Category: "Snow Science"

Two-level nature of branched crystals

December 11th, 2016

The common branched crystal looks like a paper cut-out, but actually has a complex 3-D nature. One aspect of this nature, which I have alluded to in prior posts, is the two-level structure: What appears to be happening on one plane, is actually occurring on two. For example, consider the following dendrite of Mark's:

Two-level nature of branched crystals

The six branches of this crystal are not on the same level: the three on the right are on the top level, whereas the three on the left are on the bottom. If I could break the connection between the levels and pull them apart, they would look similar to this: 

Two-level nature of branched crystals

Actually, the connection can be broken. The fellow who first did this was Ukichiro Nakaya back in the 1930s. 

Two-level nature of branched crystals

Instead of using photoshop (as I did above), Nakaya (or rather Nakaya's assistant) used a razor blade in a very cold room. His assistant must have been both highly skilled as well as very patient, because each level is separated by less than half the width of a typical human scalp hair. 

The levels themselves are even thinner. For a fern-like dendrite, which may be 2 mm across, the thickness of one level may be 300 to 500 times thinner. A recent study ** by Wataru Shimada and Kazuki Ohtake of Toyama Univ. in Japan used a laser-imaging device to map out the contours on such a branch. The result shows an intricate 3-D structure: 

Two-level nature of branched crystals

(Thanks to Prof. Shimada for sending me this image. I have slightly simplified it.) The image shows the central part of the branch as a ridge, with numerous valleys running down both sides. The thickness of the region in red is only 5 micro-meters (5 millionth of a meter or about 0.2 thousandths of an inch).

None of this is the flat facet that we imagine a snow crystal to be. There is one flat facet however -- it is on the bottom side. 

-- JN

**The study is here, though not freely accessible:


How some snow crystals hide their droplet origin

December 5th, 2016

Look closely at the center of a snow crystal. In many, or most, you will often not find a droplet center as we described in the previous post. Indeed, for the columnar crystals, you may never see a droplet center. As an example, look at the center of the dendrite crystal below (one of Mark's):

How some snow crystals hide their droplet origin
Why? Do these not also start on droplets?
Or are the droplets just too small?

This crystal, like all snow crystals did start on a frozen droplet, but the vapor deposited all around the frozen droplet (also called a 'droxtal'). The resulting growth can vary quite a bit, but roughly proceeds in a way first described in detail by the physicist Sir Charles Frank:

How some snow crystals hide their droplet origin

The crystal will still develop its two levels, top and bottom, just like we saw in the previous post, but in this process, it takes a little longer for the two levels to develop. The first stages involve the frozen droplet gaining flat faces (see steps (i) to (ii) below). Initially, as in (ii), there are more than 8 faces, but the fastest-growing faces soon vanish (they essentially grow themselves out of existence), leaving only the slower basal and prism faces in (iii):

How some snow crystals hide their droplet origin

The slower-growing faces win the game and are allowed to reveal themselves. With snow, we learn that sometimes slow wins.

In the above sequence, follow the red arrows for the time sequence. (From "(a)", I am borrowing some sketches I made for a publication in 2008. These differ slightly from those originally proposed by Frank.) The crystal sizes here are very small, about 1/10 to 1/2 the width of typical scalp hair (i.e., about 7 to 40 micro-meters). The axes on "(a)" show the crystallographic axes for ice, remnants of my paper.

You can see though that by stage (iii), the form of the original droplet has vanished. But let's continue, along the path to a recognizable branched crystal, roughly as described by Frank.

How some snow crystals hide their droplet origin

The crystal face grows outward by the spreading of layers. In the sketch above, the edge of these layers, called "steps", are shown by fine lines in the front view at right. The steps start near a corner, say at "A" or "C" in the sketch, and spread inward, closing in on the center. But soon a problem emerges: the steps are coming too fast and the center region cannot keep up. So a small pit emerges in the center of the face as you see at (b). On a symmetric hexagonal form like that above, this pit forms roughly at the same time on all six "prism" faces. (Pits may also form on the top and bottom faces, but for a crystal shape like that above, will not become very deep.) Here "SCR" stands for step-clumping region.

Typically, the rim of this pit expands as the crystal grows (c).

How some snow crystals hide their droplet origin

And grows. Eventually, the rim breaks through a crystal edge. Usually, it is the edge between two prism faces as shown below.

How some snow crystals hide their droplet origin

Notice that at stage (d), the crystal now has two levels, a top side and a bottom side. From this stage on, the two levels will compete with each other, with one eventually getting much larger than the other. This same process was shown in the previous post. But let's continue on and see how this develops.

