Dear Cecil,
About your column, How do snowflakes grow symmetrically?
( http://www.straightdope.com/columns/070427.html )
Your answer was insightful and well written, as usual, but you left out a crucial aspect of the problem. Your answer was
“Crystal formation isn’t random but rather is rigidly dependent on temperature, density of water vapor, and other local conditions, all of which are likely to be uniform in the immediate neighborhood of the flake — what happens to one branch happens to the rest.”
Having the local conditions uniform is no doubt very helpful in making the near symmetry possible, but is not sufficient. What is missing? Well, not only should the local conditions be uniform, but the crystal itself must respond to these conditions the same way on each branch. In crystal growth, this is far from guaranteed.
Witness an ice crystal form, common to the high cirrus clouds, called the ‘bullet rosette’. These are crystals consisting of columns that radially extend in nearly random directions (though some directions are more common than others). (A google image search under “bullet rosette” can show you a few collections of images, most with rather small images, but you can get the main picture.)
Such forms have columns of various lengths and thicknesses. I have never seen any that struck me as appearing symmetric, despite the fact that they have considerably less detail than the six-branched tabular snow crystal that grows within a few degrees C of -15 C. If your answer to the question was sufficient, then it would be hard to explain all the non-symmetric bullet rosettes.
In other words, according to your argument, if the bullet rosettes are tumbling as they fall, each ‘branch’ should look the same. The fact that they don’t casts doubt on your argument.
So let’s go back to the argument for near symmetry in the common snow crystal (the ones that grow near -15 C). Sir Charles Frank addressed the question of snow crystal symmetry in a journal article in Contemporary Physics in 1982 (title: “Snow crystals”). He pointed out that the symmetry strongly suggests that the snow crystal has an uncommon mode of crystal growth called surface nucleation. (Sometimes called ‘layer nucleation’ or ‘2-D nucleation’.) With surface nucleation the tips of each branch should respond the same way to the same conditions. Indeed, there is much evidence that snow crystals usually grow by this mode.
So, is the apparent symmetry explained by the uniform conditions you mentioned
together with Frank’s argument that the growth mode is important?
Alas, even these two things may not be sufficient. Because if one branch grows thicker than another, then it should grow more slowly and become stunted. (There is no good reason that growth in this direction is by the same mode as that for the growth of the branch length and width.) The point here is that the crystal itself alters the local conditions, and with all other things equal, a patch of crystal surface of greater area will alter the conditions to a greater extent. With one (or more) stunted branches, there is no symmetry. Thus, to have the same branch lengths, they should also have the same thickness.
What ensures that they have the same thickness? Here we enter into further conjecture and uncertainty. I give a plausible reason for this in my 2005 article in Crystal Growth and Design (title: “Branch growth and sidebranching in snow crystals” – it’s a long article, so you may want to skip to the last section where I address this very point**)
In short, your answer gave a condition that is probably necessary for the apparent symmetry of snow crystals, but is not sufficient. Also, snowflakes, as you probably know, are never symmetric, being clumpings of snow crystals and other icy debris. The question is really about snow crystals, not snowflakes, and I have limited my comment to snow crystals.
Jon