Temperature

Temperature is probably the most widely recognized factor in the process of crystal growth. It is surprising, therefore, that much of the basic information on the relationship of temperature to crystal size has been derived from a study of metals. In the case of a metal of hexagonal symmetry such as zinc or magnesium it has been demonstrated that when a rolled and, therefore, stressed sheet composed of either of these metals is heated for a short time new crystal nuclei form in regions of high internal stress and begin to grow at the expense of existing crystals. If such heating is sufficiently prolonged a process of crystal growth occurs which generally results in an increase in the average size of the individual crystals (Reference Perutz and SeligmanPerutz and Seligman, 1939, p 355–59).

If ice is temporarily placed under a stress which is later removed, the resulting growth in grain-size will be very much retarded if the temperature is below −5°C. and almost negligible if the temperature is below −10°C. (Reference RigsbyRigsby, 1960, p. 604).

Stress

In contrast to temperature, high stress appears to have an adverse effect on the growth of ice crystals. When Reference BaderBader and others (1939, p. 54–55) attempted to make the first correlation between stress and the orientation of ice crystals, they discovered that while the ice was being subjected to shear stress, the crystals were observed to grow. Reference PerutzPerutz (1940, p. 133–34) corroborated the observation of Bader and others, and stated that an increase in grain-size is the inevitable result of strain. More recently, Reference SteinemannSteinemann (1958, p. 46–50) was able to produce such an increase during recrystallization under a load, “primary parakinematic recrystallization”, as well as the normal increase in crystal size when the load was released, “post-kinematic recrystallization”.

Reference ShumskiyShumskiy (1958, p. 246) repeatedly showed that recrystallization under stress results in a reduction not an increase in the average grain-size. [Reference KambKamb] (1960, p. 365) related the fine-ice layers in the Blue Glacier to zones of high stress and the coarse-ice layers to zones of very weak stress, and both Reference GlenGlen (1958, p. 259) and Reference SeligmanSeligman (1949, p. 262) further demonstrated the close relationship between high stress and small grains.

The answer to this difference of opinion is in the temperature of the ice at the time of the experiments. It has already been noted that ice recrystallizes readily near the melting point and the above experiments which resulted in a growth in crystal size upon the application of stress were evidently not temperature-controlled. Reference BaderBader and others (1939, p. 53–55), for example, subjected their ice to average stresses of 4.5 kg./cm.², but at an initial room temperature of only −4° to −5°C. Since an increase in pressure of 100 atmospheres will raise the temperature approximately 1.1°C. and will lower the freezing point 1°C., the ice used by Bader and others at the time of their experiments was close to the melting temperature. Consequently, it appears that any increase in crystal size under conditions of moderate to great stress is the result not of the stress factor but of the closely related temperature factor.

Release of stress will cause an increase in crystal size. Reference SeligmanSeligman (1950, p. 380–81) observed an eight-fold increase in the crystal size in blocks that had been cut from ice tunnels in Switzerland and left standing for decoration. He attributed this increase to the release of stress, but he also admitted that the better circulation of air around the blocks might have favored the growth. To provide more positive evidence of recrystallization after release of stress, Reference GlenGlen (1958) subjected thin sections of ice to varying amounts of stress and found that the sections that had been under stresses of 8.5 kg./cm.² had smaller crystals than those that had been under stresses of 3.6 kg./cm.². Ice that had been under stresses of over 5.0 kg./cm.² actually recrystallized again in the thin section, which indicated to Reference GlenGlen (1958, p. 259) that large stresses had been trapped in the deformed sections.

It has frequently been assumed that ice will flow faster under a high hydrostatic stress. The basis for this hypothesis seems to have been the proposal of an extrusion flow theory by Reference DemorestDemorest (1943). He assumed that ice at depth would flow faster as a result of the weight of the overlying ice thus causing the ice to become more plastic. True, it is generally recognized that shear stresses at the bottom of a glacier are greater than those near the top, but it was not known what effect the hydrostatic pressure had on the shear forces. Reference RigsbyRigsby (1958[a], p. 276–77) determined that if the temperature difference between the ice temperature and the melting point were kept constant there would be little or no effect by increased hydrostatic pressure on the rate of deformation. With an increase of 350 atmospheres in the hydrostatic pressure, the temperature was raised 4°C. and the melting point was lowered more than 2.5°C. It was concluded that the temperature is far more important than the hydrostatic pressure in the regulation of the deformation rate and, hence, the rate of recrystallization (Reference RigsbyRigsby, 1958[a], figs. 7–10, p. 276).

