On snowflakes and crystallography

Plate XIX of ‘Studies among the Snow Crystals … ‘ by Wilson Bentley, ‘The Snowflake Man.’ From Annual Summary of the ‘Monthly Weather Review’ for 1902.
Wed, 30.12.2020

There is no better time to be thinking about crystals and symmetries – many of us have already experienced the first snowfall of this winter and perhaps admired perfectly-shaped snowflakes. Little is it known that the origin of crystallography has everything to do with snowflakes, their hexagonal structure and happenstance. How so? A snowflake ends on Johannes Kepler’s coat and the 17th century German mathematician starts musing at the intricately repetitive design of the minuscule ice crystal. His 1611 study ‘Six-cornered Snowflake’ is the first scientific description of crystalline substances, pioneering aspects of modern structural crystallography like the principle of closest packing and anticipating ‘The Law of Constant Angles’.  

Following Kepler’s investigations, we can also ask ourselves – why do snowflakes always display a six-cornered structure? The water molecules form a regular hexagonal lattice during the process of crystallization, since in their solid state (ice, snow) – water molecules form weak bonds (hydrogen bonds) with each other, often resulting in the mentioned six-sided arrangement. However, despite their predominant hexagonal symmetry, the snowflakes may display many different designs – this differentiation originating in the fact that each snowflake is a separate crystal, subject to various specific atmospheric conditions upon crystallization. As temperature drops, the ice crystal grows, water freezes and crystallises in its six corners continuously, branches sprout from the six corners when the crystal grows larger, causing the distinct design of each snowflake.

Howard T. Evans, Jr., X-ray crystallographer and scientist at the U.S. Geological Survey, adds more about the topic in the following fragment:

‘Snowflakes are mysterious things. Their fundamental form derives from the arrangement of the water molecules in the ice crystal. When liquid freezes, the molecules tend to settle in the lowest-energy state, and that almost always involves some form of symmetry. The higher the symmetry, the more stable the crystal is.

Water molecules floating freely in a vapor begin to arrange themselves into a crystalline solid when the temperature drops below freezing. The two hydrogen atoms of the molecules tend to attract neighbouring water molecules. When the temperature (thermal motion) is low enough, the molecules link together to form a solid, open framework that has a strict hexagonal symmetry.

But why are snowflake shapes so elaborate? Nobody has a good answer for that. The general explanation is that snowflakes form in the atmosphere where conditions are very complex and variable. A crystal might begin to grow in one manner and then minutes or even seconds later something changes (temperature or humidity), so it starts to grow in another manner. The hexagonal symmetry is maintained, but the ice crystal may branch off in new directions. The changes in environmental conditions take place over a large area compared with the size of a single snowflake, so all regions of the flake are similarly affected. In the end, there are all kinds of forms that can arise: everything from prisms and needles to the familiar lacy snowflakes. Water is an amazing substance!’1


Why are snowflakes symmetrical? How can ice crystallizing on one arm ‘know’ the shape of the other arms on the flake? – Scientific American

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