Emerging Technology from the arXiv

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Solving the Puzzle of Triangular Snowflakes

Snowflakes ought to be hexagonal. So why are triangular ones so often observed?

  • November 27, 2009

The beautiful six-fold symmetry of snowflakes is the result of the hydrogen bonds that water molecules form when they freeze.

But snowflakes can form other shapes too when the growth of the crystal is perturbed on one side. In theory, diamonds, trapezoids and other irregular shapes can all occur. And yet the one most commonly observed (after hexagons) is the triangle. The puzzle for is why? What process causes deformed snowflakes to become triangles rather than say squares or rectangles?

Today, Kenneth Libbrecht at the California Institute of Technology in Pasadena provides an answer. Libbrecht, you may remember, has built an amazing snowflake machine to study the formation of these remarkable tiny crystals.

Their growth and shape, he says, is governed by two processes: the diffusion of water molecules through the air and the molecular dynamics on the surface of the crystal and it is the former that explains triangular crystal formation.

Libbrecht says various phenomena influence the way water molecules get to the surface of a snow crystal but perhaps the most important is aerodynamics. This orients the crystals and ventillates it, determin the rate at which it can grow.

Libbrecht has calculated how small perturbations in the growth rate on one side of a crystal change its shape. He says that whatever the cause of the perturbation, a hexagonal crystal will always continues to change shape in one way or another.

But the curious property of triangular crystals is that they are stable against this kind of change. So when a crystal has become triangular, other perturbations cannot change its shape further.

Triangles are a kind of valley in the energy landscape of snowflake morphology. And this explains why they are so common. Cool!

Keep an eye out for one next time you’re out in the snow.

Ref: arxiv.org/abs/0911.4733: Aerodynamical Effects in Snow Crystal Growth

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