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Dec. 12, 2012

Vol. 113, No. 5


A world in a grain of sand

Paul Steinhardt’s long, improbable search for a natural quasicrystal

By Mark F. Bernstein ’83
Published in the December 12, 2012, issue

Members of the July 2011 expedition to Russia stand in front of trucks fitted with tank treads to crawl across the permafrost; from left, Bogdan Makovskii, Glenn MacPherson *81, Will Steinhardt, Chris Andronicos *99, Marina Yudovskaya, Luca Bindi, Victor Komelkov, Olga Komelkova, Paul Steinhardt, Alexander Kostin, Valery Kryachko, Michael Eddy ’11, and Vadim Distler.
Members of the July 2011 expedition to Russia stand in front of trucks fitted with tank treads to crawl across the permafrost; from left, Bogdan Makovskii, Glenn MacPherson *81, Will Steinhardt, Chris Andronicos *99, Marina Yudovskaya, Luca Bindi, Victor Komelkov, Olga Komelkova, Paul Steinhardt, Alexander Kostin, Valery Kryachko, Michael Eddy ’11, and Vadim Distler.

With apologies to William Blake, who once urged us to “see a world in a grain of sand,” the speck that Paul Steinhardt is holding — glued to the point of a glass needle because you’d never find it again if it weren’t — is barely visible to the naked eye. Steinhardt’s enthusiasm notwithstanding, a visitor to his fourth-floor office in Jadwin Hall is only being polite when he acknowledges that he can see it at all.

But Steinhardt is a theoretical physicist, so let your mind bore in to the atomic level. This speck is called a quasicrystal, a rare 20-sided clump of atoms that violates what were long believed to be the most basic rules of crystalline structure. Three decades ago, an Israeli physicist, Daniel Shechtman, stumbled upon man-made quasicrystals in a piece of industrial aluminum and later received the Nobel Prize for his discovery. But Steinhardt already had deduced that such structures might exist, and it was he and his co-author who explained what Shechtman had found. 

Having looked within, now pull back. Rewind the probable history of this speck like one of those reverse-action films in which the diver emerges feetfirst from a pool and arcs up onto the board. Follow it back to the piece of khatyrkite, the rare mineral in which it once was embedded; back into the white cardboard box in the collection of the University of Florence; back into the black-market collection of an Amsterdam gem dealer. Go further, to the remote Russian stream bed where a platinum prospector first picked up the khatyrkite 32 years ago, to the glacier that dropped it during the last Ice Age 15,000 years ago, to the meteorite that disintegrated in the atmosphere and rained stardust over Siberia. 

Don’t stop. Reassemble that meteorite and pull it back into the sky, out of our galaxy, out into the farthest reaches of space, where Steinhardt thinks it may have formed in a collision with another meteorite. Chemical analysis suggests that this little bit of metal ricocheted around the universe for 4.5 billion years. It is older than our solar system yet something never seen before, and it could fit on the head of a pin. 

How about that, William Blake?

Officially, Steinhardt is the Albert Einstein Professor in Science (and director of the Princeton Center for Theoretical Science), but his three-decade investigation of quasicrystals has required him to be part Carl Sagan, part Indiana Jones, part Lewis and Clark, and part Sherlock Holmes. Throw in a touch of Captain Ahab, as well, for it is not too much to say that in the world of ­crystallography those rare specks of metal have become —  if one can lurch to the opposite end of the metaphorical scale — the Great White Whale.

Face to face, Steinhardt is mild-mannered and engaging, with an uncommon ability to explain opaque scientific concepts in layman’s terms. That is helpful, for his interests range among particle physics, dark energy, astrophysics, and cosmology. One of the founders of an inflationary model of the universe, which holds that the early universe underwent a period of exponentially rapid expansion, he since has developed a competing theory, a so-called cyclic model, which posits that the universe oscillates through periods of expansion and contraction. (See “The Cosmic Apocalypse,” PAW, Feb. 11, 2009.) A prolific writer and lecturer, Steinhardt has co-authored one book and edited four more, published more than 200 journal articles, and received six patents relating to quasicrystals, with two more pending.

