Physics of Snow
Length: 2464 words (7 double-spaced pages)
The hexagonal prism includes two hexagonal "basal" faces and six rectangular "prism" faces. Note that the hexagonal prism can be "plate-like" or "column-like", if the length along the c-axis is short or long compared to the length along the a-axes.
What kinds of snow crystals fall from the sky?
Before answering this, it is useful to define what a snow crystal is. Types of frozen precipitation include:
Snow crystals -- Individual, single ice crystals, often with six-fold symmetrical shapes. These grow directly from condensing water vapor in the air, usually around a nucleus of dust or some other foreign material. Typical sizes range from microscopic to at most a few millimeters in diameter.
Snowflakes -- Collections of snow crystals, loosely bound together into a puff-ball. These can grow to large sizes, up to about 10 cm across in some cases, when the snow is especially wet and sticky.
Rime -- Supercooled tiny water droplets (typically in a fog), that quickly freeze onto whatever they hit. For example, one often sees small droplets of rime on large snow crystals.
Graupel -- Loose collections of frozen water droplets, sometimes called "soft hail."
Hail -- Large, solid chunks of ice.
A simple observation on a snowy day, with a low-power microscope or hand magnifying lens, quickly reveals a great variety of snow crystal shapes. Some different types include basic plate-like forms.
1) Simple sectored plate; 2) Dendritic sectored plate; 3) Fern-like stellar dendrite
and basic column-like forms:
1) Hollow column, or sheath-like crystal; 2) Needle crystal
More crystal types can be listed, as are described under Classification schemes. These other forms are mostly variations and combinations of the above basic types, such as plates with dendritic extensions, capped columns, etc.
Under what conditions do the different types of snow crystals form?
By growing snow crystals in the laboratory under controlled conditions, one finds that snow crystals grow in different forms depending mainly on the temperature and supersaturation level during growth. This is shown in a "morphology diagram," which gives the crystal shape under different conditions.
At very low supersaturation levels, say less than a few percent relative to ice, crystals grow mostly as simple hexagonal prisms. The aspect ratio (ratio of sizes along the a-axis and c-axis) varies somewhat with temperature at low supersaturation, changing from plates (-2 C) to columns (-5 C) to plates (-15 C) and back to columns again (-30 C).
At higher supersaturation levels the aspect ratios move to more extreme values, and are strongly temperature dependent. Thus we see long needle-like crystals (a/c <<1) at -5 C, and very flat plate-like crystals (a/c >>1) at -15 C. At still higher supersaturations the crystals become more structured; for example at -15 C one sees sectored plates at intermediate supersaturation levels, and fern-like dendrites at high supersaturations.
In the sky the supersaturation level is usually at or below the saturation level of water (the marked line in the morphology diagram); in a cloud the supersaturation level is fixed near that of water, since the cloud contains a great many small supercooled water droplets. From the morphology diagram we might thus expect never to see stellar dendrites in natural snowfall, in contrast to reality. The solution to this paradox is that snow crystals in the atmosphere are blowing around, and their motion raises the effective supersaturation level, to the point where dendrites can form.
Why do snow crystals grow differently at different temperatures?
The reason we see the above morphology diagram stems from the way ice crystals grow. For example, at -15 C the basal surfaces of a snow crystal grow very slowly, while the prism surfaces grow very rapidly, producing plates. At -5 C the prism surfaces grow more slowly than the basal surfaces, producing columns. The physics behind this depends on the (temperature dependent) surface structure of ice, and how vapor molecules are incorporated onto the growing surfaces. This physics is complex and not well understood, and is the subject of considerable current research in our own lab and elsewhere.
There are a few different schemes for classifying natural snow crystals and other types of frozen precipitation. The classifications all distinguish between the basic plate-like and columnar crystal morphologies, but differ in the number of categories and other details. The categories are all arbitrary to some degree, but are useful for defining a common language with which to describe snow crystal observations. The classification schemes also provide a convenient "field guide" when observing natural snowfalls.
