7. Mechanism of morphological instability

Another important point about the pattern formation is the mechanism of morphological instability occurring on the polyhedral snow crystals. In general, this problem relates to the interaction between the local distribution of supersaturation on the crystal surface and the growth kinetics along the surface[13]. How does the morphological instability develop on the snow crystals as a function of supersaturation?

Now we consider the diffusion field of water vapor around the snow crystal[38,39]. When a snow crystal is growing in the atmosphere, the water vapor near the surface is consumed by the growing crystal and the diffusion field conforms around the crystal, as shown schematically in Fig. 9. The equi-concentration lines should be almost concentric, but the snow crystal has a polyhedral shape. Then the corners and/or edges of polyhedral crystals stand out toward the higher concentration region. This phenomenon is called as Berg effect[40] and very general for the diffusion field around the crystal. Consequently, the supersaturation along the surface should be the highest at the corner and/or edge but the lowest at the center of facets. This configuration of the diffusion field allows the corners and/or edges of polyhedral crystals to grow faster than the central parts of facets and drives the development of unstable shapes. This process also can be simulated by numerical calculations. Fig. 10 shows an example of the simulation results which were carried out for the two-dimensional ice crystals by Yokoyama and Kuroda[41]. The development from a circular plate, to a sector crystal through a hexagonal plate, and then to a dendrite is clearly found in this illustration.

Snow crystals are one of the most popular natural products. Their beautiful and minute structures still include many intriguing mysteries. We have found a possible mechanism to explain the various patterns of snow crystals, but it is still only beginning to satisfy our spirit of inquiry.

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