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The cup and the butterfly
In early January, while visiting a cold, dry region, I saw this frost on a wooden fencepost.
The pattern resembled a cluster of butterflies. In the shade, these "butterflies" were blue, reflecting the blue sky. In the sun, they were bright white:
These are a type of hoar-frost, and though hoar-frost grows by the same processes as snow crystals, they can take on an even greater variety of forms. That they have more forms is a consequence of the fact that they can experience much greater levels of humidity, that is humidity relative to their temperature. This greater degree of humidity produces faster growth. Frost forms can also be more unusual because the proximity of the crystals alter the vapor gradients.
A closer look at this "butterfly hoar" shows the form to be closely related to the basic hexagonal plate form.
Butterfly hoar is like a more-open version of the cup form (shown in the Feb. 9 post on hoar), both of which arise when the growth is very fast, and the temperature just right. The temperature has to be near that at which the two main growth directions have nearly equal growth rate, which is about -10 C (another transition temperature is about -3 C, but exposed objects this night got much colder than -3 C). See the diagram below.
At the top row of the diagram, you see the solid column type of crystal. The green arrows show that the growth rate along the column (or basal) axis is much more than that in a prism direction. At the bottom, you see the solid plate type, where the opposite holds. In between, and with higher growth rates (relative humidity) you have the cup form, in which the basal growth rate is just slightly more than the prism; and you have the butterfly, in which the prism has a slightly greater growth rate. In the cup and butterfly cases, the humidity relative to the ice must be quite high, higher, at any rate, than that which can occur in clouds. The growth is not solid; that is, the entire facets do not grow, just the rims grow, which produces hollowed-out or branched forms.
Another factor with the butterfly, is that the "plates" stick out so much that the vapor gradients allow just one or two of the prismatic sides to grow outward. It is like breaking off a rim sector of a widely flaring glass cup, and just viewing the broken-off sector, as sketched in the diagram above.