Priscilla Inglis, of Dunedin, asks :-
During a heavy frost, ice made a very attractive pattern on the glass roof of our conservatory. Why did this pattern form?
John Campbell, a physicist who grows single crystals at the University of Canterbury, responded.
The pattern is produced by crystals of ice growing on the glass, rather than water quickly freezing into an amorphous lump, such as an ice cube in your freezer.
If the atoms condense slowly enough they have time to jostle into the position where they have the lowest energy. In many materials this is the crystalline state in which the atoms are in very regular arrays. If you look at salt from your salt shaker under a magnifying glass, you will see the grains are cubic, which is how the sodium and chlorine atoms pack down most economically in energy. If you make your own ice-cream the old fashion way in the freezer, large hexagonal ice crystals grow inside the ice-cream. (The ice-cream must be beaten to break these crystals into smaller fragments).
The ice on your glass roof was formed when water vapour condensed out from the cooling air. This always needs something to nucleate on. For example, raindrops form by water vapour condensing on a speck of dust. Next time you open a bottle of fizzy drink notice how the bubbles always stream from just a few places, where there is a sharp point to help nucleation.
Once one crystal starts growing the vapour will condense on it, rather than starting new crystals, so the already formed crystals get bigger. When water molecules pack down into a solid they do so in a hexagonal array. Hexagonal ice crystals high in the winter sky produce nice halos about the sun because of their shape. All snowflakes have hexagonal symmetry too. However the ice crystal grows more quickly in some crystal directions than others and that is what you are seeing, dendritic growth.
As another example, I grow ruby crystals (which is just aluminium oxide) by condensing them from some aluminium oxide dissolved in a flux. They form very thin hexagonal plates. I add another chemical to slow down the growth in the fast growth direction, so with care I can grow cubic rubies. This takes typically 4 days. If I cooled down more quickly I would get patterns related to the ones you saw.