On the Structure of Ice

W. H. Bragg1

In recent years, in the study of the crystalline character of ice and snow, certain facts have become clear which make it possible to obtain new explanations of old problems. One of these is the motion of ice and snow on mountains, which has always been a subject of wonder. In order to determine the nature of the large-scale motions of Alpine glaciers, attempts at systematic measurements were undertaken in the middle of the nineteenth century. It was found that ice flows, adapting itself to the bends and descents in valleys, like water. It was also established then that the middles of glaciers move faster than the edges. In 1857 these studies were continued by Tyndall, who vividly described these phenomena in his book Glaciers, from which Figs. 1–2 are taken, showing the confluence of separate ice streams into a “glacial sea.” The explanation of this curious plasticity of ice, which at the same time is a very brittle substance, encountered great difficulties in those days, but now this problem may be considered solved.

Fig. 1. Alpine glaciers

At the end of the last century it became a common custom to visit the Alps in winter for sporting purposes. This sport was greatly promoted by the astonishing variety in the structure of snowy mountains. Dr. Seligman, who was one of the most perceptive observers, devoted an entire book (Nature of Snow) to these questions; Fig. 3 here is also taken from it. It now turns out that there is an astonishing connection between these majestic scenes and the minutest details of the structure of water molecules and ice crystals.

The subject of attention of earlier observers was also the astonishing regularity in the structure of snowflakes, especially striking

Fig. 2. Diagram of glacier movement (after Tyndall)

to the eye when observing them in northern countries. However, only at the end of the last century was this fact subjected to systematic

Fig. 3. Stratification of a snow block (after Seligman)

observations, which subsequently served as the subject of classification. At the same time, the perfect similarity between each of the six rays in any snowflake, and at that ...

same time an enormous difference in the structure of different snowflakes. Examples of them are shown in Fig. 4.

Recently the arrangement of atoms and molecules in crystals of ice and snow has become a subject of extraordinary interest for chemists and physicists. This is understandable, since the known substances

Fig. 4. Forms of snowflakes

of the earth’s surface are half composed of oxygen; moreover, its compounds with hydrogen, with the formation of water H₂O or the hydroxyl OH, play a fundamental role in an enormous number of processes in nature.

The main features of the crystalline structure of ordinary ice were elucidated by means of X-ray methods of investigation

Fig. 5. Model of an ice crystal:
A — when it is viewed in a direction perpendicular to the layers, i.e. along the optical axis;
B — when viewed in a perpendicular direction.
The crystals consist of alternating layers. The distance from the center of each oxygen atom to the center of each neighboring oxygen atom in one layer is 2.74 Å. The distance between the layers is the same. The position of the hydrogen atoms is unknown.

fifteen years ago. The oxygen atoms in ice crystals are arranged in the same way as the spheres shown in Fig. 5. Each oxygen atom lies at the center of a regular tetrahedron, the four vertices of which are occupied by other oxygen atoms. The structure as a whole is hexagonal and in this respect differs, for example, from the related structure of diamond. In the latter case the carbon atoms are likewise situated at the corners of a regular tetrahedron, but their general arrangement makes the crystal belong to the cubic system.

Fig. 6. Faraday’s experiment on the freezing together of floating pieces of ice

The first attempt at a physical explanation of the so-called plasticity of ice was undertaken by Tyndall and Huxley in 1857. The explanation was based on the remarkable phenomenon, observed by Faraday, of the freezing together of two pieces of ice brought into contact. Such freezing together occurs with the slightest contact in the case when the pieces are in water (Fig. 6). Faraday says that water molecules pass from the liquid to the solid body much more readily when they are surrounded by a considerable mass already solidified. A thin layer of water near the places of contact of the two pieces freezes and binds them together, even if it could not freeze by itself while being away from the mass of ice. According to this view, freezing depends not only on temperature but also on the surrounding conditions. In an analogous way, water vapor inside a crack, i.e., between two surfaces, will condense and turn into ice much more readily than in an open place, where contact is possible with only one surface of ice.

Ice under stress cracks. Tyndall and Huxley supposed that the cracks “heal” as a result of the deposition of vapor or liquid coming from the surrounding parts of the ice. Therefore an ice mass can adapt itself to the shape of its bed, and for this same reason a glacier as a whole seems to flow.

James Thomson (Kelvin’s brother) in 1860 proposed another explanation of this phenomenon. While recognizing the fact observed by Faraday, Thomson nevertheless rejects his earlier explanation; he attributes the cementing of pieces of ice to one another to the action of pressure that the pieces exert on one another. Indeed, if water expands on freezing, then any pressure, insofar as it hinders this expansion, must hinder freezing as well, and this is equivalent to a lowering of the freezing point. Therefore at 0° ice under pressure must melt.