Reference SteinemannSteinemann (1958, p. 32) studied the effect of hydrostatic pressure on the rate of shear strain on specially shaped rings of ice and concluded that up to 90 atmospheres pressure (the limits of his experiment), hydrostatic pressure had no direct effect on the plastic properties of polycrystalline ice. The conclusion is, therefore, that since the ice layer near “Camp Michigan” was under a normal pressure ranging from 141.73 g./cm.² (1.14 atmospheres including the 1 atmosphere pressure at the surface) at the trough of the fold to only 39.84 g./cm.² (1.04 atmospheres) at the crest (computed from data of Giovinetto, figures 13–14 in Reference ZumbergeZumberge and others (1960)), the effect of hydrostatic pressure on this ice layer can be disregarded completely.

Orientation

More pertinent, perhaps, than a general relationship between stress and recrystallization is the combined relationship between orientation, stress and recrystallization. Reference SteinemannSteinemann [1956] made a series of observations on the preferred orientations produced by compression and found that recrystallization of grains under such compression favored those grains whose basal planes were 45° to the compression direction, i.e. parallel to the plane of maximum shear. Conversely, crystals orientated with their basal planes perpendicular to the active shear plane are under the greatest stress and will therefore recrystallize the most rapidly (Reference ShumskiyShumskiy, 1958, p. 245), and “crystals having the right orientation for yielding to stresses by glide along their basal planes would have a higher energy than others which cannot yield; the former would therefore have a tendency to grow at the expense of the latter by molecular exchange across the crystal boundaries” (Reference PerutzPerutz, 1940, p. 132–33).

Impurities

Another important factor which regulates the rate of recrystallization is the amount of impurities present in the ice. Reference CahnCahn (1949, p. 134) discovered that the greater the purity of zinc crystals (hexagonal) the easier they recrystallize. Reference Nickelson and GrossNickelsen and Gross (1959, p. 285) found that quartz, when it is surrounded by other minerals, commonly shows poor preferred orientation which, in turn, indicates a lack of recrystallization. As for ice, Reference RigsbyRigsby (1960, p. 602) noted that “bubbles apparently inhibit the growth of crystals even at the melting temperature” and suggested that either the bubbles interfered with the migration of crystal boundaries, or “possibly the strains are relieved readily by migrating to a bubble-ice boundary so there is no need to recrystallize”. Ice from the “Camp Michigan” area seems to substantiate Rigsby’s observation, for there are frequently found only very small crystals in the bubbly portions of otherwise coarse-grained, bubble-free ice (see for example thin sections 1b, Figure 4). It is further suggested that the relief of strain by the bubbles is more important than the prevention of migration of the crystal boundaries.

Time

Very little information is available on the importance of time on recrystallization, but many casual observations have been made which note that it is a real factor. For example, Reference SeligmanSeligman (1949, p. 262) stated that crystals generally increase in size from the source to the snout of a glacier and that the longer the glacier, the larger the crystals at its end. Furthermore, where stress is at a minimum, usually in the stagnant ice at the snout, the ice crystals are larger than those in the stressed ice of the actively flowing ice mass. He surmised from these observations that “crystal growth is, to a greater or less extent, dependent upon time”. Reference RigsbyRigsby (1958 [b], p. 357) concluded that “crystal size increases with temperature and time in glaciers in the inactive or stagnant state, whereas the size decreases with increasing strain-rates of the more active glaciers”.

