Quasicrystals: a new ordered structure.

For decades, crystallographers have assumed that the solid state was an orderly place where crystals were made up of atoms arranged in neat patterns that repeated themselves at regular intervals. Successive steps of the right length along any given direction within this lattice would take a microscopic traveler to new locations indistinguishable from the starting point. The conventional wisdom was that crystals must have this kind of periodic structure. This complacency was shattered recently when a group of researchers discovered a material that doesn't fit the traditional rules of crystallography.

The new material, a metallic solid discovered by Daniel Shechtman of the Israel institute of Technology while he was working at the National Bureau of Standards (NBS) in Gaithersburg, Md., is an alloy of aluminum and manganese. When a beam of electrons bombards this solid, the electrons scatter to form a set of sharp spots indicating that the material's atoms are highly ordered. At the same time, however, the pattern created by the spots implies that the crystal's atoms can't be arranged within a regularly repeating, or periodic, framework.

The result was so surprising that "we stalled for a good long time" before publishing details, says NBS materials scientist John W. Cahn. "All my training had been with this assumption that crystals are strictly periodic." More than a year after the discovery, their report appeared in the Nov. 12 PHYSICAL REVIEW LETTERS. The researchers plan to present additional findings at a meeting in March.

The alloy discovered at NBS may be an example of a new class of structures that "sit somewhere between the crystal and glass state," says Paul J. Steinhardt, a physicist at the University of Pennsylvania in Philadelphia. Several years earlier, Steinhardt and a colleague had been studying the structure of glasses by simulating on a computer what happens to atoms in a liquid as it cools befow its melting point. These studies led him to look for a "quasicrystalline" structure that was fhighly ordered but not periodic. He found such an example in tw dimensions in the work of British mathematical physicist Roger Penrose, who looked at ways of laying tiles of particular shapes to cover a floor without creating a repeating pattern -- the kind of problem mathematicians explore just for fun.

Steinhardt extended one Penrose tiling scheme to three dimensions, coming up with two shapes, both looking like squashed cubes or rhombohedra. Groups of these shapes fitted together to fill space in a pattern that showed the same symmetry as an icosahedron (a 20-sided solid with triangular faces) but was "quasiperiodic" instead of periodic. Last fall, just after he had calculated what an electron diffraction pattern for that structure would look like, he saw the NBS paper and its diffraction pattern.

"It was quite exciting," says Steinhardt. "There the two were, sitting right next to each other, the result of completely disconnected pieces of work." The two patterns were very similar. Steinhardt and Dov Levine quickly reported the possible existence of "quasicrystals" in the Dec. 24 PHYSICAL REVIEW LETTERS.

"This model looks very promising," says Cahn. Because periodicity was built into so much of the study of the properties and nature of solids, "almost everything has to be reexamined," he says. Various groups throughout the world have already started to look at how the properties of such a material would be different from those of an ordinary crystal. Others are trying to find different combinations of metals that cool to form larger and more pure quasicrystal samples.

"It's not every day that one comes across a new kind of atomic structure," says Steinhardt. "There's the obvious hope that something really interesting will come from it."