This is indeed observed experimentally. If some sharp object, for example the tip of a knife, is placed on a piece of ice, then such an edge penetrates into the depth not because the ice is cut or crumbled, but because the ice melts under pressure. According to Thomson, when two pieces of ice are pressed together, melting must occur at the point of contact; the water formed in this way is squeezed out and somewhere nearby freezes again, since it is no longer under pressure.

Tyndall demonstrated the effect of the freezing together of pieces of ice in the following manner. Ice was broken into small pieces, which were then subjected to compression in a special mold. As a result, a fused transparent mass of ice was obtained. In this way, by subjecting ice powder to a pressure of several hundred kilograms per \(1\ \mathrm{cm}^2\), one can make ice cups and other objects of various shapes.

The explanation of the phenomena of glacier flow would now seem to become obvious. According to Thomson and Tyndall, the change in shape of a moving glacier occurs as a result of the melting of ice in places of strong pressure and the subsequent solidification of the water released by this melting.

Of course, Thomson’s assertion that ice melts under pressure is entirely correct. However, one cannot agree with his supposition that Faraday’s regelation of floating pieces of ice is based on this same principle. Thomson maintained that even with simple contact of pieces without external pressure, some pressure nevertheless arises owing to capillary action, and that this pressure is the cause of Faraday’s effect. To show the groundlessness of Thomson’s objections, Faraday, in 1860, set up his experiment under such conditions that capillary action was absent. He made several disks of ice, giving them a plano-convex shape, and set them floating on water with the convex side upward. Under such conditions the pieces could touch one another only under water, and not along the waterline, as in Fig. 6. When they were brought into slight contact with one another, they froze together so firmly that, in order to set the whole mass in motion on the water, it was enough to act on only some one point. At the same time, wooden disks under the same contact, both along the waterline and under water and, consequently, in the presence of capillary action between them, showed no signs whatever of being fastened together.

Nevertheless, neither Faraday’s principle nor Thomson’s principle gave a satisfactory explanation of the motion of glaciers. For example, they did not explain the process of the freezing together of ice at those low temperatures at which some glaciers of the world exist. Indeed, Faraday himself pointed out that two pieces of ice do not freeze together under pressure if they are cooled below zero.

Many years later these questions were again taken up by McConnel (1891), who for a long time had had to live in Davos—

in Switzerland. Some of his preliminary experiments led him to the conclusion that the secret of the plasticity of ice can be explained only by studying the properties of a single crystal of ice. Most varieties of ice, however, especially artificial ice and glacier ice, are a conglomerate of separate, relatively small crystals (Fig. 7). Single crystals of sufficiently large

Fig. 7. Section of a piece of glacier ice, showing its polycrystalline character. The various parts have different orientations

Fig. 8. Diagram of McConnel’s apparatus for observing the elasticity of an ice crystal

sizes were cut by McConnel from ice formed on the surface of a lake or in an open vessel. One axis of such a crystal is always directed perpendicular to the surface of the water on which the crystal formed. In McConnel’s experiments elastic and plastic deformations were studied under the following conditions:

1. The specimen was taken in the form of a plate several inches long and about one inch in width and thickness, and was placed (Fig. 8) on two supports with the natural surface of the ice upward.

2. The same specimen was turned through a right angle so that the “lake surface” became vertical.

3. A long column was taken as the specimen, which in the original mass had been vertical.

The first two examples, together with the effect obtained under load, are shown in Fig. 9, A, B, and C. In the first case the specimen proved to be bent like an ordinary rod. In the second, the deformation was the same in character, but considerably smaller in magnitude. In the third case the deformation acquired an entirely peculiar character (Fig. 10), showing that this time motion along the plane of slip is taking place. The sliding of vertically arranged glass plates, joined to one another by means of oil or another viscous medium (Fig. 9 D), serves as a good model of this deformation. The arrangement shown in the figure...

ON THE STRUCTURE OF ICE

...was carried out by hand, without suspending any load, since in the latter case all the sliding under the action of the load would have had to occur only in a small group of plates. But the model nevertheless illustrates the phenomenon quite well. In this third case the process of deformation continued continuously and for an indefinitely long time, i.e. this deformation is plastic. On the contrary, in the first two cases the deformation was elastic, since it did not change with time and proved to be proportional to the load.