How some snow crystals hide their droplet origin

Either one, or both levels may sprout branches. In the case (e) above, both have sprouted (note the notches that divide the just-sprouted branches). So far, both levels are developing at the same rate. But that cannot continue: the situation is unstable because if one level gets just a little bit ahead, it will stay ahead and increase its size difference with time. In fact, the smaller level will hardly grow at all - it is stuck in a region largely devoid of vapor excess.

How some snow crystals hide their droplet origin

Typically, it is the bottom level that gets ahead, as shown in (f) above because the crystal is falling down through the onrushing vapor-laden air. (The interior lines labeled in (f) above will be discussed another day.) Looking directly down on this crystal, it would look roughly like the following.

How some snow crystals hide their droplet origin

Consider that every crystal is a little bit different, but the basic features in (f) exist in the original picture at the top. I reproduce it below with a close-up of the center.

How some snow crystals hide their droplet origin

Some of these finer details will be discussed in a later post.
Finally, as to why this process sometimes occurs but sometimes the process of the previous post occurs instead remains a mystery. There are a few factors that will favor this process though: smaller initial droplets, and conditions of slower growth.

-- JN

How the water molecules make corner pockets

November 11th, 2016

As I mentioned in my previous post, the formation of corner pockets on ice crystals is inexplicable by the standard theory of snow-crystal growth. Akira Yamashita had recently proposed a mechanism for corner pockets, though he had applied it to a different situation. In his case, he observed the early growth stage of a relatively large frozen droplet as it transitions into a faceted crystal. So, his situation dealt with a round crystal becoming sharp-edged. In our case, we started with a large sharp-edged crystal, then made it become round by sublimating (analogous to evaporation, but for a crystal), and finally made the crystal re-sharpen by growing it. The process is sketched below. You may want to open the image in another window and enlarge it.

How the water molecules make corner pockets

At the top, you see the simple hexagonal prism crystal in its initial stage. At stage B, the crystal sublimates (we reduced the amount of vapor), meaning that it is starting to shrink. The shrinking starts from the corners, making them become rounded. Then, in stage C, we start growing the crystal again, and the interesting things start to happen.

As the water molecules from the vapor stick to the surface, they remain mobile on the surface. On the surface, they wander around until latching into a little nook. (In crystal-growth theory, these 'nooks' are actually tiny kinks in a surface step.) The region just over the edge has plenty of nooks, as it is rounded. So, the edge grows fast and starts to protrude and overhang (stage D). Overhangs from the top and side faces merge in stage E, creating the pocket. Afterwards, water molecules in the pocket surface move about making a more round, disk shape.

About being inexplicable by the standard theory of snow-crystal growth, this standard theory does not include the wandering of the mobile surface molecules over the edge. Now, if the new theory applied only to this corner-pocket formation, then it would be of little importance. But the wandering process cannot apply to only this situation (how would the molecules know when to start or stop?): It must ALWAYS be happening. And, as I mentioned earlier, I realized that the wandering process may help explain many other curious snow-crystal features that I had previously found inexplicable. In other words, it may be a fairly important discovery.

-- JN

Akira's Corner Pockets

May 10th, 2016

The evanescent snow crystal

appears out of nowhere

The lines and boundaries

on its faces record a story

a story of a crystal's birth

a story of a crystal's life

But before the record vanishes

Who will hear its story?



A few years back, a correspondent of mine, Professor Akira Yamashita of Japan, long retired, sends me an email. In the email, he had a document with words and pictures of some small crystals that he'd captured back in the 70s. They were small crystals, essentially freshly "hatched eggs" from the frozen droplets upon from they had started. But some had small pockets of air near their corners.

To those who have studied any sort of crystal growth and have some familiarity with crystal-growth theory, these corner air pockets, or "bubbles", were in impossible locations. They should not be there. Pockets will form near face centers, not corners. But Prof. Yamashita also had a theory about their formation. His theory first looked sketchy to me, but I appreciate hearing about new ideas, so over the following years kept revisiting his theory, getting to think that it had merit, and wondering if it had other applications.

Then, just this past year, in our own ice-crystal experiments, we did something that apparently had never been done to small ice crystals in the lab before. We slowly grew a crystal in air. And we cycled it from slightly growing, to slightly sublimating (i.e., shrinking in size), to slightly growing again. A cycle that must happen in some regions of cloud. And here is what we saw:




Corner pockets!


After the sublimating, the subsequent growth kept a permanent record of the sublimation cycle in the form of 12 corner pockets, one pocket for each of the 12 corners of the crystal. These are pockets of air, just like the six large 'petal-shaped' pockets of air you see nearer the center of the crystal. They are forever stuck in the crystal. Stuck there until the crystal, with all of its features, vanishes back to air.