A totally contrasting idea was proposed by Demorest, but it was not fully elucidated at the time of his death in 1942. He maintained that under stress a crystal is deformed and often bent. When this occurs, some undulatory extinction will result. With further stress the lattice may become energized to an unstable condition and immediately there will occur a rapid re-organization of the lattice, which Reference DemorestDemorest (1953, p. 202) termed “instantaneous re-crystallization”. Reference GlenGlen (1953) agreed that rapid recrystallization does in fact occur, but not instantaneously! Grains under conditions assumed by Demorest grow “at a definite, and sometimes quite slow rate”. Reference KnopfKnopf (1953) claimed, however, that the recrystallization was actually instantaneous as was illustrated by time-lapse photography which showed recrystallization occurring within a period of a “few minutes” when the ice was near the melting point. Thus, temperature is again important, but instantaneous recrystallization appears to have some support. As a matter of fact, the recrystallization of the studied ice layer near “Camp Michigan” (after initial solidification) probably was instantaneous. However, subsequent recrystallization of the ice at the crest has been and is most likely the result of migrational recrystallization.

Previous work

The efficacy of two-dimensional size analysis of grains has been questioned by many researchers. Reference BaderBader (1951, p. 525), for example, noted that isolated rubbings of stagnant ice at the front of the Malaspina Glacier in Alaska suggest an average grain-size of only a few inches, which is a great underestimate because the shape of those grains is very long and exceedingly complex. In order to attempt a correlation of grain shapes and sizes Bader made a series of 26 rubbings at 0.2 in. (0.5 cm.) intervals and even then he found difficulty in correlating the grains from one rubbing plane to the next.

Fortunately, not all ice masses are composed of such complexly shaped grains and, therefore, if it can be determined that a mass is composed of more or less equant grains, two-dimensional measurements may be useful. Nevertheless, it must be remembered that a single plane, whether it be represented by a rubbing or an actual thin section, will only by coincidence intersect the maximum diameter of a given grain. Consequently, an average observed grain-size in the section will, by necessity, he less than the actual average grain-size.

Reference SeligmanSeligman (1949, p. 256) accepted this deficiency as unimportant as long as relative results could be obtained. He therefore employed a method of the least circle diameter using standard root mean square diameters of 0.25, 0.4, 0.6, 1.0, 1.6, 2.5, 4.0, 6.3 and 10.0 cm. in order that there be a constant ratio between each size and the next. He applied the measurements to rubbings of ice blocks from various glaciers in the Alps.

Reference Ahlmann and DroesslerAhlmann and Droessler (1949) preferred to measure the longest and the shortest axes of the grains in a section and to compute the area from these data. Reference Boyé and CailleuxBoyé and Cailleux (1954) employed both methods and concluded that since the results were reproducible by both methods and since the latter involved more time, the root mean square method was more desirable.

On the basis of Seligman’s studies (Reference Seligman1949, p. 265) the following conclusions were reached:

1. “The crystal size observed at or near the glacier surface of an Alpine glacier shows an increase from bergschrund to snout. [Probably as a result of the factors of temperature and time.]

2. In active ice the crystals of the tongue are smallest on the lines of fastest flow, that is normally in the centre of the stream. They increase gradually towards the margins [where the stress is less and where the air content is less].

3. The longer the glacier, the larger the crystals. [As a result of a greater amount of time for the crystals to grow.]

4. The steeper the glacier, the smaller the crystals. [Due to faster flow and therefore greater stress.]

5. The relationships of crystal size to length of travel and to glacier speed indicate that while time must influence crystal growth in active ice there are probably other agencies as well.

6. Glacier movement may cause crystal growth by local shear stresses and by local pressure variations.

7. Crystals grow to very large size in dead ice even in the absence of stream flow [through migrational recrystallization with the aid of the temperature and the time factors].

8. Low temperatures retard crystal growth; warmth stimulates it even when no melt water is present.

9. The freezing of melt water does not play any important part in the growth of the crystals of pure ice.”

Each of these observations have since been corroborated through subsequent research both in the field and in the laboratory. (See, for example, Reference MacGregorMacGregor (1951, p. 569); Reference Ahlmann and DroesslerAhlmann and Droessler (1949 p. 274); Reference ShumskiyShumskiy (1958, p. 245); Reference RigsbyRigsby (1958[b], p. 357); Reference CahnCahn (1949, p. 140); and Reference SchyttSchytt (1958, p. 128–45).)