International Commission on Snow and Ice
A fairly simple and widely used classification for solid precipitation is that proposed in 1951 by the International Commission on Snow and Ice. This scheme defines the seven principal snow crystal types as plates, stellar crystals, columns, needles, spatial dendrites, capped columns, and irregular forms. To these are added three additional types of frozen precipitation: graupel, ice pellets, and hail.
Nakaya identified seven major groupings of snow crystals, which subdivide further into 41 individual morphological types.
Magono and Lee
The most complex classification scheme is an extension of Nakaya's table, published by Magono and Lee in 1966. A few of the 80 separate morphological types are shown at the left, and the full version can be seen by clicking on the image. An inspection of all the entries in this table gives one a good feel for the full range of snow crystal precipitation.
Preserving Snow Crystals
It is possible to preserve newly fallen snow crystals, creating one's own snow crystal fossils. These preserved replicas can then be examined by microscope any time, in a comfortable indoor climate, thus obviating the need for doing photomicroscopy in sub-freezing conditions.
Formvar Replicas. A popular snow crystal preservation technique is described by Schaefer and Day for making permanent plastic replicas of crystals. One gram of Formvar (polyvinyl acetal resin) is dissolved in 100 milliliters of ethylene dichloride to make about a 1 percent solution of the plastic. A glass slide is wetted with this liquid after both the slide and solution have been cooled below 0 C. The wet slide is then held in the falling snow. After a sufficient number of crystals have fallen on the slide, it is place in a protected (cold) area until the solvent has evaporated, which takes about five minutes. (The Formvar solution has the interesting property of creeping up over a snow crystal that may rise considerably higher than the depth of the liquid on the slide.) Once the slide is dry, it may be warmed; the water then passes through the plastic shell, leaving behind a replica of the surface features of the original snow crystal. It is sometimes best to let the ice slowly evaporate at cold temperatures; melting can produce enough surface tension to alter some of the delicate features in a crystal. The image at right is from Schaefer and Day.
According to Mason, best results are obtained when the Formvar solution is dehydrated by shaking it up with calcium chloride or phosphorus pentoxide to remove the dissolved water, which otherwise will come out when the solution is chilled and form spurious ice crystals. Also, it is particularly important to use a solution of the right strength. If it is too viscous, small crystals will not become submerged and merely make a crater on the surface; if it is too thin, the solution will run off the slide and not cover a large crystal. Good replicas of natural snow crystals may be obtained with a 1-3 percent solution, but for small crystals less than 0.1 mm in diameter, such as may be produced in laboratory experiments, a 0.1 percent solution can be used.
A slightly different procedure is to catch snow crystals on a piece of black velvet, which can be examined to find particularly interesting specimens. To preserve a particular crystal, one then places a drop of the cold Formvar solution on a cold glass slide with a toothpick, and uses the still-wet stick to gently pick up the chosen crystal. The crystal should adhere to the tip of the stick, and can be placed in the center of the drop. This way one can select and preserve several crystals on a single slide.
Acrylic Replicas. Another effective method uses clear acrylic spray paint, which is readily available in hardware stores. The spray is especially effective for replicating windowpane frost and similar ice structures. The (cold) spray must be applied lightly, since the solvent in the spray can dissolve the ice if too much liquid is present. The best procedure is to precoat the glass slide with the plastic film, place snow crystals on it, and then spray the surface again until the surface is moist. The image at right is from Tape, and was obtained by spraying over a crystal that was placed on a glass slide.
Temperature, humidity shape snow crystals.
As snow crystals form they take on a six-sided, or hexagonal shape, but with what seems like an infinite number of variations of being six sided. The temperature at which a crystal forms, and to less extent the humidity of the air, determine the basic shape. The many things that happen to snow crystals as they fall, such as collisions, partial melting and colliding with water drops that freeze to them, create even more shapes. This is why irregular crystals with no easily identifiable form are the most common. Some times crystals are a combination of more than one form. For example, hollow columns that form in air colder than -8 Fahrenheit could grow thin plates on one or both ends as they fall through warmer air. While most people refer to shapes like those in the graphic above as snowflakes, flakes are really made of many snow crystals that have stuck together.
