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Why six branches?


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#1 dophinsluv

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Posted 01 March 2008 - 03:50 PM

Do snowflakes always have six branches? Why is this?

#2 Jon Nelson

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Posted 29 December 2008 - 09:11 AM

The simple answer is no. For example, the columnar crystals have no branches.

Even if you restrict your question to the tabular crystals, the answer is still no.

What do I mean by columnar and tabular? Consider a basic shape of a tiny ice crystal growing in the atmosphere (i.e., in air and water vapor). This shape is just like that you would get if you made two cuts directly across the axis of a six-sided pencil. If the length of your pencil stub is greater than its width, the shape is columnar. If the opposite holds, the crystal is tabular.

Now consider the tabular crystal. Branches usually form at each of the six corners that separate the six sides. But once the branches start growing, some may grow faster than others. The slower ones grow into regions that have already been partly depleted of water vapor that stuck to the faster-growing branches. So the slow branches slow their growth even further, and end up largely stunted. Eventually, only the faster-growing branches stand out, and these may number 6 or fewer. Another way for a crystal to have fewer than six branches is if one or more branches break off during a collision with another crystal.

More than six branches may also occur with tabular crystals. Here is why. Snow crystals are thought to originate mostly from supercood droplets that freeze. But when the droplet is large enough or the temperature cold enough, such freezings can often result in more than one crystal joined at their centers. This can result in tabular crystals with up to 12 branches (called, not surprisingly, 'twins'), up to 18 branches (no official name, but one might call them 'triplets'), and even up to 24 branches ('quadruplets' (?)).

You might still wonder if there is some simple rule to remember about the branches. The answer to this is yes. For the droplets that froze into a single crystal, if you imagine placing the crystal over the face of a clock and line up one of the branches to point at 12:00 o'clock, then the other hands, how ever many there are, can point only at even-numbered hours: 2,4,6,8, and 10 o'clock. So, if someone shows you a crystal with branches sticking out the four corners of a square, that is, at 12, 3, 6, and 9 o'clock, then you know that cannot be a snow crystal.

If, on the other hand, the droplet froze as a twin, you effectively have two clocks upon which to line up the branches. These two clocks may be rotated from each other by any angle. A similar situation applies to triplets, and higher-order cases.

This o'clock business is just a way to picture the angular relation between the crystal branches. In the study of other crystals, the angular relations are often crucial for identifying the type of crystal.

Jon




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