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Curiosity about crystals led to theory about instabilities

Monday, January 27, 2003

By Byron Spice, Post-Gazette Science Editor

As tiresome as this winter's lingering cold may have become, it nevertheless provides ample opportunity to ponder the wonders of snow.

Robert Sekerka, above, and William Mullins authored the clumsily named, but exquisitely practical, Mullins-Sekerka Theory of Morphological Stability. (Matt Freed, Post-Gazette)

"Snow is really very special," said Robert Sekerka, University Professor of physics and mathematics at Carnegie Mellon University. "The world would be a very different place if, whenever ice precipitated out of the atmosphere, it took the form of some kind of pellet other than snow."

While admittedly making his observations last week from the comfort of his warm, dry office in Wean Hall and not from behind a snow shovel, Sekerka, 65, is unusually qualified to discuss the form and structure of snow.

It was his work in the early 1960s with his colleague and mentor, the late William Mullins, that explained why snowflakes develop the spiny structure that makes each unique, beautiful and light. Known as the Mullins-Sekerka Theory of Morphological Stability, it applies not only to snowflakes, but to the formation of crystals in general.

"The thing that is striking is the interdisciplinary appeal of his work," said Jeffrey Rickman, a materials scientist at Lehigh University. The theory has provided a framework for study all sorts of instabilities and continues to be widely cited by chemical engineers, physicists and mathematicians, he noted.

Sekerka is an enthusiastic downhill skier, but his scientific interest in the early '60s really didn't concern snow so much as the tree-like forms the snow crystals take. Called dendrites -- from dendros, the Greek word for tree -- they form naturally as liquids transform into solids. He and Mullins, then part of the metallurgical engineering department, were particularly interested in dendrites that form in metals.

 
 

A symposium, "Moving boundary problems in Physics, Mathematics, and Materials Science," has been organized for April 11-12 at the Mellon Institute in Sekerka's honor. For details, visit the symposium Web site at www.csit.fsu.edu/rfs/

   
 

As liquid metal cools, it is at least theoretically possible for it to grow as a regular geometric shape. But Sekerka compares that possibility to that of balancing a pencil on its point: sure, it's possible, but it's not easy. And even if a pencil is momentarily balanced, something always happens to disturb that balance, whether it's a waft of air, a vibration in the table or tiny fairies dancing on the eraser end.

"If there isn't already an instability, you figure God will provide one," Sekerka said.

As metal transforms from liquid to solid -- or as water vapor turns to ice -- you can bet something will happen to disturb it. If a metal is solidifying into a sphere, even a little bump on the sphere will alter the rate at which heat is dispersed, causing the bump to become exaggerated and perhaps form itself into a branch.

"Once one starts to form, a whole bunch of them will form," he added.

Though any distortion tends to enhance itself, "what really happens is a little more subtle," Sekerka continued. For instance, as crystallization occurs, not only do dendrites form and grow longer, but the total area and volume of the solid also grows, a stabilizing force that tends to counteract the crystal's dendritic tendencies.

It's ultimately a balancing act between these forces and, like a pencil on its tip, any balancing act is inherently unstable.

Scientists in the 1940s and '50s were well aware of instabilities and knew they played a role in formation of dendrites. But until Mullins and Sekerka published their first paper in 1963, no one had ever been able to explain the mechanisms that accounted for instabilities.

The Mullins-Sekerka theory provided a method that scientists and engineers could use to quantify all sorts of instabilities, said Jorge Vinals, an associate professor of computational science and information technology at Florida State University and a former post-doctoral fellow who studied under Sekerka.

Understanding instabilities is the first step in controlling them, so this methodology is important for engineers who need to make industrial processes as stable as possible, Vinals said. Physicists, on the other hand, find that interesting things happen when systems become unstable and so have an entirely different sort of interest in the theory. Mathematicians, for their part, have launched entire fields, such as non-linear dynamics and bifurcation theory, that explore the underlying mathematical descriptions of instabilities.

One example of how the theory has been put to use is in the semiconductor field, where computer chips are made out of large, single crystals of silicon that are sliced into thin wafers. In the early years, these single crystals measured just an inch in diameter; today, 12-inch diameter crystals are produced, resulting in wafers that each can yield hundreds of fingernail-size computer chips.

"You don't just walk into the lab and build a bigger [silicon crystal] machine because in a bigger machine these instabilities can eat you alive," Sekerka said. But by understanding the instabilities that occur as liquid silicon crystallizes, engineers have found ways to greatly reduce the formation of dendrites.

Sekerka, a Wilkinsburg native who earned his doctorate in physics from Harvard University, said he and Mullins weren't thinking about such applications 40 years ago. Though working in a metallurgy department during Pittsburgh's steel and aluminum heyday, they weren't especially inspired by the needs of the metals industry, either.

"We were driven by intellectual curiosity more than the need to solve any particular problem," he said. "Some of the greatest discoveries come from following intellectual curiosity."

And as wondrous as snowflakes might be, Sekerka said he has much the same reaction to the recent cold and snow as anybody else.

"I certainly prefer winter when I'm on the ski slope. There's a time and a place for it, shall we say?"


Byron Spice can be reached at bspice@post-gazette.com or 412-263-1578.

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