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Snowflake physics

Although all snowflakes are hexagonal, each one is unique. (photo: <magic mom> @ Flickr.com)

Although all snowflakes are hexagonal, each one is unique. (photo: @ Flickr.com)

Britain is under siege. Forget terrorism, forget recession. The snow is here. Anxious parents queue for hours stocking up on 40 jumbo-sized loo rolls and loaves of bread. Previously benign neighbours steal salt for their driveways. Camera crews aim their sights at the elderly, the gangly and the irresponsible in cynical hope of dramatic collapse and newscasters talk in hushed, alarmist tones, professing apocalypse. There is no doubting it: there is nothing we love more than to complain about our weather.

Not wanting to look outward at the world, I stared at the snow. This got me thinking; can it be that no two snowflakes are identical? The answer is a resounding no. Because water is not isotopically pure the probability of two crystals, with unimaginable numbers of molecules having exactly the same distribution is vanishingly small; in fact, so small that it probably has never happened. What of the wonderfully intricate crystals that adorn knitwear? Mathematical permutation can answer this. Suppose we have 15 snowflakes on a scarf and there are 15 positions for the first snowflake, 14 for the second, and so on, which multiply to over a trillion orderings! If you could ‘build’ a snowflake using but a 100 ‘pieces’, the number of permutations would exceed the number of atoms in the observable universe! Hence, no two complex snowflakes have looked, or will ever look, identical.

Nakaya, a Japanese nuclear-physicist-turned-snow-crystal extraordinaire, painstakingly classified the crystals into 41 different morphological types, from hollow columns to sharp needles, to curious columns capped on either end. How on earth do we explain such diversity, and indeed, what is the cause of the beautiful six-fold symmetry?

Let me take you on a journey, far up in the clouds. Inside each snow crystal, there is a dust particle which along with other gases, is required for the initial attraction of water molecules. The fate of the flake depends on the temperature and the Supersaturation (a measure of water concentration). A slight change in either direction has a beautiful effect on the form.

On a molecular level, the corners of a snow crystal stick out so water molecules more rapidly diffuse and condense upon them. For a while, the edges can keep up, as they become rougher and rougher as the corners extrude outwards. But eventually, they’re as rough as it gets, and the corners win out. The snow crystal has grown arms! This keeps happening, arms growing arms resulting in fractals.

As the snow crystal flutters about in space, its microclimate changes, so its pattern of growth changes. Due to the diminutive size of the crystal, all arms are exposed to the same environment, and thus, symmetry is maintained. No two snow flakes take exactly the same path, and so no two are exactly alike. thus, in principle, one should be able to infer the ‘history’ of a snowflake from its form; or to quote Nakaya, “Snowflakes are hieroglyphs sent from the sky.” Snow isn’t a time to fret and moan, it’s a time to awe at the beauty of the natural world.

Read more at http://www.its.caltech.edu/~atomic/snowcrystals/

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