The beauty, symmetry and diversity of snow crystals have long fascinated scientists. Snow crystals come in endless variety of six-fold symmetric shapes, sometimes thinner than a sheet of paper and up to 3 millimeters across. How can they grow in a three dimensional bath and yet be thin? What natural processes could lead to great diversity of shapes that are complex yet symmetric? What keeps opposite sides of the growing crystal in step even as a unique shape is forming? And with slightly different temperature or humidity produces sensible hexagonal columns instead? Is there any rational explanation for the generation of these crystals out of thin air? Can you formulate a hypothesis that even has a chance? The Japanese scientist Ukichiro Nakaya, working in the nineteen thirties through nineteen fifties was the first one to develop methods to grow individual snow crystals under carefully controlled conditions. (2) Nakaya had intended to be a nuclear physicist, but he got a professorship on the Japanese island of Hokkaido where there no nuclear facilities. There was, however, lots of snow. Nakaya's 1954 book, Snow Crystals, Natural and Artificial, "...offers a superb look at a scientific investigation which begins with almost nothing, and proceeds through systematic observation toward an accurate description of a fascinating natural phenomenon." (2) Most of his experimental discoveries are summarized in what is now called the snow crystal morphology diagram.After this storm cloud, there came another, which produced only little roses or wheels with six rounded semicircular teeth ... which were quite transparent and quite flat ... and formed as perfectly and symmetrically as one could possibly imagine. There followed, after this, a further quantity of such wheels joined two by two by an axle, or rather, since at the beginning these axles were quite thick, one could as well have described them as little crystal columns, decorated at each end with a six-petalled rose a little larger than their base. But after that there fell more delicate ones, and often the roses or stars at their ends were unequal. But then there fell shorter and progressively shorter ones until finally these stars completely joined, and fell as joined stars with twelve points or rays, rather long and perfectly symmetrical, in some all equal, in others alternately unequal. (1)
The morphology diagram does not show all possible types of snow crystals. It shows only shapes that grow under fixed conditions. But knowing both the morphology diagram and that natural snow forms in turbulent storm winds gives us a big boost toward understanding how such diverse yet symmetric shapes are formed. Each crystal follows its own essentially random path through the sky and hence through conditions that will stimulate different sorts of growth, and so gains a different form. Conditions do not vary significantly over the size of a crystal though. So each crystal takes on a different symmetric form.
Nakaya's work beautifully lays out the snow crystal puzzle. Now all we have to do is solve it. In very broad terms snow crystals happen the way other things happen in nature, especially things with complex symmetry. 
They result from a combination of natural regularities, surprising threshold effects, and a sequence of frozen accidents. But what are the regularities and nonlinearites? How does it happen, for instance, that at a supersaturation of around .1 g per cubic meter, crystals are (with decreasing temperature) hexagonal plates, then columns, then plates, then columns again? How can the morphology diagram be explained?
This is what physicist Ken Libbrecht is trying to find out. While Christmas shopping last month I couldn't help noticing the beautiful snow crystal on the cover of the new American Scientist. This led me to Libbrecht's article The Formation of Snow Crystals (3). The article was quite intriguing, but there was a key point I couldn't follow. On page 57 he seems to say that his experimental measurements of the growth velocity of different facets were contrary to what the morphology diagram predicts, yet the diagram is still correct. How could this be? This led me to read his The Physics of Snow Crystals (4), a mere forty pages with one or two equations, and then another paper with actual data (5). Finally I gained some idea of what's going on.
But to begin at the beginning: warm moist air rises and rises until it expands and cools. Cold air can hold less water vapor than warm air, and so, especially if the air becomes very cold, it will become supersaturated with water vapor. Air is full of vast numbers of tiny dust particles; very tiny water droplets form on these particles. Even well below the normal freezing point, these droplets do not freeze into ice, but instead most persist as supercooled water. Different ones freeze at different temperatures, due in part to the surface characteristics of their dust particle. Those that freeze may grow into snow.
The minute supercooled liquid droplets have so much surface area in relation to their volume that they are constantly evaporating and reforming. Once a vapor molecule sticks to an ice crystal, though, it tends to stay there. Thus the crystals grow at the expense of the droplets. The droplets are so small that a good sized snow crystal may have consumed a million of them (3:52). To a first approximation, crystal growth is diffusion limited A growing crystal uses up nearby vapor molecules and cannot grow larger until more vapor diffuses to it.
Early in its growth nearly every snow crystal experiences faceting. This is a normal feature of crystal growth in which rough spots smooth out and the crystal takes on a characteristic shape with several plane faces, or facets. For ice crystals in normal winter conditions, this shape is a hexagonal prism.