Similarly to ice masses, metals also constitute an agglomerate of individual crystallites, in each of which there are slip planes. The plastic deformation of such a mass under bending or stretching without rupture is effected by sliding along various planes. It is possible to prepare a single crystal of some metal, for example copper, which will very clearly show the nature of such motion. With a single-crystal length of 30–50 mm and a thickness of 5 mm, it can easily be bent with the fingers of the hand. However, after one or two such deformations it acquires such high mechanical strength that it no longer yields to the action of the fingers. It turns out in this case that the metal has ceased to be a single crystal, and contains small crystals of every possible size down to submicroscopic ones, so that no series of slip planes parallel to one another remains. In the case of ice, such “work-hardening” does not occur.

Fig. 9. A—a model made of rails, illustrating McConnel’s experiments; B—the same model under load; the black line is a vertical straight line, but in reality it consists of zigzags; C—the same model, placed on its edge; D—a model illustrating the plastic deformation of ice; made of glass plates lubricated with glycerin.

The existence of slip planes in a single crystal of ice makes it possible to explain the motion of glaciers precisely on the basis of phenomena observed in the case of plastic metals.

The differences in the behavior of metal and ice—the absence of work hardening during treatment, and the absence of an analogy in the dependence of the melting point on pressure—play a secondary role.

Fig. 10. Plastic deformation of an ice crystal whose axis was vertical when the ice formed on the surface of a lake

To obtain a clearer idea of the slip effect in ice, let us turn to the model of its structure studied with the aid of X-rays. It turns out that an ice crystal may be regarded as an aggregate of parallel layers connected with one another by bonds perpendicular to these layers. Each layer has a folded structure (Fig. 5, B); it must be assumed that it should possess considerable internal strength and a comparatively small ability to resist displacement in its own plane with respect to neighboring layers. During such slip, the bonds perpendicular to the layers between two atoms are broken and are immediately re-established between another pair of atoms. This motion may be compared with the motion of a brush over a rough surface: individual bristles alternately yield to the action of the force and then spring back again, in order subsequently to find a new contact. These layers in an ice crystal prove to be parallel to the surface of the ice on the surface of a lake or vessel. Returning to McConnel’s experiments, we may say that the orientation of the crystal described in the third case is indeed well represented by layers of glass which slide relative to one another. In the first two cases, however, the bending of the ice specimens occurs analogously to the bending of a wooden strip under load. In this case the deformation is smaller when the strip is placed on edge (the second case) than when it is laid flat (the first case).

McConnel made an interesting observation of the behavior of ice in the first case. When water freezes on the surface of a lake, bubbles are formed in the ice, having the form of thin vertical strips. When such a specimen of ice is tested under load, these bubbles remain vertical and cease to be parallel to the axis of the crystal, which remains perpendicular to all points of the surface of the deformed crystal. To represent these effects on the model (Fig. 9, A–B), a vertical black line was drawn on one side of the strip binding the rods. When the strip under load bends, the line breaks up into separate strokes which, however, are still arranged on one vertical line. On the model these strokes are clearly noticeable…

...noticeable, but on ice, naturally, it is impossible to see them. With such bending the laths slide relative to one another, which also demonstrates the mechanism of sliding.

MacConnel also observed that in the third case there occurs a slight, slow restoration of the shape of the bar that had been under load, i.e. an increase of the obtuse angle formed to 2–3°. Owing to this, straightening of the bonds between adjacent layers must take place.

In contrast to metals, an ice crystal is not strengthened by cold working. The layers, when sliding relative to one another, remain undistorted and unbroken, so that the conditions of existence of the crystal do not change. In a metal, however, the former arrangement of the atoms is disturbed and the conditions become more complex.

The freezing together of pieces of ice with one another and the melting of ice under pressure are consequences of the peculiarities of the structure of ice, which in turn is a consequence of the special character of the bonds holding the atoms and molecules of ice together. Recent years have been marked by significant advances in our knowledge of atomic bonds. For the present purpose it is sufficient to note that in some cases one atom attaches to itself other atoms only at certain special points on its surface. It would be more correct to express this thought by saying that the points by which atoms are bonded to one another are distributed over the surface of the atoms according to a definite rule. In particular, the carbon atom attaches to itself four other atoms at points that lie on the surface at the four vertices of a regular tetrahedron. In other cases there is no such regular arrangement of the bonding points, as, for example, in the case of liquid mercury. And indeed, the intrinsic property of a liquid is determined by the absence of such directional bonds, which create a structure, or by their masking by other, stronger bonds.