After seeing this, we ran a few more experiments, and each time we slowly grew, then sublimated, then grew again, we got corner pockets. The name 'corner pockets' refers to their location when they are formed; namely at the corners, next to the crystal perimeter. However, they remain essentially fixed in position as the crystal grows, and this means that as the crystal perimeter expands outward, the corner pockets will appear further within the crystal. Analogously, the 'center pockets' shown above formed at the face centers, on the crystal perimeter, back when the crystal was much smaller.



As to the theory of their formation, and how the theory can explain other observable features of snow crystals, you'll have to wait for a subsequent post.



- Jon

A Change in Habit

November 23rd, 2014

The two main growth modes of snow and hoar (i.e., ice growth from the vapor) are columnar and tabular. In columnar, the shape is long and thin, like a pencil or cluster of pencils (bound snugly with a rubber band). In tabular, the shape is plate-like or fan-like. When a crystal form has an easily expressed shape, like a column or plate, we say it has a certain habit.

In hoar frost that had been growing for several nights, I saw some that had changed their habit.

On the first night, when the vapor was more plentiful, large columnar forms appeared. This habit grows between -3 and -8 C. On a subsequent night, the temperature got colder, below -8 C, leading to tabular growth. More vapor exists out near the ends, so this is where we see the tabular habit.

The arrows above show the fast growth directions. There is a transition that sometimes happens when both of the main growth directions are fast, making a flare, or trumpet-horn shape (other times, it may be more of a cup or vase). Such a transition is far more common in hoar than in snow, because, I believe, hoar on the ground can experience a much higher excess of vapor.

The dark region in the background is the water of a creek.


New habit diagram for branched tabular crystals

August 24th, 2014

You might call these “snowflakes”. But let's be specific here with the names.

Anyway, a close associate who has been sweating over his snow-crystal growth machine in Japan for many years has just published his latest results. His machine is a vertical supercooled-cloud wind tunnel, which is like a thin column of cloud in which one can observe a single floating crystal. The crystal is in a climate-controlled box containing a droplet-infused stream of uprising air.

For this study, he focused on the crystal habit (i.e., shape) in the temperature range that we tend to get the large six-pointed stars. In addition to varying the temperature, he varied the density of droplets in the air. Nobody had done this before, certainly not as carefully and complete as he. Though he found lots of interesting results, I'll focus here on the following diagram:

Given its similar layout to the well-known Nakaya habit diagram, let's call this the Takahashi habit diagram. Whereas Ukichiro Nakaya showed us the crystal shape as he varied the temperature and humidity, Prof. Tsuneya Takahashi varied the temperature and droplet density (“LWC” on the vertical axis stands for liquid water content).

The basic findings: As the temperature decreases from left to right in the diagram, the crystal form goes from the very wide-branched sector crystal (see the “sectors”?) to the longer branches of the broad-branch crystal, to the even longer and narrower branches of the stellar crystal, to the crystal with sidebranches on each branch, called a “dendrite”, and then the pattern reverses back to sectors.

In the middle of this temperature range, something else happens. If he increased the density of cloud droplets in the dendrite regime, he got the more finely sidebranched fern forms. Ferns differ from dendrites only in the number of sidebranches they have. Fern crystals look more like fern plants because they have more offshoots. But at other temperatures, adding more droplets did not change the crystal form. In fact, the crystal size did not increase with more droplets, although the mass did increase.

If you observe some crystal that looks similar to one on the Takahashi diagram, you may infer that it grew under the indicated conditions. But this is not yet the final story: for instance, the amount of sidebranching is also thought to depend upon the temperature and humidity fluctuations. More fun ahead!

- JN

The new ice-crystal-growth apparatus

July 1st, 2014

After a few years in the making, our new device for growing single ice crystals in a well-controlled laboratory environment is nearly ready. We are just adding a few small accessory pieces to allow us to start testing. I was to describe the apparatus at the cloud-physics conference this month in Boston, and made a poster to present, but decided to opt out. But, having spent a few days making the poster, I present it below.

As with all images here, click on image to see large-scale view.

And below is the same, but in blog format.

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Halo in the sky? Uh, I don't see no halo...

April 20th, 2014

After a few days of fine bright spring weather, the barometer falls and a south wind begins to blow. High clouds, fragile and feathery, rise out of the west, the sky gradually becomes milky white, made opalescent by veils of cirro-stratus. The sun seems to shine through ground glass, its outline no longer sharp, but merging into its surroundings. There is a peculiar, uncertain light over the landscape; I 'feel' that there must be a halo round the sun!
And as a rule, I am right.