Growth of the crystal facets. Once a crystal takes on this basic shape, growth tends to be normal to the facets, at least as long as growth is not too fast and the crystal is not too large, say less than half a millimeter across. Growth is controlled by attachment kinetics, which is in turn controlled by the still mysterious surface physics of the growing snow crystal.
Modern equipment makes possible measurements Nakaya couldn't make, including the growth rate of individual facets. This measurement is important because of its quantitative relation to other factors. But it isn't easy: "... a critical examination of the literature reveals that essentially all the results published to date suffered from systematic errors to some degree." (4:878) On the basis of recent measurements though, Libbrecht suspects that growing snow exhibits a previously unknown type of instability - which brings me back to the unexpected data I mentioned earlier.
Low pressure is the key - to normal crystal growth. When grown at -15 degrees Centigrade and high supersaturation, right where the morphology diagram predicts the thinnest crystals, but at less than one quarter of normal atmospheric pressure, all the facets grow at about the same very slow rate and the crystals look blocky and ordinary. But merely increase the pressure and the prism facets (but not the basal facets) start growing up to 50 times faster! How can ordinary air have this effect? Libbrecht gives a very partial explanation in (5): a thin but growing facet is expected to have a parabolically curved edge, with a small radius of curvature. The radius is inversely proportional to pressure according to a certain formula that can be derived with some simplifying assumptions. Compared to a flat crystal surface, this curved surface will be rough on a molecular scale. This makes it easier for some ice molecules to form hydrogen bonds with passing vapor molecules and hold on to them. Evidently, when there is enough pressure, and hence enough curvature, growth becomes much faster. Libbrecht refers to this as a knife edge instability resulting from structure-dependent attachment kinetics.
As Libbrecht says, "This is a speculative model, without a strong theoretical foundation, so additional work is needed to understand this aspect of the growth dynamics." (4:881) But as he explains, the knife edge instability is consistent with both the crystal growth data at different pressures and notable features of natural snow. These features include the extreme thinness of large stellar crystals (about .01 millimeter) and the abrupt transition observed in capped columns (see the first illustration). "... instabilities tend to amplify small changes in initial conditions. If the local environment changes just slightly to prefer platelike growth over columnar growth, then the instability kicks in to immediately produce thin plates." (3:58)
Branching and dendritic growth. Growing perpendicular to the facets is not the only way snow grows. Snow crystals are famous for their complex branched and dendritic forms. This type of growth too has been modeled and studied experimentally. As each crystal facet expands, its center is slightly starved of vapor molecules compared to its corners. This makes the facet just slightly convex although it looks flat to the eye. The convexity, greatest at the center, amounts to roughness on the molecular scale - the scale where the action is. This roughness leads to a little greater percentage of incident vapor molecules sticking to the crystal, and so the center's growth keeps up with the corners - until it doesn't. When the crystal is large enough, say about half a millimeter across, and/or growth is fast enough, branches spout from the six corners of the hexagon. This is called the Mullins - Sekera instability, or simply the branching instability.
The corner branches may become long dendrites; these may sprout dendrites of their own, or in other conditions may even sprout six new flat plates. A dendrite's rate of elongation, and hence rate of vapor consumption, may become so great that the growing tip is in a region of reduced vapor density. Nonetheless the highly curved, and hence molecularly rough, tip keeps on growing. Dendritic growth is observed in other sorts of crystals and is thought to be fairly well understood. Snow crystal branches and dendrites are unusual, though, in that they retain their basal non-growing facets. Faceted dendrites are not so well understood. (4)
Has the challenge of the morphology diagram been met? There is reason for optimism about future research. The identification of systematic errors in previous experimental data should result in more precise data in the future, and the structure-dependent attachment kinetics hypothesis is a promising lead. But for now, the explanation (above) of capped columns, for instance, includes these words: "If the local environment changes just slightly to prefer platelike growth over columnar growth ...." But why would a slight change in conditions have this effect? That was the question. In the end Libbrecht admits
Mystery is still in the air. ============================================================= Acknowledgment All the illustrations except the pine lily are courtesy of Ken Libbrecht with permission. ============================================================= Activities and additional reading Get to Ken Libbrecht's www.snowcrystals.com to find lots of activities, movies and books on snow crystals. There is no snow in my neighborhood, but I'm interested in hearing your experiences. Can anyone match Descartes' observations, even with the help of a hand magnifier? Meteorological background: Snow Formation in the Atmosphere Snow Flakes and cellular automata ============================================================= References 1. René Descartes 1637. Les Météores (a series of essays attached to his Discours de la Methode), as cited in The Snowflake: Winter's Secret Beauty -- by Kenneth Libbrecht and Patricia Rasmussen. 2. www.snowcrystals.com 3. Libbrecht KG 2006. The Formation of Snow Crystals. American Scientist (95:1, 52-59). online 4. Libbrecht KG 2005. The physics of snow crystals. Reports on Progress in Physics 68 (2005) 855--895. online 5. Libbrecht KG 2003. Explaining the Formation of Thin Ice-Crystal Plates with Structure-Dependent Attachment Kinetics. J. Cryst. Growth 258, 168-175. onlineThe growth of plain hexagonal ice prisms remains perhaps the most puzzling aspect of snow crystal growth, in spite of its apparent simplicity. The snow crystal morphology diagram, well documented now for 75 years, has still not been explained at even a qualitative level. (4:891)
35 Comments
Mike Elzinga · 15 January 2007
When I was at the University of Michigan back in the late 1970s and early 1980s, Len Sander (http://www.lsa.umich.edu/physics/peopleprofile/0,2708,,00.html?ID=283) was modeling this kind of thing on the computer and producing some remarkable results. He is still at it and has extended his research to biological systems as well.