One may imagine the following limiting cases. In one of them there exist only forces of the first kind. This means that atoms have mutual attraction only when they are applied to one another by the contact points present on their surfaces. An aggregate of such atoms could be either a solid body or a group of atoms not bound by mutual attraction. In the latter case, in the presence of sufficient thermal energy, the group of atoms would have to form a gas. It may, however, be assumed that under such circumstances accidental cohesion could occur. If the store of heat decreases, then such a combination of atoms becomes more frequent and more permanent, as a result of which solidification begins in separate places. Each group of atoms joined in this way becomes a crystal, if, of course, the process does not proceed so rapidly as to make the formation of a true crystalline arrangement impossible. Atoms or molecules must strive to occupy the places prepared for them on the already formed...

aggregates. In this way crystals grow from vapor without the formation of a liquid as an intermediate phase.

In the other limiting case, one may imagine atoms or molecules that have no directed attraction. If the thermal vibrations are not strong enough for the atoms or molecules to be isolated from one another, then they gather together and form a liquid, whose viscosity will depend on how easily individual molecules can move among a host of other molecules. Upon further cooling the viscosity may increase continuously, or by sudden jumps, up to the degree at which this assemblage of molecules may be called a solid.

It is interesting that already in Newton’s Opticks there are vague indications of two different models of interatomic attractions: “the parts of all homogeneous bodies, which wholly touch one another, are bound to one another very strongly. To explain how this can happen, some think that atoms have a hooked form, others affirm that the atoms of which bodies consist are in close contact and are glued together by some hidden quality, or, rather, are not glued together by anything; in the opinion of still others this connection is effected through certain motions or through the relative rest of atoms with respect to one another. On the basis of the fact of cohesion of bodies I am inclined rather to admit that particles attract one another by means of some force which, at immediate contact, is exceedingly great and which, at small distances, produces chemical actions, while at a not very great distance between particles it gives no appreciable effect. Consequently, there exist in nature agents capable of making particles unite with one another by means of very strong attractions. The study of these is also a task of experimental philosophy.”

Natural substances lie between these two extremes, and ice, apparently, is closer to the first of them than are other substances. Indeed, its crystals form directly from vapor. Ice “sublimes.” On the other hand, molecules of water vapor continuously break away from the crystal as a result of the action of heat or for some other reason and mix with the molecules of the surrounding medium. The ease or difficulty of condensation and of the detachment of molecules must be determined by some relation between the density of the vapor, the temperature, and the surface conditions. In cracks the chances of condensation are greater than in open places, since in cracks, beginning from their edges, the molecules are under a double action. The detachment of molecules occurs with greater probability from a convex surface. This effect is entirely analogous to the effect of the dependence of the elasticity of vapor on the form of the liquid with which the vapor is in contact, as was indicated by Faraday. In a crack the equilibrium between sublimation and deposition must be different than outside it, the latter increasing at the expense of the former. In other words, the vapor elasticity is lowered, or the freezing point is raised.

When water freezes and the open structure of ice is formed, an expansion results, which is partly restrained by pres-

...than by pressure. Thomson's principle asserts that pressure destroys the structure altogether, breaks some of its bonds and, in this way, converts it into a liquid.

At ordinary pressures water has its greatest density at a temperature of \(4^\circ\). With a further lowering of temperature, down to the freezing point, the density becomes smaller and smaller. It is evident that some of the molecules form complexes that occupy more space than the same molecules taken separately, since interatomic forces compel the atoms to assume a definite arrangement in space. At the same time there is no need at all to regard these complexes as permanent: in all probability, they are continually arising, breaking up, and arising again (Bernal and Fowler, 1933).

Let us now consider snowflakes (Fig. 4). The two principal facts requiring explanation are these: the infinite variety of hexagonal forms and the symmetry of each snowflake. The hexagonal form of snowflakes is evidently connected with the hexagonal form of ice crystals, but it has always been very difficult to explain why the six rays of each snowflake are so similar to one another and at the same time differ so greatly from the rays of any other snowflake. A satisfactory explanation may be given in the following way.

The whole question may be considered in the light of the same effects of sublimation and deposition as in the case of the freezing together of pieces of ice. When such a hexagonal structure grows from some nucleus in an atmosphere of water vapor or in a liquid containing dissolved water, the character of the growth must depend on the conditions under which this growth takes place. If in the surrounding space there is much vapor or the temperature is low, then growth proceeds rapidly and the rays of the snowflakes tend to penetrate into the surrounding space, in which numerous water molecules are still contained. Growth occurs at the ends of the rays and on the auxiliary branches, which form with the former an angle of \(60^\circ\). If, however, the snowflake is transferred into a space with a low vapor density or with a higher temperature, the reverse process takes place. Molecules detach themselves much more easily from the ends of the branches than from the central regions of the snowflake, and are not deposited on it at the former rate. Owing to this the snowflake thickens in its central part, while its branches shorten and even become rounded. Since snowflakes are not large, often no more than a few millimeters in diameter, the conditions around each of them may be regarded as identical at all points. If one ray lengthens, then the other rays lengthen as well; if the recent spaces near the center become filled, then the same thing occurs near all six rays. But with all this, of course, snowflakes may, as they fall to the earth, pass through the most varied local conditions, in consequence of which they may acquire a multitude of different forms, while the rays of each individual snowflake remain entirely similar.