Median diameter

Table I is a summary of the crystal-size data and Figures 6–8 depict graphically the relationships between the distance from the crest of the fold and the respective median diameters, the percentage of grains larger than 1.0 cm. in diameter, the sorting coefficients and the depths below the surface. From these data several conclusions have been drawn. First, it is apparent that proximity to the open crevasse wall along which the layer was exposed is a very important factor in the control of ice crystal growth. Figure 4 illustrates two separate sets of evidence which verify this conclusion. First, thin sections 1a, from the crevasse wall, contain larger crystals than sections 1b which are located 37.5 to 52.5 cm. in from the crevasse wall at the same station on the fold. The former sections have a median diameter of 0.45 cm. while that of the latter sections is only 0.31 cm. Secondly, thin sections 6a which are also from the crevasse wall, but in the trough of the fold rather than at the crest, have a median diameter of 0.38 cm. and thin section 6c which is from a point 165.0 to 172.5 cm. in from the crevasse wall at station 6 has a median diameter of only 0.31 cm. At both lateral extremes of the fold there is evidence that the ice at the crevasse wall receives more radiation than ice within the wall. The result is that ice under slightly higher temperature during the warmer season grows more rapidly than the ice that is more protected from radiation.

Table I

Location and Statistical Analysis of Grain-Size, Data

Fig. 6.

Relationship between sorting and depth of ice thin-section grains with distance from crest of anticline

Fig. 7.

Relationship between grain-size and distance from crest of the anticline

Fig. 8.

Relationsbip between sorting and median diameter of ice grains

In addition to the distance from the wall, the depth below the snow surface is important because this also regulates the amount of radiation that the ice layer will receive. This explains why sections 1a, which are only 83 cm. from the surface, have a larger median diameter than sections 6a which are 317.5 cm. below the surface; the former sections are both closer to the snow surface and are from the crevasse wall.

The ice grains in sections 6a are controlled by one other radiation factor; the crevasse at this location is covered with a snow bridge which prevents direct radiation. However, the sections do have a relatively large median diameter and they are at the crevasse wall. The larger diameter must be explained as the result of circulating relatively warm air (during the summer season) even though the crevasse is not open to direct radiation. The snow forming the bridge is very permeable and movement of air during summer storms, when the temperature is usually higher than normal, is perceptible within the covered portion of the crevasse. The high median diameter of sections 1a is explained, therefore, both by the proximity to the open wall of the crevasse and by the very shallow depth below the snow surface. The ice along the wall, but beneath the snow bridge, has large grains only because it is exposed along the crevasse wall. It may be argued, however, that the large grains in the trough area may be the result of release of stress when the crevasse opened. But, the ice layer was traced through the lower portion of the snow bridge at this location, indicating that the crevasse was open at the time that the layer formed and that the bridge was in the initial stages of formation; the stress had already been released, if it is assumed that crevasse formation releases stress!

If exposure to radiation is the only controlling factor in the growth of large grains, it should be expected that other thin sections which are also from points close to the crevasse wall should also have large median diameters. Such is not the case. Although none of the sections displayed in Figure 4 are from the actual surface of the wall, several are from the zone that should be affected by direct radiation. For example, thin section 5 is from ice located approximately three-quarters of the distance from the crest to the adjacent trough of the fold and 30.0 to 37.5 cm. in from the wall. Despite this short wall depth, the section has a median diameter of only 0.31 cm., the same diameter as sections from the crest and the trough which are as much as 172.5 cm. in from the wall. For its location, thin section 5 has a smaller median diameter than it should when compared to the others. This is explained by the greater shear stress on the ice layer at this point on the fold.

Theoretically, such a fold, under a relatively constant stress from outside the area, is under varying stress from within. The surface at the crest of the anticline, for example, will be under a negative compressional stress and a positive tensile stress, whereas the same surface in the trough of the adjacent syncline will be under a positive compressional stress and a negative tensile stress. Consequently, somewhere between the crest and the trough there should be a point or area where compression is equal to tension. This location should reflect a condition of pure shear. Under such stress conditions growth of ice grains is inhibited (see p. 196). Because ice from station 5 has such a small median diameter it may be near this zone of pure shear.