Corbs · 15 January 2007
Get ready for the Goddidit.
Henry J · 15 January 2007
If the people studying this need more snow samples for their studies, they can take all they want from the area where I live! ;)
Henry
JimV · 15 January 2007
Stephen Wolfram's "A New Kind of Science" discusses snow flake formation and presents a cellular automata model which simulates snow flake generation.
("http://www.wolframscience.com/nksonline/page-370-text")
Reed A. Cartwright · 16 January 2007
Very cool, thanks Dunk.
So did you go to the penguin exhibit at Seaworld to do your research?
Pete Dunkelberg · 16 January 2007
No, I captured the wild Pine Lily at Tosohatchee. ;)
JeffInRR · 17 January 2007
My design detectors are off the charts. This just couldn't have occurred naturally.
Torbjörn Larsson · 18 January 2007
Nice article, and it was cool to finally see some snow this year.
anna · 8 November 2007
it is amazing how snow looks allways the same, but it is allways diverse.human eye is so limmited of seing and axploring the real beautiful shapes, and going underneath of what sth. looks like.
Ric gems & minerals co · 17 June 2008
We are minner of Holy Himalayan crystals, all quartz family stones, quartz lumps (35 kg of single piece is available) and blood stone (clear red color)
Amanda N · 18 December 2008
After you see the beauty and wonder of all this, how can you not be thankful to God for this amazing and devout scientific world.
Dave Luckett · 18 December 2008
Corbs called it in #2.
Stanton · 18 December 2008
Ed · 20 November 2009
With all of the mixed up "religion" out there, I can understand your aversion to it.
You are in good company, by the way, God reserved His greatest condemnation for "religious" people who lead people away from the Truth with their own man-made views.
If you look at the scientific data with an open mind, however, I do believe it leads you to the undeniable conclusion that there is an all-powerful and infinitely wise Creator behind it all - not an explosion.
19 ¶ Because that which may be known of God is manifest in them; for God hath shown it unto them.
20 For the invisible things of Him from the creation of the world are clearly seen, being understood by the things that are made, even his Eternal power and Godhead; so that they are without excuse. Romans 1:19-20
I understand how this sounds to you, because, when you are taught that something is true (evolution) all your life, you tend to believe it - even if truly, the evidence is missing. I have always been very interested in science and have gathered a lot of information on this topic on the link
"Evolution or Creation, What are The Scientists Saying?" which can be reached from the page www.Godhastheanswer.com.
Please just give it a look with an open mind - I look forward to hearing your feedback.
-Ed
Dave Luckett · 20 November 2009
Here's some feedback for you, Ed. I'll confine myself to the document you mention.
In the first sentence under the head A I count three obvious errors, demonstrating that you have no knowledge of physics. In the last sentence of the that paragraph I count four more, demonstrating that you have no knowledge of biology.
What you think you are doing, writing about either subject, I cannot imagine.
Your quote mines are the usual nonsense. Most of them only go to prove that the scientists quoted were not in the least hostile to religious belief, and hence actually undermine your own position. But some are outrageous. For example, the first Darwin quote only demonstrates his own humility, and to use it to attempt to insinuate that he doubted his own theory is a subtle and contemptible lie. The second states his willingness to defend his theory in the full, hard light of the facts, a process which it has been undergoing for a hundred and fifty years, and triumphing. The Whitten quote is a quote mine, and misrepresents him. Whitten wrote later: "saying anything that would support creationism could not have been further from my mind. Of course, my whole working life have been around a Darwinian framework."