Fig. 11. A—ice crystals arising in a mixture of water (85%) with glycerin (15%) at low temperature, B—the same with a lower rate of freezing, C—crystals arising during slow melting, analogous to those shown in Fig. B—D—the same, at an enlarged scale, E—hexagonal pyramids of ice obtained during sublimation, F—ice “flowers” in a piece of ice, arising under the action of heat rays, G—a separate ice flower.

According to this explanation, the great variety of snowflake forms is based on the coexistence of two opposite processes: the rapid growth of branches, leading to their feathery form, and compaction in the centers of this feathery structure. In the first process growth predominates over sublimation to a greater degree than in the second, so that the two differ rather in degree than in quality. The form of each snowflake tells us the history of those changes in atmospheric conditions which it has had to undergo. An even slower growth of ice crystals can be achieved if ice is kept at a temperature just below the freezing point in one part of an evacuated vessel and is allowed to sublime onto a metal plate in another part of the vessel, maintained at a considerably lower temperature. The crystals then assume the form of hexagonal prisms (Fig. 11, E).

The feathery forms shown in Fig. 11, A, were obtained by rapidly cooling a mixture of glycerin, alcohol, and comparatively large amounts of water. The denser hexagonal prisms in Fig. 11, B, were obtained by more slowly cooling the same mixture, but with a smaller amount of water. If prisms obtained in this way are made to melt or sublime, then at a certain moment there appears a stage of a more open structure, very reminiscent of natural snowflakes in some of their forms (C and D). Such processes can be observed on a screen.

Tyndall performed a beautiful experiment by means of which he was able to demonstrate the structure of ice. This experiment is called “the production of ice flowers.” A beam of light from an arc lamp is passed through a piece of ice. At various points of this piece, where there are impurities or irregularities, heat is retained and causes melting. The cavities thereby produced (Fig. 11, F and G) have a hexagonal form, since the destruction of the structure proceeds in the direction exactly opposite to growth. These figures are, so to speak, negative snowflakes, less finely expressed than real ones, but nevertheless preserving their form exactly. With the aid of suitable apparatus these figures can be projected onto a screen.

Fig. 12. Phase diagram of ice according to Bridgman

If a cuvette with water is placed in the path of the rays from the lamp to the ice,

then the heat rays are absorbed, and the growth of such voids in the crystal ceases.

Bridgman (1912) showed that at high pressures ice changes its structure. He succeeded in observing several varieties, and in accordance with this a complete phase diagram was constructed for ice (Fig. 12). The structures of two of these new forms—ice II and ice III—were studied by MacFarlane (1936) with the aid of X-rays. The principal lines

Fig. 13. X-ray photographs of ice I, II and III. Only the principal lines are shown.

Fig. 14. Model of the crystal of ice II. The layers are not changed, but are brought closer together.

of the X-ray spectra of ice I (ordinary ice), ice II and ice III are shown in Fig. 13. It is evident from them that all these three forms of ice are crystalline and that their structures are very different.

According to Mac-Farlane, ice II retains the folded layers practically unchanged, but they are brought closer together, of course, through the bending of the bonds between them. The distance from the center of one oxygen atom to the center of another, i.e., the length of one bond, remains unchanged. The density of the crystals is approximately 1.21. Ice III is also compressed, but in this case the layers themselves are already subject to compression, while the distance between adjacent layers changes almost not at all. As in the first case, the distance between the centers

Fig. 15. Oxygen octahedra in three forms of ice, shown on the basis of Mac-Farlane’s investigations. In each case the four oxygen atoms at the vertices \(A\), \(B\), \(C\), and \(D\) are at the same distance from the central oxygen atom

of neighboring oxygen atoms still has the same value. A photograph of the model of ice II is shown in Fig. 14 in two projections, \(A\) and \(B\). It is, however, more difficult to examine them here than the model itself. The structure of ice III is more complex than that of ice II. The main features of its structure in comparison with the structure of the two other ices are presented in Fig. 15 by means of tetrahedra which, in each of these cases, surround the oxygen atom. The dimensions indicated here are in agreement with Mac-Farlane’s X-ray observations.

1. William Bragg, Proc. Roy. Inst. Gt. Brit., March 18, 1938. Translated by N. A. Shishakova. ↩