly lower, since this direction is located closer than the others to the already grown needle. Thus, the \([1\bar{1}1]\) needle bifurcates at point \(A\), near the cover glass. The newly formed needles grow until they come into contact with the object glass at points \(B_1\) and \(B_2\). At these points the same bifurcation occurs as at point \(A\). The \([1\bar{1}1]\) needle gives the needles \([111]\) and \([11\bar{1}]\), while the \([11\bar{1}]\) needle gives the needles \([111]\) and \([1\bar{1}1]\). Thus we obtain two new \([111]\) needles, parallel to the first. These two new needles bifurcate in exactly the same way at points \(C_1\) and \(C_2\) near the cover glass, giving two \([\bar{1}11]\) needles and two \([11\bar{1}]\) needles. It would seem that

that the subsequent process should proceed without any changes whatsoever, continually doubling the number of needles \[III\]. Here, however, we encounter a new circumstance. Two needles—\[ĪĪI\] and \[III\]—must arrive at point \(D_2\) from points \(C_1\) and \(C_2\). No collision can occur, since they grow at the expense of the salt present in the solution. Then one of the needles, for example \[ĪĪI\], reaches point \(D_2\) first. The second needle stops growing before reaching point \(D_2\). Now needle \[III\] cannot bifurcate. It gives only one needle \[III\], since the direction \[ĪĪI\] is already occupied by the needle \[ĪĪI\] that has grown toward it. Thus, the development of the crystallization process in any one direction proceeds with an increase in needles \[III\] in the order of the natural series of numbers.

It is not difficult to see that the projections of all the needles onto either of the glasses form angles of \(120^\circ\) with one another. This is precisely why, when observed in a microscope with one eye, a picture is obtained that externally resembles the cells of a honeycomb.

A stereomicrophotograph of the described structure is shown in Fig. 14.

Fig. 14. Honeycomb-like dendrites of ammonium chloride. Urea 6%; ×24.

It should be noted that honeycombs not complicated by the appearance of a large number of side branches can be obtained only at very small distances between the glasses, when the cover glass is simply placed on the slide. At larger distances, each of the needles, before reaching the opposite glass, gives many branches, naturally parallel to the main needles. Then the honeycombs turn out to be as if filled with branches, and the cellularity may be less clearly expressed.

Conclusions

1. The technique of stereomicroscopic investigations makes it possible to detect such details as are completely missed when observing with an ordinary microscope using one eye. Stereomicrophotography is a very convenient means of documenting the observed processes.

2. In order to eliminate confusion in the terminology concerning skeletal and dendritic crystals, it is necessary to bear in mind the following distinction between these two forms: skeletal forms are characterized by retardation of the growth of faces, but by the possibility of forming more or less developed edges typical of crystals of the given substance. Dendritic forms, however, are characterized by retardation not only

faces but also of edges, which leads to the formation, at the corners of crystals, of branches or “axes” of dendrites.

1. Substances crystallizing in the cubic system, in the case of dendritic crystallization in the presence of impurities that enter into chemical interaction with them, may give two forms of dendrites—octahedral and cubic. Dendrites of the octahedral form have angles between branches of \(90^\circ\). Dendrites of the cubic form have angles between branches of approximately 70 and \(110^\circ\), i.e., the angles at which the diagonals of a cube are situated. The forms depend on the supersaturation of the solution. One of them appears at slight supersaturation, while the other appears at strong supersaturation. The transition from one supersaturation to another in the process of crystallization is accompanied by a change of form, i.e., by the appearance of new angles between the branches and of new faces on these branches.

LITERATURE

1. D. D. Saratovkin. Dendritic Growth of Crystals. Moscow, Metallurgizdat, p. 30, 1950.

2. D. D. Saratovkin. Dendritic Crystallization. Moscow, Metallurgizdat, p. 93, 1953.

3. S. P. Ivanov. On Color Stereoscopic Photography. Moscow, 40 pp., 1951.

4. Philip M. Morse, Herman Feshbach. Methods of Theoretical Physics. New York, Toronto, London, 1953.

5. Ya. S. Umansky, B. N. Finkelshtein, M. E. Blanter, S. T. Kishkin, N. S. Fastov, S. S. Gorelik. Physical Foundations of Metallography. Metallurgizdat, 1955.

6. V. A. Mokievsky, S. N. Semenyuk. Skeletal growth of crystals in a viscous medium. Proceedings of the All-Union Mineralogical Society, issue 2, pp. 100–108, 1952.