Geometric properties of platelet ice crystals

The problem

Each year, the area of sea ice around Antarctica grows from a minimum of 3 million to 20 million square kilometres (Gordon, 1981). The crystal structure of that ice is used to study the conditions under which it grew. Near an ice shelf, supercooled water containing small ice crystals reaches the underside of the sea ice (Lewis and Perkin, 1986). Thin discs of ice called platelets rise and collect there in a loose, porous layer that may be metres thick (Crocker and Wahhams, 2004; Dempsey et al., 2010). The sea ice then freezes around the upper part of this layer to form incorporated platelet ice (Jeffries et al., 1993; Smith et al., 2001).

Ice is commonly studied in thin sections, slices less than 1 mm thick viewed between crossed polarisers. Our goal in this study was to test how well 2-D sections represent 3-D crystals, and whether the orientation of a crystal could be estimated from its outline in a photograph. For some historical datasets, only such photographs remain.

What we did

In late 2007 we took two ice cores from the sea ice of McMurdo Sound, Antarctica. At 1.6 m depth, the first core showed draped platelet ice, with millimetre-scale serrations along the boundaries between crystals. From the second core we cut ten horizontal thin sections, about 9 mm apart, between 1.55 and 1.63 m depth.

On a universal stage (Langway, 1958), we measured the c-axis direction of every grain larger than 20 mm². We matched grains between sections by c-axis orientation and position, and stacked them to rebuild crystals in 3-D. We also traced each grain outline by hand on a photograph and fitted an ellipse to it. This is because a freely growing crystal forms a disc. Ice grows faster in its basal plane than along its c-axis. A horizontal slice through such a disc is close to an ellipse whose short axis lies along the horizontal direction of the c-axis. Finally, we cut the rebuilt crystals with imaginary vertical planes at 0, 45 and 90° to the c-axis.

What we found

The 400 cm³ of core held 108 separate crystals, sampled as 249 grains. Two large crystals each first appeared as a pair of separate grains, which joined in deeper sections. This suggests that the upper surface of each crystal has two prongs. We favour a scenario in which a crystal settled into the layer of platelets beneath the sea ice and then grew upwards into voids in the porous ice, although we did not extract enough information to establish this. Two other crystals appear to have grown into each other.

Across all 249 grains, the direction from the ellipse differed from the measured c-axis direction with a standard deviation of 28.9° (95% confidence interval 24.9 to 34.1°). Restricting the fit to grains larger than 300 mm² with an eccentricity above 0.87 (an ellipse about twice as long as it is wide) reduced this to 6.0° (4.7 to 8.6°). The improvement requires excluding most grains, and the method is less accurate than direct measurement on a universal stage, ±5° (Langway, 1958). However, it needs only a photograph of the thin section and the grain outlines.

The shape of a grain can depend on the angle of the cut. A vertical plane close to the c-axis gave a narrow outline stretched vertically. As the plane approached the basal plane, the outline broadened. We classified some grains as draped platelet ice, with serrated boundaries, and others as resumed columnar ice, with near-horizontal c-axes. This distinction may depend largely on the plane in which the ice was cut.

Our illustration above assumes a disc five times wider than it is thick. Its outline is five times taller than wide when cut along the c-axis, and as tall as it is wide when cut across it.

One boundary between two crystals had seven serrations. Its steep segments lay at 81° to the horizontal and the boundary overall at 71°. These angles are close to the c-axis tilts of the two crystals, 82° and 70°. A c-axis tilted 82° from the vertical puts the basal plane at 82° to the horizontal. This suggests the serrations follow the basal planes. We propose that they form in a groove where the basal planes of two crystals diverge downwards. The flat faces of the groove cannot grow until the water is supercooled by about 0.03 K, or three hundredths of a degree (Hillig, 1959). As the groove deepens, the temperature at its bottom falls (Wilen and Dash, 1995) until a new layer starts on the steeper crystal and grows rapidly. Repeated cycles fill the groove with stacked, tilted layers. Photographs of platelets grown on cables in supercooled water show concentric boundaries. We suggest these are layers of the same kind. The serrated boundary spans 60 mm of ice depth. At late-season growth rates of 10 mm per day (Purdie et al., 2006), this suggests several days of growth with no new crystals entering the groove.

Limitations

Grain boundaries were resolved vertically only to 9 mm. An ellipse gives no c-axis tilt, and it cannot tell a direction from its opposite. For smaller grains, direct measurement remains the only accurate technique. The serration mechanism is based on the angles of a single boundary in one core. However, for historical datasets without the original ice samples, fitting ellipses to grain outlines may offer the only way to estimate c-axis directions.

Glossary

Sea ice is ice formed by freezing of seawater.

An ice shelf is a floating extension of the Antarctic ice sheet.

Supercooled water is colder than its freezing point but has not frozen.

Platelets are thin discs of ice that form in the water column and rise to the base of the sea ice.

Incorporated platelet ice forms when the sea ice freezes around the upper part of the layer of platelets beneath it.

A thin section is a slice of ice less than 1 mm thick, viewed between crossed polarisers so that individual crystals can be told apart.

A grain is the cross-section of a crystal in a thin section.

A universal stage is a tilting microscope stage used to measure crystal orientations in a thin section.

The c-axis is a direction fixed in the structure of an ice crystal, the direction in which ice grows most slowly.

The basal plane is the plane at right angles to the c-axis, in which ice grows fastest.

C-axis tilt is the angle between the c-axis and the vertical.

Eccentricity is a measure of how elongated an ellipse is, from 0 for a circle towards 1 for a long, thin ellipse.

Standard deviation is a measure of the spread of a set of values, here of the error in the ellipse method.

A 95% confidence interval is a range calculated so that, if the measurement were repeated many times, about 95 in 100 such ranges would contain the true value.

Draped platelet ice is incorporated platelet ice whose grain boundaries show millimetre-scale serrations.

Resumed columnar ice consists of large crystals with c-axes near horizontal. It develops once the supply of platelets falls.

K (kelvin) is a unit of temperature. A difference of 1 K equals 1 °C.

mm² and cm² are square millimetres and square centimetres, and cm³ is cubic centimetres.