Introduction
Lake ice consists of an interlocking aggregate of columnar crystals which commonly increase both in size and complexity of grain shape with depth. Normally such ice has a preferred fabric, with horizontal or vertical c-axis orientation. Where both orientations occur near the surface, or where there is some randomness, there may be a progressive increase in horizontally oriented c-axes with depth (Reference RagleRagle, 1962). The inverse relation is apparently unknown.
Crystallographic orientation is a significant strength parameter for melting lake ice. Because of the basal glide properties of ice, one would expect lake ice with horizontal c-axis orientation to have a lower ultimate strength under vertically directed stress than lake ice with other orientations. Nevertheless, significant differences are not detected in field tests conducted while the ice is at sub-freezing temperatures (Reference BarnesBarnes, 1960). With the onset of melting, Tyndall figures and vapor bubbles develop and migrate rapidly along the vertically oriented basal planes of ice with horizontal c-axes (Reference BarnesBarnes, 1960). Albedo is lowered, and the ice greatly weakened. If the c-axes are vertical, Tyndall figures are incapable of appreciable migration, nor can the vapor bubbles readily escape. Albedo is raised, and the ice strength tends to be preserved.
Growth Rates in Ice Crystals
An ideal anistropic crystal forming from a solution in which a thermal gradient has been established should have growth velocities proportional to thermal conductivity vectors of the crystal (cf. Reference SaratovkinSaratovkin, 1959, p. 104). In ice, thermal conductivity, parallel to the c-axis is approximately 5 per cent greater than that parallel to the basal plane (Reference Landauer and PlumbLandauer and Plumb, 1956). Nevertheless, all determinations of growth rates of ice from solution (cf. Reference Hillig and DoremusHillig, [1958], fig. 1) have shown that the velocity of growth parallel to the basal plane may be as much as 100 times more rapid than growth in the c-axis direction. Thermal conductivity, therefore, cannot be a significant parameter controlling ice growth rates or orientations.
Fig. 1. Mechanism proposed by Reference Perey and PounderPerey and Pounder (1958) to explain cutting-out of ice crystals with vertical c-axes with progressive thickening of an ice sheet. Dotted lines are the basal pales of the crystals. Reproduced by permission from Canadian Journal of Physics
Experimental Observations on Ice Orientation
In undisturbed supercooled water (Reference DevikDevik, 1942), ice growth is generally initiated by nucleation and rapid expansion of dendrites or needles along an a-axis. When an offshoot develops along a second a-axis, the resulting platelet floats. Expansion, coalescence, and eventual thickening of these plates explain the texture and orientation of “normal” lake ice.
The above explanation cannot hold for lake ice of horizontal c-axis orientation (Reference BarnesBarnes, 1960; Taylor, unpublished), nor for the case described by Reference OwstonOwston (1951), where rain water was caught in a tarpaulin, and frozen; the resulting ice aggregate had all c-axes horizontal. Because heat loss in Owston’s case was multidirectional, and in lakes is unidirectional, one must also conclude that the heat flow vector, like thermal conductivity, does not directly control ice orientation in nature.
Reference BrillBrill (1957) has grown ice with horizontal c-axis in the laboratory, using a shallow, well-insulated container fitted with a bottom stirrer. Crystallization at the container walls was prevented by electric heating, and edge effects were thereby eliminated. More recently, Reference Perey and PounderPerey and Pounder (1958) grew ice in plastic containers so insulated that heat flux was vertical. They found that the fractional area, but not the relative number, of crystals with horizontal c-axis increased with depth.
We have repeated the Perey-Pounder experiments but have also varied the direction of heat flux, allowing the ice to solidify from the top, the bottom, or all sides simultaneously. Commercially grown ice was also studied as a check on the last experiment. As a last factor, we have added wind (provided by an electric fan). Reservoir water was used in all runs, and the ice crystallized in a cold room with −10° C. ambient temperature.