The best way to understand quasicrystals is to look at something two-dimensional. Think of your bathroom floor. Chances are, the tiles are laid in a regular, repeating pattern. If the pattern is made with a single type of tile, only certain shapes — three-, four-, or six-sided — can be used to fill the space completely. Use pentagons, octagons, or any other shape, it was believed, and there will be space left over. 

Physicists long thought that the atoms inside a crystal also arranged themselves in repeating patterns. Like those floor tiles, only certain shapes were permissible, and only certain types of symmetries — two-, three-, four-, or sixfold — were possible (in other words, each piece or atom  could be rotated a certain number of degrees and still fit  in the pattern). Starting in the 1960s, mathematicians tried to see if it were possible to arrange tiles in a pattern that  never ­repeated itself — that was, to use the scientific term, ­nonperiodic. A British mathematician, Roger Penrose, created such a pattern using two shapes, a fat and a thin rhombus. 

In the early 1980s, Steinhardt began working with a graduate student, Dov Levine (now a theoretical physicist in Israel), when both were at the University of Pennsylvania, to see if they could find atomic arrangements with supposedly impossible symmetries. Looking at Penrose’s two-dimensional mosaic, they discovered that the pattern thought to be nonperiodic was actually quasiperiodic, meaning that the pieces did follow a pattern, although that pattern never perfectly repeated itself.

At the same time, Shechtman, working at what is now the National Institute of Standards and Technology, accidentally discovered an aluminum alloy that, when viewed under an electron microscope, was seen to contain crystals with fivefold symmetry. Not only did no one believe him — crystals couldn’t have fivefold symmetry — his supervisor reassigned him and suggested that he learn something about crystallography. It took two years before any scientific journal would agree to publish Shechtman’s findings.

Post Comments
7 Responses to A world in a grain of sand

Beth Kirksey Says:

2012-12-04 14:37:29

Part adventure tale, part mystery, part inspirational story. With only the barest of science education, I found this article fascinatingly instructive. Not to mention humorous and emotionally compelling. No mean feat.

Richard Sorrenson *93 Says:

2012-12-11 09:31:40

A marvelous story in every way and beautifully written, Mark.

Allen C. Myers '65 Says:

2012-12-17 14:43:14

A superbly-written article! I plan to read it aloud to my Introduction to Physical Geology student next month -- it touches on so many personal and structural aspects of the process of "doing science." Thank you.

David Lewis '83 Says:

2012-12-19 15:11:57

Mark - thanks for bringing this amazing discovery to life as a riveting tale.

Stefan Burr *68 Says:

2013-01-02 10:41:24

This is a very good article, but I would like to point out an error, or possibly two. First, the author calls the Penrose tiles "rhombi." Neither is a rhombus, which has four equal sides. Each Penrose tile has two pairs of (different) equal sides, and an axis of symmetry, but they are not rhombi. In fact, one tile is concave, which is impossible for a rhombus. I also have a concern for saying that cosmic inflation was "exponential." While the word is used by laymen in the sense of "very rapid," it has a very specific meaning in science. Perhaps the inflation really was exponential; was it? The answer is important; I hope that the author got it right. "Exponential," like "parameter," is a useful word in scientific contexts that has had its meaning polluted by popular misuse. Improper use of these words has added considerable difficulty to my teaching of these vitally important concepts. While it is probably too late to restore their meanings as used by the public, it is wrong to use them improperly when writing about science. Even then, if used properly, their true meanings should be explained.

San Le Says:

2013-01-15 15:46:02

In reference to Stefan Burr's comments about Penrose tiles not being rhombi, there are 2 sets of Penrose Tilings, the fat and thin rhombi tiles and the kite and dart tiles. I think you are referring to the latter. In 2nd and 3rd images of this article, they are referring to the former.

Robert Cowen '61 Says:

2013-03-12 11:20:56

A beautiful example of how inspiration coupled with hard work can pay off! Should be read by all budding scientists.
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