If you look at snowflakes you’ll see that they’re usually symmetrical, or nearly so. Different snowflakes have different patterns, and some of them are pretty complex, but the patterns on each branch or arm of a flake are more-or-less the same.
How does this happen? I assume that water molecules from the atmosphere freeze onto the extremities of a snowflake as it forms. What causes the crystals to take the same shape on each of the arms? I’m sure there’s no external directing force, and I know that water molecules can’t communicate with each other. Is the shape of a snowflake predetermined by some set of initial conditions?
You guessed it correctly. The shape of the snowflake is mostly determined by its initial conditions. Snowflakes form starting with just a few molecules, and due to the way that water freezes and forms crystals, these mini-snowflake seeds will have some sort of hexagonal symmetry. The snowflake “grows” by adding one molecule at a time, so each added molecule ends up following the original symmetry pattern.
Well, there’s that, and there’s also that the environment the snowflake is in will vary in temperature and humidity. If conditions are right for one arm to branch, they’re right for all arms to branch.
So are there liquids other than water that would freeze in normal Minnesota winter temperatures (-20º to -30º) that would form something other than hexagonal symmetry? Like pentagonal or square?
But I imagine that if there could be a temp differential across the snowflake, such that one side was, say, 30 °F, and the other side was -20 °F, then we wouldn’t get any axial symmetry?
Well, the freezing point of salt isn’t anywhere near -20 to -30 deg, but you can probably find plenty of salt on Minnesota roads in the winter. Sodium Chloride forms cubic crystals, which I suppose you could call “square” symmetry but I think it’s more properly referred to as “octahedral” symmetry.
That’s a pretty darn steep temperature gradient.
You can get asymmetrical snowflakes under significantly less bizarre circumstances. Snowflakes are often asymmetrical or misshapen.
Pentagonal symmetry, meanwhile, is nearly impossible. You can’t have a crystal with pentagonal symmetry. Though you can get pseudocrystals with something that looks a lot like pentagonal symmetry, based on something like a Penrose tiling.
Well, they don’t have cellphones, but they do exert influence on each other. Chemistry is basically electricity; the interactions between molecules are electrostatic ones. While water molecules aren’t charged, they present zones which are “sort of negatively charged” (the oxygen) and others which are “a bit positively charged” (the hydrogens): the interactions which involve those charges of different molecules are called “hydrogen bonds”. There are also weaker interactions due to short-term variations in the amounts of charge (van der Waals forces).
Water is peculiar precisely in that in its liquid form, those hydrogen bonds are unusually strong; they are also unusually strong in its solid form (water solidifies at much higher temperatures than similar molecules). There’s several solid forms of water, of which the most common one has cubical symmetry: that’s the symmetry we see in snowflakes.
Why does it have to be within that rigid temperature range, or work by a freeze process. Crystals of various types form with a variety of symmetry types: Crystal - Wikipedia
Everything is there: ice cubes are polycrystals… Some crystals have defects, or are misshapen by the space they grow in. However, crystals grow, one sub-unit at a time, in a defined pattern based on the sub-units’ physical chemistry.
Also, the geometry of a water molecule is fixed in a “V” formation of 104 degrees. I’d imagine this-along with the charge dispersal previously mentioned-goes a long way towards dictating ice crystal morphology.
While this is true,
it is interesting to note, I think, that we get *pentagons *in crystals all the time. They’re just not constrained to being regular, and are actually an artifact of a*cubic *symmetry.