Artificial ice grown under conditions of upward vertical heat flux consists over most of the surface of an aggregate of coarse crystals with mean diameters up to 5 cm., and a narrow perimeter in which the grain diameters are 0.5 cm. or less. The coarse central crystals have vertical to sub-vertical c-axes, the peripheral crystals horizontal to sub-horizontal c-axes. At depth there are relatively more crystals with horizontal c-axes. The reason becomes apparent if one arrests the growth process. Shortly after surface crystallization has commenced, the entire column of water in the container achieves a temperature of ±0.15° C., as indicated by thermocouple measurements. Crystals at the perimeter of the block grow downward far more rapidly than the others, extending dendrites into the water bath and under the central (vertical c-axis) crystals. There is no new nucleation below the upper ice surface, and elimination of c-axis crystals with depth is due to a growth-geometric factor. Note, however, that edge effects are significant here, and natural conditions are not satisfactorily reproduced.
When ice is grown under conditions of all-sided or vertically downward heat flow a columnar ice aggregate results, as before. Except near the central upper surface of such blocks, crystals have their basal planes normal to the cooling surface. The general textural characteristics of such ice blocks are identical to those in metal castings, even to the development of the familiar globular texture at the center. In metals, however, the long direction of the columns is the vector of both maximum thermal conductivity and maximum growth velocity; in ice it is only the vector of maximum growth velocity.
Striking alterations in the normal orientation patterns of artificial ice are produced when a steady air stream is directed tangentially toward the surface of a water container so insulated that an upward heat flow has been established. At low wind velocities (e.g. 1.5 m./sec. or less) the only perceptible change in the crystallized ice is a decrease in grain diameter, to an average of 1 cm. or less at the surface. If the wind velocity is increased to 2.7 m./sec., the grain diameter is diminished still further to 0.15 cm. or less, and the petrofabric diagram of all grains coarse enough to be optically identifiable shows sub-horizontal orientation of c-axes. As these crystals are traced downward, some enlarge and others are wedged out, for no obvious reason; at a depth of 10 cm. their average diameter increases to 0.7 cm.
Discussion
Percy and Reference Perey and PounderPounder (1958) have proposed that geometric arrangement of the rapidly growing basal planes of ice crystals is the fundamental control on take ice crystal orientation (cf. Fig. 1). This is partially correct; but does not explain (1) how a random orientation of ice nuclei may be set up, and (2) why intermediate orientations are relatively rare.
Rubbings (Fig. 2) of the surface of wind-blown artificial ice suggest a rather simple explanation for obviating these difficulties. This surface, with its strikingly atypical grain-boundary relations, results from fragmentation of thin early formed ice plates or dendrites. During incipient ice growth, jostling in the well stirred upper water surface (1) thickens the supercooled surface water layer, and (2) makes it progressively more difficult for flat dendrites or plates to persist. A mush of broken crystals accumulates; when this mush attains a thickness of a millimeter or so, a condition is reached in which further horizontal crystal growth is virtually impossible. Thus shards or intergranular crystals which rotate or nucleate in such a position that their basal planes are sub-vertical grow most rapidly immediately below the disturbed surface layer. At a few millimeters depth, this orientation becomes dominant by the operation of the geometric (or Perey-Pounder) factor. The development of a crystal mush in agitated water is therefore a crucial step in initiating horizontal c-axes orientation in the case described, and probably in most lakes.
Fig. 2. Rubbing of brecciated upper .surface of ice grown at wind velocity of 2.7 m./sec.
A question not yet answered is why, in experiments carried out under conditions of vertical heat flux, perimeters of the ice blocks have horizontal c-axis orientations; or why, when heat flux is all-directional, the c-axes are sub-parallel to the container walls. The standard explanation for orientations in metal castings (i.e. preferential growth of nuclei favorably oriented with respect to heat flow vectors), probably applies here. The experiments themselves, however, have no natural applications or analogues to lake ice.
Acknowledgements
Laboratory and field investigations reported upon in this study were supported by the Geophysics Research Directorate, Air Force Cambridge Research Laboratories, Office of Aerospace Research. We are also indebted to Mr. George Fisher for excellent assistance in the laboratory.
