Dendritic snow crystals

Snow crystals [4] Their macroscopic structure is different from a bulk three-dimensional ice crystal, but they are formed by homologous pair-pair interaction between water molecules and are static and in thermodynamic equilibrium. It should be noted, however, that dendritic crystal growth is a common phenomenon for metals [5-7] and polymers. The crystals grow under non-equilibrium conditions, but the final crystal is static. 

Figure 2.1. Various forms exhibited by crystals, (a) Polyhedral crystals (b) hopper crystal (c) dendritic crystal (snow crystal, photographed by the late T. Kobayashi) (d) step pattern observed on a hematite crystal (0001) face (e) internal texture of a single crystal (diamond-cut stone, X-ray topograph taken by T.Yasuda) (f) synthetic single crystal boule. Si grown by the Czochralski method (g) synthetic corundum grown by the Verneuil method.

Crystals are solid materials having regular atomic arrangements characterized by periodicity and anisotropy. These properties are universally present, irrespective of whether the crystal is inorganic or organic, in living systems or in the inanimate world. Crystals exhibit various external forms, as represented by the elaborately varied dendritic forms of snow crystals or the hexagonal prismatic forms of rock-crystal. This variety of shape has stimulated scientific curiosity since the seventeenth century, since when intensive efforts have been made to understand the reasons why and how crystals can take a variety of forms. 

A small selection of the over 2000 photographs of W. A. Bentley of snow crystals as seen in Vermont, ranging from close to singlecrystalline hexagonal to dendritic. 

Figure 3 Nature s dendritic structures (http //www.sxc.hu). Snow crystals, erosion fractals, and neurons are other examples of dendritic structures on the centimeter to micrometer (nanometer) scale.

The crystal is a fractal structure and the organization of the primitive unit cells can often be seen in the shape of the macroscopic crystal. A classic example of the fractal repetition of the unit cell is the crystalline structure of a snowflake. The unit cells have the ability to build into a variety of complex shapes, yet each unit cell retains its perfect structure. The primary unit cell structure in the case of a snowflake is hexagonal and undergoes dendritic growth to produce an array of different macro crystals (Figure 2.4). The final shape of the snow crystal will depend on the conditions used in the growth process (temperature, humidity, etc), which leads to a wide variety of observed morphologies. 

Dendritic patterns are one of the most frequently observed forms in both abiotic systems and biological systems. Examples include the roots and branches of trees, snow crystals, neurons, and capillary vessels. Dendrimers are macromolecules, which are based on repeatedly branched building blocks from a core molecule. The name dendrimer, comes from the Greek dendron, meaning... 

FIGURE 18.3 Snow crystal sketches describing recently deposited dendritic snow with large surface area (left) and isothermal aged snow crystals with small surface area (right) both exhibit similar porosity. Dendritic snow consists of six-branched crystals with a diameter of a few millimeters and a thickness of a few tens of micrometers. (Adapted from Domine F. et al. 2008. Atmospheric Chemistry and Physics 8, 171-208.)... 

Figure 5.58 represents a polyethylene dendrite still floating in the solvent out of which it was grown (causing the reduced contrast). It reveals that dendrites do not grow flat, as the snow flakes of Fig. 5.1, but splay apart from a common center, the crystal nucleus. Only on settling on the microscope slide is the regular nature of the dendrite shown as seen in Fig. 5.56. Similar three-dimensional shapes are also found...

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