Two weeks ago most of Europe had been covered under the white blanket of freshly fallen snow. While sudden snow storms brought traffic and public transport to a screeching halt in some places winter sport enthusiasts could enjoy their hobbies even in places that usually boast a milder weather.
But the falling snow can also bring joy to the scientists who have identified one of the most beautiful models to study crystal growth: The snowflake. Rumor has it that no two snowflakes are alike. But why is that? And how do we end up with the plethora of shapes that snowflakes present?
Snowflakes are formed when the water vapor in clouds goes directly into the solid phase at subzero temperatures. This does not happen homogeneously, rather little dust particles serve as nucleation centers for the ice crystals [1]. This nucleation in it self is a widely studied topic in condensed matter physics but presents only the first step in the formation of a snowflake and maybe the one that is understood best.
Once the crystal nucleus is formed it will grow as other water molecules from the vapor attach to it. How this attachment happens strongly depends on the surrounding conditions, e.g. the temperature and the humidity, and in turn influences the shape of the resulting snowflake. This complex interplay has been summarized in a so called morphology diagram that details what type of snowflake one can expect under which conditions. For example at high humidity and temperatures around -15°C Snowflakes as the one in the picture prevail while at lower temperature only column like snowflakes are produced.
This sensitivity to environmental conditions is related to a number of instabilities associated with the growth of crystals from vapor. One example for such an instability is the faster accumulation of material on protruding features, which leads to dendritic growth. Such processes are called instabilities because they amplify the features that caused the process in the first place. Thus a larger protrusion grows even faster than a smaller one. With this positive feedback instabilities can enhance rudimentary features quickly. Considering the ever changing conditions snowflakes face on their way to the surface and how they can quickly change their growth pattern it becomes plausible that no two of them would look alike
How different processes influence the growth and shape of snowflakes has been studied for a long time (see [2] for a review). But because the instabilities are very sensitive to the environmental conditions most of the explanations available are limited to certain regions of the morphology diagram. How the transition between these regions is happening is not always clear and experiments to illuminate the growth patterns are difficult to realize. because they traveled on slightly different paths.
One could then try to model the whole system in a computer. But these approaches also reach their limitations. Since features from different parts of the snowflakes can influence the growth of each other it is not sufficient to study only small parts of the ice crystal. Rather micron sized objects need to be considered, which can not be simulated in atomistic detail with current computers. This means one needs to model the growth process. One particularly successful approach has recently been presented by Barret et al. who were the first to model growth over different domains in the morphology diagram [3].
Their model does however not include one important instability: The so called knife-edge-instability [1,4], which is the reason why snowflakes are usually flat. The mechanisms related to this instability are not yet understood and require more experimental and theoretical study. Additionally it is still not well understood what effect impurities and electric fields have on the growth.
With all of this it is clear that snowflakes are one of the most familiar examples in everyday life that can teach us about crystal growth from vapor, but many a thing still remains unclear. So if you have never noticed the variety of shapes that snowflakes present let some fall on your sleeve the next time it is snowing; take a closer look and imagine all the complex processes that are needed to produce the intricate patterns you see.
Stephan Koehler
Read more:
[1] Libbrecht, K. G. Ken Libbrecht’s Field Guide to Snowflakes. St. Paul: MBI Publishing, 2006.
[2] Libbrecht, K. G., “The physics of snow crystals,” Rep. Prog. Phys., 68, 855-895 (2005).
[3] Barret, J.W., Garcke, H., N?rnberg, R., “Numerical computations of faceted pattern formation in snow crystal growth ”, PRE 86, 011604 (2012)
[4] Libbrecht, K. G., arXiv:1111.2786.
Picture: http://commons.wikimedia.org/wiki/File:Cristal_de_hielo.jpg