The quote, from Minneart* describes a common ice-related atmospheric apparition. It appears in skies all over the world far more often than the rainbow, yet few notice it. As a graduate student, I read about halos and often looked for one, but didn't notice it myself until someone else pointed it out. As a post-doc in Boulder, I was out walking with Charles Knight, and I mentioned my lack of success. He glanced up near the sun, pointed, and said “why there's one right now”.

What I had missed in my readings had been the fact that most halos are rather indistinct and often incomplete circles. Indeed, now when I point out the most common one (the 22-degree halo) to someone nearby, they often don't see it. But occasionally, it is sharp enough (and colored) to the extent that anyone will see it if they bother to look up and glance toward the sun. And often it occurs with other ice-crystal apparitions that are even more obvious.

Last fall, while perched high on a rock face, belaying my partner up**, I saw such a vivid display.

The bright spot is called a “sun dog”, “mock sun”, or “parhelia”. They, one on either side of the sun, usually appear together with the 22 degree halo. Indeed, the sun dogs very nearly mark the spots where that halo intersects another arc called the parahelic circle. Their cause: horizontally oriented, tabular ice crystals.

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The fun of shooting down your own theories

April 10th, 2014

Thomas H. Huxley once wrote the famous line:

The great tragedy of Science: the slaying of a beautiful hypothesis by an ugly fact.

Great man, catchy phrase, but perhaps a bit overdramatic. To me, the slaying of a “hypothesis” (i.e., pet theory or just idea, really) can be the beautiful thing. It means that one can do a lot of damage with just a simple observation. I like it, even when I'm shooting down my own theory. Here's an example:

Some time ago in my experiments, I saw the following ice growth sequence:
The fun of shooting down your own theories

What you see there is an extremely small, thin ice crystal growing from the tip of a glass capillary into air. (Size-wise, the glass capillary is about 5 micro-meters in diameter, or about 1/10th the thickness of the hair on your head.) I saw it happen several times. As the crystal grew, it developed the prism facets that generally define the hexagonal crystal shape. Other people had seen such rounded growth before, generally within a few degrees of zero (C), though in all cases, the crystal had been extremely thin. You can also see this thin, rounded (non-facetted) form in some hoar-frost formations.

The mystery here is why the disk grows without the prism facets for awhile. I never saw this with thicker crystals, so I formed a little theory. The theory involves the source of the water molecules to the curved region of crystal: some come from the vapor in the air and some wander over from the flat, non-growing crystal faces on front and back. In the 1960s, people had tried to measure this “wandering distance”, but never determined a consistent value. My theory predicted that once the crystal thickness exceeded about twice this distance, the curved edge would transition to flat, giving rise to the hexagon.

But then I looked closely at this case:
The fun of shooting down your own theories

That sequence shows the side and front view. The crystal doesn't discernibly thicken when the flat prism facets appear. Zing! That theory shot down.

On to the next pet theory. So maybe the key factor is the diameter of the disk: One might argue that the curvature of the crystal surface must be below a certain value, which means a large enough diameter is needed, for the flat facets to appear. Or, the size of the resulting prism faces must be larger than that needed to have several surface steps (which help ensure flatness).

But then I look at this case:
The fun of shooting down your own theories

In that case, I see both smaller and larger prism faces forming at the same time (same thing can be seen in the previous image). So, I guess the curvature or size of the resulting face is not the main factor. Zing!

Some researchers had observed slight bending of the prism facet above -2.0 C in equilibrium. They postulated a “roughening temperature” at -2.0 C. This might explain the rounded disc edge, but wait! 1) This disc edge becomes facet as it grows, so it is not merely temperature, and 2) these crystals are below -2.0 C.
Zing again!

Well, there are always “impurities” to blame! Crystal growers are fond of blaming some trace, active chemical, or “impurity” for inexplicable results, so we could theorize that the above show the effect of surface impurities. As the crystal grows, the area over which the impurities distribute increases, thus diluting their concentration, and thus reducing their effect. Yes! This could explain these results.

But, wait, what about this:
The fun of shooting down your own theories

The above shows two sequences (same capillary) in which some prism facets have formed, but some remain round. In the right-side case, one corner even rounds as it grows. Hmm, not a likely result of impurities. Zing!

So, I am down to one last theory. I do not yet have the data to shoot it down. And I'm not telling you, or I'd ruin the fun. We just need more data.

All in all, I think Huxley needs a little tweaking to serve my view:

The great beauty of science: the slaying of a pet idea by a simple observation.


The cup and the butterfly

February 25th, 2014

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.

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