Hoar Frost

A good friend of mine back in Wisconsin got some great photos of hoar frost during a recent cold snap. What you see in the first photo is hoar frost formed on the twigs of a tree in his yard. Note how the crystals grow perpendicular to the twig itself and form dendritic structures. Note also how they form preferentially on one side of the twig — that’s the downwind side.

If you need some background on the various types of frost and frozen rain, see my Feb 8,2021 post Rime Ice vs. Hoar Frost. You can get all the detailed science there, which I’ll include only minimally in this post.

Hoar frost requires near-freezing temperatures, but low enough humidity that microdroplets of water are not present, as is the case with fog. If microdroplets are present, they would form amorphous rime ice instead. The presence of dendritic crystals is the signature of hoar frost.

His next photo surprised me. He claimed it showed a single hoar frost crystal formed on a piece of metal near his shed. It too was tilted in the downwind direction. I asked if it was maybe an icicle (which often form at a slant in winds). He replied “Definitely not. It disintegrated when I touched it, just like a snowflake.” I had never seen such a long crystal of hoar frost (≈ 12″) and was surprised they could grow to this size. But as you can see from the photo, the crystal was downwind of the shed and thus protected from stronger gusts:

The structure of hoar frost crystals results from the dipole nature of water molecules. At the microscopic scale, the molecules arrange themselves in a hexagonal lattice which gives rise to the symmetry observed in hoar frost crystals.

The conditions for hoar frost growth are: clear sky, cold air just above freezing, low relative humidity, and relatively calm winds. Under those conditions, here’s what happens at the molecular scale:

The substrate, which is below freezing temperature due to radiative cooling, provides a surface on which water vapor molecules can attach in a process called deposition. Irregularities in that surface cause the water to first form a thin layer of amorphous ice (like rime ice), but as more molecules join the party, eventually full hexagonal crystals will form. The graphic shows a 2D version of the process. In 3D the structure is a bit more complex.

It’s worth noting that these hexagonal crystals are why ice is less dense than liquid water. The average distance between the water molecules in the liquid state is about 0.31 nm (roughly equal to their size). But when in the crystalline state that average distance increases by 9% — ice has 91% the density of liquid water. The empty space in the center of the hexagonal crystal is the reason.

The patterns that Jack Frost leaves on windows are actually 2D renderings of hoar frost. It’s most often seen on older less-efficient single-pane windows. When the temperature outside cools the window glass to below freezing, water vapor in the house will attach to the glass forming hexagonal patterns that can be quite beautiful. Here’s one example from Wikipedia:

But more about that next week.

Crystals of any substance are the result of molecular geometry. For water, the 2D hexagonal crystal gives rise to everything from snowflakes to hoar frost to icicles in 3D.

Next Week in Sky Lights ⇒ Window Frost

Golden Sunsets
Window Frost

2 comments on “Hoar Frost”

  1. Two questions:
    1. Since water molecules form themselves into a hexagonal lattice to make snowflakes, plates, and pencils it would seem that the two hydrogen atoms would be positioned 120 degrees from each other. But your illustration shows them at 104.5 degrees. What gives?
    2. How can we measure this angle at the molecular scale?

    1. Excellent question sir. The 104.5° of a free water molecule cannot be directly measured, to my knowledge, but it can be calculated using the laws of chemistry and quantum mechanics. 104.5° is close enough to 120° that, as the crystals form, the atoms can distort a little bit to achieve the stable hexagonal configuration. Molecules aren’t like Legos® … they can flex somewhat when interacting and bonding with other molecules.

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