Why are snowflakes symmetrical? How can ice crystallizing on one arm 'know' the shape of the other arms on the flake?















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Miriam Rossi, a professor of chemistry at Vassar College, offers the following reply:

Snowflakes are symmetrical because they reflect the internal order of the water molecules as they arrange themselves in the solid state (the process of crystallization). Water molecules in the solid state, such as in ice and snow, form weak bonds (called hydrogen bonds) to one another. These ordered arrangements result in the basic symmetrical, hexagonal shape of the snowflake. In reality, there are many different types of snowflakes (as in the clich¿ that 'no two snowflakes are alike'); this differentiation occurs because each snowflake is a separate crystal that is subject to the specific atmospheric conditions, notably temperature and humidity, under which it is formed.

The second question has to do with the way in which snowflakes are formed. The growth of snowflakes (or of any substance changing from a liquid to a solid state) is known as crystallization. During this process, the molecules (in this case, water molecules) align themselves to maximize attractive forces and minimize repulsive ones. As a result, the water molecules arrange themselves in predetermined spaces and in a specific arrangement. This process is much like tiling a floor in accordance with a specific pattern: once the pattern is chosen and the first tiles are placed, then all the other tiles must go in predetermined spaces in order to maintain the pattern of symmetry. Water molecules simply arrange themselves to fit the spaces and maintain symmetry; in this way, the different arms of the snowflake are formed.

Howard T. Evans, Jr., an x-ray crystallographer who is now scientist emeritus at the U.S. Geological Survey, adds a few details:

Snowflakes are mysterious things. Their fundamental form derives from the arrangement of the water molecules in the ice crystal. When a 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 neighboring 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!


Answer originally posted October 21, 1999.



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  1. 1. JDrewRd 01:37 PM 8/6/08

    I read in one study that the symmetry in the formation of a snowflake is not due to any internal process and simply do to the fact that all six branches of the snow flake are under the same conditions at the same time. Hogwash I say! There has to be an internal feature that causes this balance. Possibly when the flake is not balanced, its motion tends to right itself, or maybe somehow it is due to the polar nature of the water molecule. I don't know, but I'm not buying what I read.

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  2. 2. rockjohny 05:05 PM 10/8/09

    I'm going to venture a theory that the structure of a snowflake has more to do with the "nuclear magnetic properties of the nuclei of hydrogen atoms. NMR active nuclei, have a magnetic moment and can be thought of as miniature bar magnets with a north and south pole. These poles are usually randomly orentated" ( borrowed from www.cardiff.ac.uk page on MRI's)
    So you have one precursor water molecule that freezes not only does it freeze but its internal structure of protons freezes in position and subsequent molecules join to this one in a pattern determined by the precursor molecule. The arrangement of protons at the time of freezing in position would have an infinite number of possibilities and therefore, so would the structure that follows. What is curious is the fact that the stucture only gets so big, then terminates in a uniform fashion and yet certain molecules take their position in different areas of the flake. It makes me think of DNA and how it's instructions are carried out from a nucleus with the subsequent cells all carrying the entire blueprint yet taking their position in a specific area and function. I wonder if snowflakes can shed light on the growth of an organism from a single cell.
    I think the opposite is true. I would postulate that it really is the magnetic properties of the precursor molecule that dictates the subsequent position of the following joining water molecules just as if you position two magnets next to each other, they will flip sides automatically to match direction of polarities. This literally "freezes" this next water molecule in position according to the already frozen combination of protons in the precursor molecule. What limits the growth is the available free water molecules in the immediate vicinity of air at the time of growth which occurs in an instant like a 'snap'. It can be imagined as a company of soldiers with no leader, they all look alike but have no order to them until a seargeant appears giving orders to line up. The precursor molecule freezing becomes the leader dictating the position of the rest.
    I can be found on YIM as rockjohny.

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  3. 3. DavidSpector 01:18 PM 11/13/09

    I think that physicists don't know why branching snowflakes form the way they do:

    * They are globally planar, except for linear dislocations.
    * They are thin.
    * Arm dislocations are rare, and are ALWAYS corrected. The global pattern perfection is unique in nature. The global nature of temperature changes as a snowflake floats in a cold fog does not seem to explain the dislocation corrections.

    I think their familiarity with the well-known principles of crystal growth make physicists "wave their hands" when it comes to the details of their explanations. They may be too complacent to perform the necessary submicroscopy and experimentation.

    Like other familiar phenomena that are finally researched adequately (example: the floating of a ball in vibrating sand), discovering why snowflake arms are so similar may yield very useful techniques for science and engineering.

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  4. 4. RLLJR in reply to JDrewRd 12:30 PM 3/24/12

    Maybe when the snowflake is off balance the bond is so weak that the molecule attempting to bond breaks off. So the only way a bond can form is if there is an equal and opposite bond forming to keep the crystal symmetrical and balanced.

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  5. 5. RLLJR in reply to RLLJR 01:12 PM 3/24/12

    You might simulate the process with a random number generator. Find all positions on the molecular structure where a bond could be formed. Select one of these positions to form the next bond with a random number. Once a position has been selected your software has to find the matching position to conserve symmetry and then add the matching bond. The structure continues to form as long as the flake is suspended and the surrounding moisture content is suitable. I'm assuming all possible positions to form the next bond are equally likely, but there are most likely some inevitable caveats there. Any volunteers? Might be a neat project for a graduate student (actually any student with the knowhow and available software).

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  6. 6. RLLJR 04:05 PM 3/24/12

    Actually there could be more than one possibilitiy for n>1 number of molecules to bond simultaneously and maintain symmetry, and the program would have to find these possibilities for each value of n and then randomly select from all the possibilities.

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  7. 7. quack929 07:09 PM 1/28/13

    Diffusion-Limited Aggregation

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  8. 8. outslider 08:45 AM 2/22/13

    Here is an article about the snowflakes growth:

    http://arxiv.org/pdf/1202.1272v1.pdf

    Currently in might be the best explanation...

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