4. Model for habit change of snow crystal

It may be supposed that the habit change of snow crystal patterns strongly relates to the temperature-dependent surface structures mentioned in the previous section. Kuroda [24] proposed a new model for the habit change of snow crystals on the basis of surface melting during his stay at the laboratory of Professor Lacmann of the Technische Universitat Braunschweig. At present, it is thought that this model is one of the most reasonable explanations for the habit change of snow crystals. Here, let us present a qualitative explanation of this theoretical concept.

Growth velocities of each surface with their various structures depend strongly on the growth mechanisms, because each mechanism results in a different rate determining process for the growth. Growth mechanisms for ice surfaces with various structures are summarized as follows;

Surface covered with qll: The growth rate is determined by the balance between the incorporation rate of water molecules from the vapor to the qll and the solidification rate from the qll to the crystal lattice. This is called as the V-QLL-S mechanism[25]. Growth rate (RI) may depends on the thickness and dynamic properties of qll.

Rough surface: Incident water molecules from the vapor are directly incorporated into the ice crystal lattice. Namely, the adhesive growth mechanism. The growth rate (RII) is dominated by the diffusion process of water molecules in the atmosphere.

Smooth surface: Incident water molecules from the vapor are incorporated only at the kink sites along the growth steps. Namely, layer by layer growth mechanism. Growth rate (RIII) is determined by the surface kinetic process.

Consequently, we can easily understand that the growth rate (RIII ) below the critical temperature TII/III is the lowest and that (RII) in the temperature range between TI/II and TII/III is the highest. The growth rate (RI) for the surface covered with the qll can also be estimated, and we obtain that RI is intermediate between RII and RIII. Namely, the relation of RII＞RI＞RIII is generally accepted for the growth rates of ice surface with various structures.

On the other hand, the thickness of qll on the surface with a larger Δσ∞ is larger than that with a smaller one at the same temperature. Using a model of broken bonds and the experimental values for each ofσ, we can show that Δσ∞(1010)＞Δσ∞(0001). Therefore, the qll on the {1010} face is always thicker than that on {0001} face at the same temperature. It means that the surface melting transition on ice is anisotropic, and the transition temperatures of surface structures are bounded by the relations of TI/II(1010)＜TI/II(0001) and TII/III(1010)＜TII/III(0001) [24].

Fig. 6 gives a schematic representation indicating the anisotropic changes of ice surface structures as a function of temperature[24]. The transition temperatures TI/II and TII/III are assigned as TI/II(0001)=−4^oC, TII/III(0001)=TI/II(1010)=−10^oC, and TII/III(1010)=−20^oC, respectively. Eventually, we can divide the temperature region into four parts according to the combination of growth mechanisms of each surface. In the temperature range between −4 and −10^oC, since the {0001} and {1010} faces grow by the adhesive and V- QLL-S growth mechanisms, respectively, the growth rate of {0001} face, R(0001), should be much larger than that of {1010} face, R(1010). As a result, you can easily determine that the prism habit is realized in this temperature range. In the temperature range between −10 and − 20^oC, the plate habit is expected in the same way. In the temperature ranges between 0 and −4^oC and below −20^oC, the plate and the prism crystal may be expected on the basis of the detailed discussions about the step energy dependence at the two-dimensional nucleation growth, and the diffusion field effect, respectively.

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