Snow crystals form hexagonal shapes because of the way the two hydrogen atoms that join with an oxygen atom to form a water molecule attach to the hydrogen atoms of other water molecules.
Early Snow Crystal Observations
1611 -- Johannes Kepler
In 1611 Johannes Kepler published a short treatise On the Six-Cornered Snowflake, which is perhaps the first scientific reference to snow crystals. In his treatise Kepler ponders the question of why snow crystals always exhibit a six-fold symmetry. Although he doesn't refer to the atomistic viewpoint, Kepler does speculate that the hexagonal close-packing of spheres may have something to do with the morphology of snow crystals. Kepler was astute in recognizing that the genesis of crystalline symmetry was an interesting scientific question, and he also realized that he did not have the means to answer it. It would be 300 years before Kepler's question could finally be answered, requiring the development of X-ray crystallography.
"Each single plant has a single animating principle of its own, since each instance of a plant exists separately, and there is no cause to wonder that each should be equipped with its own peculiar shape. But to imagine an individual soul for each and any starlet of snow is utterly absurd, and therefore the shapes of snowflakes are by no means to be deduced from the operation of soul in the same way as with plants." -- Kepler, 1611.
1635 -- Ren Descartes
Philosopher and mathematician Ren Descartes was the first to pen a reasonably accurate description of snow crystal morphologies, about as well as can be done with the naked eye. These careful notes included observations of capped columns and 12-sided snowflakes, both rather rare forms.
"These were little plates of ice, very flat, very polished, very transparent, about the thickness of a sheet of rather thick paper...but so perfectly formed in hexagons, and of which the six sides were so straight, and the six angles so equal, that it is impossible for men to make anything so exact."
"I only had difficulty to imagine what could have formed and made so exactly symmetrical these six teeth around each grain in the midst of free air and during the agitation of a very strong wind, until I finally considered that this wind had easily been able to carry some of these grains to the bottom or to the top of some cloud, and hold them there, because they were rather small; and that there they were obliged to arrange themselves in such a way that each was surrounded by six others in the same plane, following the ordinary order of nature." -- Descartes, 1635.
1665 -- Robert Hooke
In 1665 Robert Hooke published a large volume entitled Micrographia, containing sketches of practically everything Hooke could view with the latest invention of the day, the microscope. Included in this volume are many snow crystal drawings, which for the first time revealed the complexity and intricate symmetry of snow crystal structure. (Note that an excellent, yet inexpensive, digital version of Micrographia can be purchased from Octavo.)
1931 -- Wilson A. Bentley
Wilson Bentley (1865-1931) was an American farmer and snow crystal photomicrographer, who during his lifetime captured some 5000 snow crystal images. More than 2000 were published in 1931 in his famous book, Snow Crystals, which remains in print to this day. Some images from Bentley's collection can be seen at our Photos Collections section, and at the W.A.Bentley web site.
1954 -- Ukichiro Nakaya
Ukichiro Nakaya was the first person to perform a true systematic study of snow crystals, which resulted in a giant leap in our understanding of how snow crystals form. Trained as a nuclear physicist, Nakaya was appointed to a professorship in Hokkaido, the North Island of Japan, in 1932, where there were no facilities for nuclear research. Undaunted, Nakaya turned his attention to snow crystals, which were locally very abundant. He then made a superb series of very detailed observations of all types of frozen precipitation, clearly identifying and cataloging all the major snow crystal types. Unlike Bentley, Nakaya photographed the great variety of snow crystals, not just those exhibiting great symmetry and esthetic beauty.
Nakaya's real triumph, however, came from growing artificial snow crystals in the laboratory under controlled conditions. From the study of these artificial snow crystals Nakaya was able to describe the crystal morphology under different environmental conditions, which provides an extremely important clue for understanding the physics of snow crystal formation.
The bulk of Nakaya's work was published in 1954 in a beautiful book entitled Snow Crystals: Natural and Artificial. Though long out of print, Nakaya's book 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.