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Issue No. 3
Quasicrystals: From Kepler to Shechtman
Ron Lifshitz
From Fibonacci's rabbits to the toilet paper that Penrose didn't like.
Abstract
The theory of crystallography had developed for centuries under the premise that crystals are necessarily periodic. No one had ever imagined that long-range order could be achieved by any other means. All this changed overnight, some 20 years ago, when the Israeli physicist Danny Shechtman discovered the first quasicrystal. Ever since Shechtman's discovery, crystallography has been in the midst of a scientific revolution, in which we are revising basic notions in condensed matter physics, such as the definition of "crystal" as well as the notions of "order" and "symmetry" in crystals and their implication on the physical properties of crystals.
In this article we shall try to explain, without going into too much detail, where we stand today on a number of these issues. We shall give the current definition of "crystal", demonstrate what aperiodic order might look like, and explain what it means to say that an aperiodic crystal has certain symmetry.
[I.R. Fisher et al., PRB 59 (1999) 308-321]
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About the Author
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Ron Lifshitz is on the faculty of the School of Physics and Astronomy at Tel Aviv University. He completed his Ph.D. at Cornell University under the supervision of David Mermin, from whom he learned about the symmetry of quasicrystals, as well as about the importance of writing and teaching science. During his stay as a postdoc at the California Institute of Technology, where he worked with Michael Cross and Michael Roukes, he was introduced to the wonders of physics at the nano-scale. Ron Lifshitz's research group studies quasicrystals, with emphasis on the symmetry of physical properties (such as magnetic and color symmetry) as well as the implication of quasiperiodic long-range order on the physical properties of quasicrystals. At the same time, Lifshitz's group is also carrying out theoretical research in nanomechanics, studying questions ranging from the nonlinear dynamics of nanomechanical systems, through the mesoscopic physics of phonons in nanoelectromechanical systems, to quantum electromechanics.
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