Science / Medicine : Designs...
Gathering moisture as it falls, a snowflake grows into much more than just an icy fragment. Its delicate branches record the remarkable history of a tumultuous journey through the air. Each feathery feature is a result of subtle variations in temperature and humidity.
Scientists, using new computer programs, are now beginning to decipher the message contained in a snowflake’s pattern and forming a theory of how snowflakes grow. They see an intense, exquisitely balanced competition between large- and small-scale forces in nature that influences a snowflake’s final form and explains why snowflakes come in such endless variety.
“Snowflakes are some of the most complex patterns that we know outside of biology,” says physicist Fereydoon Family of Emory University in Atlanta. Studies of the layers in snowflake patterns may lead to a deeper understanding of how storms develop in the atmosphere.
And because branched patterns are so common in nature, snowflake studies could shed light on phenomena such as why lightning follows a jagged path through space and why metals sometimes crystallize into tree-like forms.
Snowflakes, with their striking blend of symmetry and intricacy, have long attracted attention. More than 2,000 years ago, Chinese scholars recognized and noted the characteristic six-sided or six-branched form of snowflakes. In 1610, astronomer Johannes Kepler wrote a little book in which he speculated about why snowflakes always fall as six-pointed starlets.
Over the centuries, keen observers of nature couldn’t help noticing that despite similarities in overall shape, no two snowflakes ever appear to be identical in every detail. Early investigators, lacking the sophisticated tools and high level of mathematics needed to solve the mystery, had to be content with merely classifying snowflake patterns.
In the past decade, computers have shown their worth for testing theories about snowflake growth. Fereydoon Family and his colleagues were among the first to write computer programs that generate surprisingly realistic portraits of snowflakes on a computer screen.
At a National Academy of Sciences symposium last April in Washington, commemorating the centennial of the American Mathematical Society, Family explained the latest thinking about snowflake growth. This knowledge represents the efforts of mathematicians and physicists who, over the last few years, have tackled the snowflake riddle and, step by step, have developed the insights necessary to solve important parts of the puzzle.
“Snowflakes are formed in a purely mechanical way,” Family explains. The basic building blocks are water molecules. It takes many billions of billions of water molecules, each one settling into the right spot, to create even a tiny snowflake that is barely visible to the naked eye.
One secret of snowflake formation is revealed by contrasting it with the freezing of water in a pond or in a refrigerator ice tray. The water doesn’t normally freeze into a branched pattern. Ice first forms at the container’s walls, then gradually spreads smoothly toward the middle. The walls drain away excess heat--the energy that water molecules give up when they stop moving and settle into place.
Snowflakes, however, freeze and take shape in moist air, free from any walls. A typical snowflake begins as a dust particle or some other airborne impurity. That particle snares some of the water molecules that happen to be wandering about nearby. Gradually, as more molecules arrive, a microscopic layer of ice forms.
As it takes on water molecules, the snowflake must get rid of its excess heat to keep growing. That happens most efficiently when the snowflake has a wrinkled, rather than a smooth, surface. The roughness increases its surface area. The more it becomes like a pincushion rather than a ball, the more effectively a burgeoning snowflake can shed heat.
But if that were all there were to the growth of a snowflake, every snowflake would be an extremely wrinkled, feathery object. Growth would also be unstable--subject to the tiniest temperature shifts. A branch that happened to encounter a relatively cool region would shoot out faster than the others. Long branches would grow faster than short branches, and the result would look nothing like a real snowflake.
Such a pattern of unstable growth does, however, explain how tiny differences at the molecular level can be translated into a snowflake’s characteristic six-armed pattern. When water molecules form into ice crystals, they settle into a hexagonal arrangement--a kind of three-dimensional honeycomb. That structure provides a slight, built-in preference for growth in six directions. Once tips pointing in the six directions start to form, they grow faster than the rest of the crystal.
Surface tension--the force that holds a snowflake together--is the stabilizing factor. It acts like a plastic skin that restrains the faster-growing branches. “Surface tension pulls the object back so that a tip that is getting ahead of itself doesn’t move faster and faster,” Family says. “That gives time for the rest of the material to move with it.”
Given the tremendous variations among snowflakes, why do the six arms of a single snowflake look so much alike? Experimental studies show that a snowflake’s six arms, each only a tiny fraction of an inch in length, tend to experience the same temperature and humidity. Two neighboring but separately drifting snowflakes are far enough apart to encounter significant differences.
