Geometrical Selection in an Array of Ice Crystals: A Comparison with Two-Dimensional Models

The tilt angle θ and the azimuthal angle α of the crystallographic c axes of ice crystals grown in a thin water layer were determined by using a cross-polarized transmission microscope and the birefringent properties of ice crystals. Ice microcrystals originated from ice grains obtained by mass crystallization of supercooled water inside a channel between two glass slides. The experimentally found two-angle distribution N(α, θ) of crystal orientations that remained after the process of cooperative growth exhibits some peculiarities that are not predicted by known two-dimensional (2D) models of geometrical selection: (1) Instead of a single peak at zero angles α and θ, N(α, θ) has coupled peaks shifted toward larger angles. We successfully explained this behavior by the effect of the thickening of ice crystals in the c direction during their cooperative growth. In contrast, the previous 2D models consider crystals as ideally thin needles which do not grow in the transverse direction. (2) The selectivity of the c axis orientations depends more on the increase of the α angle than on θ. N(α, θ) shows high values over a wide range of θ from 0° up to 70°, which is not taken into account by the 2D models considering needle-shaped or one-dimensional crystals. In this case, turning the crystal by an angle θ means rotating the needle around its longitudinal axis. This does not actually change the crystal orientation in the 2D space. We also found that the ice–water interfaces at 0 °C of the grown crystals mainly consisted of the bipyramidal surfaces, although individual ice crystals exhibited different values of α and θ. The appearance of crystals with the prismatic and basal surfaces at the interface was less probable.