The dendritic snow crystal represented by the illustration at the right combines two qualities that give it its distinctive
character: sixfold symmetry and an intricate, branched pattern. Snow crystals of this kind have come to symbolize snowfall
because of their striking beauty and the fact that they grow large enough to be appreciated without magnification. But such
flakes are not always seen in snowfall; smaller, unbranched crystals are common, as are crystals that have clumped together.
The two qualities of the snow crystal--branching and symmetry--can be explained by two different aspects of crystal growth. The branching involves the way in which water molecules in the air move toward the crystal; and the symmetry involves their final attachment to the crystal surface, causing the crystal to grow. Although many single snow crystals do not possess the intricate, branched shape, all have hexagonal symmetry.
The hexagonal symmetry of single snow crystals results from the arrangement of the water molecules within them (see illustration below). This layered-hexagonal pattern is uniform throughout any individual snow crystal. A crystal grows in a particular shape because of the different rates at which molecules stick together at different surface orientations.
The two most common surface orientations of snow crystals are those shown: the six-sided face parallel to the layers of water molecules is called the basal face, and the rectangular faces are called prism faces. Six prism and two basal faces enclose the whole crystal.
There is a strong tendency for the crystal surfaces that are flattest on the molecular scale to grow the slowest. (This is growth on the surface, not growth of the surface; in other words, it is not an increase of surface area, but rather a movement of the surface perpendicular to itself.) It is harder for molecules to stick permanently to a smooth than to a rough surface, because a smooth surface offers fewer sites where a new molecule can bond to several of the present surface molecules at once. The two surface orientations of ice that are the smoothest are the prism and basal surfaces. They therefore grow the slowest and become flat crystal faces, or facets.
At some temperatures the growth on the basal faces is slower than that on the prism faces. Then the crystals grow as hexagonal plates or dendrites. (Dendritic growth occurs within a few degrees of -15 Celsius; the reason for the temperature effect is not known.) At some other temperatures, the prism faces grow slower and the crystals are columnar, but the symmetry--the presence of the one hexagonal axis--is the same.
The branching of the dendrites arises for an entirely different reason. Because the water molecules involved come from the air, a growing ice crystal dries the air around it. The moisture needed for continued growth has to be replenished from air farther away. This diffusion of water molecules into and through the dry layer takes longer if the layer is thicker. Thus, if the surfaces stay flat, the growth rate slows down as the crystal gets bigger.
The diagram at the top of the next page represents the growth of a simple hexagonal crystal, which grows a distance d while drying out a layer of air with thickness D. D is much greater than d because the water molecules in air are more than 10 times farther apart than those in the ice.
When the conditions are appropriate for dendrites, however, the growth does not happen in this way. Instead, starting with the same hexagonal piece of ice, the new ice now forms six projections from the corners, not the uniform layer. The diffusion path is now shorter to the ends of the projections than to anywhere else on the surface, so they grow faster, though the same amount of air is being dried out as the crystal grows.
The diagram below shows the new situation. One can think of the initial development of the projections as an instability. Any little protrusion that occurs by chance can grow faster than the flat part, so it becomes more and more pronounced as it "robs" water molecules from the air and slows growth on the neighboring area of the ice surface. The hexagonal corners provide natural starting points for the projections because they already protrude.
A well-formed dendritic snow crystal (like that shown in the first illustration) has six main arms that are 60 degrees apart, branches at 60 degrees from each arm and, sometimes, smaller branches on those branches. The most prominent branches in snow crystals often occur at the same distance from the center of the crystal on each main arm, and probably are started by an abrupt increase in the humidity of the air through which the growing crystal is falling.
The minor branches, however, are not usually as symmetrical. They are aligned along the 60-degree crystal axes, but they start more randomly. In other words, perfectly symmetrical drawings are not entirely realistic.
Answer originally published January 18, 1999.