But the conditions surrounding even a single, tiny snowflake aren’t completely uniform. A close look at any real snowflake reveals that its six arms aren’t identical. There are always some imperfections.
Snowflake growth can be described mathematically using equations that account for how heat diffuses away from an object. Solving those equations allows physicists to predict what happens moment by moment.
Finding such solutions to the diffusion equations is relatively easy for a warm, metal ball or a smooth, heated pipe in air or water at a constant temperature. But it’s much more complicated for a snowflake, where each new water molecule changes the object’s shape and the local temperature. It would be like trying to play a tune on the piano if each note played changed all subsequent notes. You’d have no clear idea of where you were going until you arrived.
Now scientists can convert the difficult-to-solve equations govErning heat diffusion into a sequence of simple steps repeated over and over again on a computer.
Researchers first draw up a honeycomb grid as large as their computer can handle. Each space, or cell, is a potential home for one water molecule. At the center sits the ‘seed’--a small number of marked cells corresponding to the dust particle at the heart of a snowflake.
For each space around the seed, the computer calculates how quickly the temperature drops off. If the gradient is larger than a certain value, then a water molecule is allowed to occupy the space and the computer-generated snowflake grows by one unit. The same procedure is repeated over and over again, and the spaces gradually fill.
When Family tried this method, he found that the resulting shape depended strongly on how he selected the cutoff value determining whether or not a space is filled. Randomly changing the value at each step created rough, irregular forms that looked like soot particles. Keeping the value constant produced lacy shapes that looked much too regular to be snowflakes. However, choosing the value so that it varies smoothly in a certain way produces patterns that are very similar to real snowflakes.
Real snowflakes also have a layered structure, reflecting the varying conditions that influence their growth as they toss and swirl on their way to earth. A snowflake’s final coat often hides a range of different structures buried deep inside. Family can simulate this layered structure by regularly changing and manipulating the cutoff value.
“It corresponds to changes in growth conditions at different times,” Family says. “Sometimes the center looks nothing like what you find at the end. Essentially, we can generate
all types of snowflakes by changing the conditions from one layer of growth to another.”
From such studies, physicists may develop insights into the atmospheric conditions that a snowflake encounters on its turbulent journey to earth. Those, in turn, could lead to a deeper understanding of cloud formation, storm development and other atmospheric phenomena.
Branching growth occurs not only when water freezes, but also when metals and other materials solidify or crystallize. Such growth patterns affect a material’s strength and other properties. By learning what factors
control this type of growth, metallurgists would be better able to tailor materials for specific applications. “Most metallurgists,” Family says, “will tell you that it’s one of the least understood aspects of solidification.
“A falling snowflake carries the clues for deciphering many mysterious, complex patterns and processes in nature. Scientists now know that a wide variety of pattern-forming phenomena have the same underlying structure and driving force as snowflake formation.’
Branching patterns show up when flames sweep down a tube, when lightning forks across the sky, when a fluid such as water intrudes into a pool of oil, and when nerve cells form connections. In each case, the patterns seem to be the result of a competition between large-scale forces promoting explosive, unstable growth and microscopic effects having a restraining, stabilizing influence.
Snowflake formation is just one example of a pattern-forming process in which simple systems spontaneously generate complex forms, says Family. The stories snowflakes tell shed light on many patterns found in physics, chemistry, biology and engineering.
FORMING A SNOWFLAKE
Snowflakes freeze in moist air, away from any container that would shape or guide the freezing pattern. A typical snowflake begins as a dust particle or impurity; water molecules form into ice crystals, settling into hexagons.
As a liquid crystallizes, it “grows” by adding layers that extend as the tip of an icicle; the surface tension of the liquid holds excess back from the tip. The falling snowflake adds microscopic layers of ice from nearby water molecules, growing at the six tips.
As the tips grow, the crystallized liquid becomes unstable; the formation sends off side-branches to help balance its growth. The structure provides a slight, built-in preference for growth in six directions.
Conditions surrounding even a single snowflake are not uniform. A close look at any real snowflake reveals that its six arms are not identical. There are always some imperfections. Tiny difference in atmospheric conditions might affect the eventual design.
Snowflake growth can be described mathematically using equations that account for how heat diffuses. Solving those equations allows physicists to predict what happens moment by moment. Scientists have used computer simulations of snowflake growth, like those shown below, to track patterns in randomness.
