Abstract
Strarting from a spherical single crystal of ice, the pattern of snow crystals grown from supersaturated vapor in clouds first becomes an hexagonal prism bounded by two basal and six prism faces. At low supersaturation, such a hexagonal prism can grow in a stable manner and retains its form. For higher supersaturations, however, it changes form by means of preferred growth of edges and corners, becoming a needle crystal for temperature between -4℃ and -10℃ and becoming a dendrite for temperatures between -10℃ and -22℃. Recently, a numerical model of the formation of patterns during the growth of snow crystals was developed by Yokoyama and Kuroda (1990). In the present article, we review briefly studies of the formation of patterns of snow crystals, and present a model that takes into account the following elementary processes relevant to the growth: (1) A surface kinetic process for incorporating molecules into a crystal lattice, and (2) a process for diffusing molecules through air toward the crystal surface. Our numerical calculations give hexagonal pat-terns, dendritic patterns and circular patterns starting from a circular crystal under various growth conditions. We discuss the transition from the hexagonal to the dendritic pattern and the conditions for kinetic roughening that lead to a circular pattern. Finally, we show that the dimensionless crystal size, relative to the mean free path of a water molecule, plays an important role in the formation of patterns during the growth of snow crystals.