Other lies: the number of scientists who doubt evolutionary theory is not growing, and almost all of the tiny proportion of those that do doubt it work in fields irrelevant to biology. The ID crowd are not scientists (they don't do any science).
Evolution does not predict increasing complexity in populations, only change by natural selection, which may favour less. It does not predict "defective forms" in the fossil record - that's Gish being ignorant and mendacious, as Gish is. There are, however, very large numbers of fossils showing forms transitional between groups. You say rightly that creationism would not predict this. Why do you ignore the ones that exist, then?
The quote mines that purport to lament the lack of "intermediate forms" in the fossil record are straightforward misrepresentations of the statements of scientists who cite these concerns and then go on to refute or explain them, and they date from the seventies or earlier. Much more has been found since then.
Setting the Bible quotes aside, the rest consists of the arguments from complexity and ignorance. These were long, long ago shown to be the foolish nonsense that they are.
Some howlers: you have managed to discuss the transition from fish to tetrapods without even a nod at the half-dozen transitional forms now known, by quoting a textbook written in 1974! This may be no more than an exhibition of shameful ignorance, but its effect is to promulgate an untruth. Your remarks about human evolution are worse, if anything. To say that no transitional forms exist in the face of Australopithecus afarensis, A. africanus, Homo habilis and H erectus requires more than ignorance. It requires a total refusal to look facts in the face, or wilful mendacity, or both.
And of course, the real killer is the utter refusal to show evidence for special creation. All of your arguments against evolution are unsound, faulty, based on lies, misinformation or misunderstanding, but even setting that aside, you show no evidence from nature for the separate creation of the species, and a total inability to grasp that some is required.
In short, your document is sheer nonsense from beginning to end. Do a little reading outside creationist tracts. Try to learn a little. It'll do you good.
Dave Luckett · 20 November 2009
Oh, and one more thing, though I will admit that this is only a personal tic: learn the difference between the possessive pronoun "its" and the contraction of the present infinitive "it's".
Rilke's Granddaughter · 21 November 2009
Wow, Ed, that site was truly a sad collection of misinformation, lies, and illogic. You're new to this, are you?
ben · 21 November 2009
Dan · 21 November 2009
ben · 21 November 2009
Anton · 23 December 2009
Man these religious folks have the answer to everything. Sure, every little snowflake is carefully designed by God himself, while He was taking a break from exploding galaxies 10 billion light years from here. (This we will find out in ten billion years, because not all astronomers were burnt.) The very fact that He has time for carefully designing each and every little snow flake proves His Existence. After all no monkey or decendant thereof could do this. QED!
david hewitt · 23 January 2010
david hewitt · 23 January 2010
a correction to my above statement, has to do with the word unbelief.don't direct the word unbelief (anti-Christ)but direct, belief, in the Lord Jesus Christ. i would suggest to anyone that does not believe, to ask himself,or herself this question. Have I read,(studied) the book,Bible, namely the new testament as a result of my unbelief? The answer most likely, is no, I haven't. I suggest that you at least study it before passing judgment to your own peril. the moment anyone directs his or her belief in the Lord Jesus Christ, a most amazing and wonderful transition takes place.Try it,(Him,you'll like it,(Him).
DS · 23 January 2010
DS · 23 January 2010
Stanton · 23 January 2010
So, in other words,
A) There is a big difference between discarding a scientific theory because of new, contradictory evidence, and discarding a scientific theory because of the alleged possibility of new, contradictory evidence
and
B) There are literal millions of examples of people who have no problem accepting Jesus and accepting the fact of evolution.
ben · 23 January 2010
Mike Elzinga · 23 January 2010
Stuart Weinstein · 23 January 2010
stevaroni · 23 January 2010
Dave Luckett · 23 January 2010
Ed · 21 June 2010
I think God has allowed the universe to have an independent nature, somehow between light and darkness, good and evil, with both having an influence, and evil is a result of allowing independence from good within the created universe. If you could not choose to do nasty stuff, you could not choose to really love someone either. Part of you living in a universe where everything is not controlled directly by God, means choice, independence from God, and evil have an outcome and impact, all be it temporarily.
Dave Luckett · 21 June 2010
So how do you account for, say, muscular dystrophy, Ed? Doesn't allow the sufferer a whole lot of independence, and here's the thing: the most severe forms occur in early childhood, and the worst affected die in early adolescence, after years of severe and progressive disability and pain.
If that's God's doing, He's got some explaining to do, for mine. Even if it's not, and it's only that He won't or can't stop it, the same applies. If he won't, he's a monster. If he can't, some God that is.
Ed · 15 August 2010
Dave Luckett · 15 August 2010
Fair enough. I don't think the problem of theodicy - which is what I was referring to - actually has an answer. I'll be interested to read your take on it.