Snow-Crystal Symmetry

 

Snow-Crystal Symmetry

 

This is an examination of snow crystal growth, and the similarity of branches within a single snow crystal.

      Snow crystals (ice crystals) are not injection molded, or made with a 3-D printer.  There is no software to guide their shape, yet there is communication and coordination that forms six nearly identical branches within a single snow crystal.  

     As freezing ice crystals fall through moist air, they randomly collide with other particles.  Those impacts create shock waves that travel to the central nub and then radiate outward to all sides.  The vibrations set up patterns that influence the shape of the water as it freezes.

 Photos: Ken Libbrecht            .       

      Studies exist to describe snow-crystal growth, the atmospheric conditions, the rate of growth, typical size and provide an explanation of why crystals are unique, however not an explanation about why the branches of a snow crystal are essentially identical to the other branches of the same snow crystal.  

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A tuning fork produces an almost pure sine wave.

 

      Most objects produce vibrational patterns with irregularities called acoustical signatures (ex: the sound of a dropped metal wrench, the bounce of a basketball, a spoon on a water glass, etc.).  The acoustical signature is unique for each object based on its shape, mass and mechanical properties.  

     The corollary is that moisture will freeze in a unique pattern in the presence of an acoustical signature.  In this situation, moisture will freeze in nearly identical shapes on the six sides of the hub while collecting more building material (moisture) in the presence of an acoustical vibration, ex.: random collisions, and minute cracking, popping and squeaking sounds that occur during freezing.  

      For reference, if water in a horizontal tube or on the surface of a container, freezes while a standing wave is being induced, it will retain that standing wave pattern.  On an ice crystal, a similar situation exists within the hexagonal geometry inherent in the 3-atom structure of an H₂O molecule.  

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Mirror-image, or cookie-cutter symmetry?

       If we examine the behavior of a tuning fork, when one tine is struck, both tines vibrate in opposition, toward, then away from the other tine, repeatedly to create the note.  The tines move as mirror images of the other about a central axis of symmetry.  This is well known but suggests that there may also be this mirror-image effect between adjacent branches of a snow crystal.  

Rather than branches of a snow crystal being essentially identical, perhaps each is the mirror image of its neighbor.  Since each branch has its own axis of symmetry, it may be difficult to determine if each branch is a mirror image or a cookie-cutter copy of its neighbor.  Time-lapse video of snow-crystal formation seems to show growth on one branch being created on the opposite side of the adjacent branches in support of the mirror-image theory.

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