Station 4, immediately up-slope from station 5, not only has the highest degree of preferred orientation of all the stations in the layer (8–9 per cent per 1 per cent area) but it is also in the zone of secondary folding (Fig. 9). This seems to imply that station 4 is closer to the theoretical zone of pure shear than is station 5.

Fig. 9.

Secondary folds in the 1952–53 ice layer near station 4

According to Kehle’s strain data (Reference ZumbergeZumberge and others, 1960), the stresses across the fold at “Crevasse Delta”, approximately 220 ft. (67 m.) south of “Crevasse Fox”, are not simple, even though the average strain for the entire area indicates that the strain in the fold approaches pure shear, i.e. the compressional strain is equal to the tensile strain. Strain values that were measured on the vertical wall of another crevasse in this same anticline illustrate the relative movements in the crest and the trough (figure 26 in Kehle’s contribution in Reference ZumbergeZumberge and others (1960) ). The crest is expanding upward and the trough is being compressed downward. Deviations from this general tendency can be clearly seen in that figure.

In summary, the ice layer at the crest has undergone an increase in crystal size because it was exposed to direct radiation; the same layer in the trough has also undergone an increase, but as a result of the restricted circulation of relatively warm air during summer seasons.

The layer in the vicinity of the secondary folds (thin section 4) did not undergo this increase in grain-size, because at the time of recrystallization, which probably was more or less instantaneous, the grains became preferentially orientated and were in equilibrium both with each other and with the shear stress, which is at a maximum here. There was a minimum of growth of the favorably orientated grains at the expense of those which were less favorably orientated; the grain-size was already adjusted to the stress conditions.

Sorting

Figure 6 shows that the sorting of the ice grains becomes more perfect with increasing depth, but there are many exceptions to this generalization. The ice in the layer at the crest, for example, has parts which are poorly sorted and some which are fairly well sorted; the parts away from the wall of the crevasse (1b) have a sorting coefficient of only 1.47 and are among the poorest sorted ice in the layer. Those sections from the same station, but at the wall (1a) have a more moderate sorting coefficient (1.39). Part of the answer to this difference probably lies in the fact the ice sections lb contain abundant air bubbles which are not evenly distributed throughout the sections and which therefore have a varying effect on the rate of crystal growth; where the bubbles are most abundant, the grains are the smallest and, where bubbles are essentially absent, the grains are more uniform in size and larger.

Thin section 3 also contains bubbles, but it has a better sorting of grains (So = 1.37) than the crest ice from the wall. The bubbles, however, are more evenly distributed and the crystal growth was apparently more uniformly inhibited. Thin sections 4 and 5 are also fairly well sorted (S₀ = 1.37 and 1.36) which reflects both the almost complete absence of bubbles and the high shear stress which seems to be present at these locations.

The sorting of the ice in the trough is much more difficult to explain, for since the sorting generally increases with increasing depth, this ice should theoretically be the best-sorted ice in the layer. Such is not the case. The deviation of the sorting coefficients within this station is as great as the total deviation of the remaining sections. The poorest-sorted sections are not the farthest from the crevasse wall, as was the case at the crest, but they are instead at the wall. Sections 6a have a sorting coefficient of slightly less than 1.39, whereas section 6c which is 165.0 to 172.5 cm. from the wall has a coefficient of 1.29. Furthermore, section 6b which is intermediate in distance between the other two locations, has a coefficient of 1.26 and is the most perfectly sorted ice in the layer. Bubbles are abundant only in this last section and are uniformly distributed throughout the section. The variability of the sorting in the trough station is therefore probably the result of several factors, including the fact that the ice at this location is not under great stress and the sections from this station were taken over a greater distance from the open crevasse. There is also the possibility that this station demonstrates the fallacy of these measurements in that any or all of these sections might have been cut through an unrepresentative part of the layer. It has already been stated that the median diameter, as measured in these sections, is much less than the absolute median because the grains in the sections were measured in two dimensions only. Consequently, generalizations may be valid but specific answers are almost impossible because of the large errors inherent in this technique.

Skewness

There appears to be no significant trend of the values for skewness. They range from 0.89 at station 2 to 1.08 at station 6 with no regularity of the trend between the two localities. This parameter appears to be the least valuable of the statistical parameters.