Eli Rotenberg, a staff scientist at the Advanced Light Source (ALS) at the Department of Energy's Lawrence Berkeley National Laboratory, Karsten Horn of the Fritz-Haber Institute, Max-Planck Society, Berlin, and their colleagues investigated the electronic structure of a quasicrystalline alloy of aluminum-nickel-cobalt (AlNiCo) by means of angle-resolved photoemission. They report their findings in the August 10 issue of the journal Nature.

THE CONSTANT ENERGY CONTOURS FOR NEARLY FREE S-P ELECTRONS IN AlNiCo QUASICRYSTALS (DATA, TOP) ARE DERIVED FROM THREE-DIMENSIONAL SPHERES DISTRIBUTED APERIODICALLY IN MOMENTUM SPACE (MODEL, BOTTOM).

They found that rather than moving around arbitrarily, electrons in quasicrystals travel in "bands" with distinct momentum and energy. The data show that electron momenta and energies are correlated with the structure of the quasicrystal.

Band-like properties, common in metals and other ordinary crystals, were not expected in quasicrystals. But then quasicrystals themselves are an unexpected phenomenon.

"Before quasicrystals were discovered by Dan Schechtman and his colleagues in 1984, most people would have said they were structurally impossible," says Rotenberg. "You can tile a plane with equilateral triangles or squares -- shapes with three-fold or four-fold rotational symmetry -- and you can fill space periodically with tetrahedrons or cubes, which are two of the ways that atoms are typically arranged in ordinary crystals. But you can't tile a plane with pentagons -- not without leaving gaps -- and you can't fill space with dodecahedrons."

Yet, although quasicrystals display five-fold symmetry and other "forbidden" symmetries locally, they still possess perfect long-range structural order. So complex is their geometry that it has taken years to understand how their long-range atomic structures could arise.

Other investigations have centered on potentially useful properties. Quasicrystalline alloys are durable, stable at high temperatures, and make excellent nonstick coatings -- and they can store hydrogen at high density.

Though they are composed of excellent electrical conductors such as aluminum and copper, quasicrystalline alloys themselves are extremely resistive -- the more perfect the quasicrystal, the more resistive it becomes. At low temperatures their resistance changes markedly in response to changing magnetic fields, which makes them interesting for applications in magnetic devices.

"But few experiments have been done on the basic properties of their electronic states," says Rotenberg. "In other words, where are the electrons and how do they move? These were unresolved questions."

Ordinary metals are good conductors because their valence electrons can move freely from atom to atom; this freedom is facilitated by long-range periodic structure. Since quasicrystals lack periodic structure, theorists expected no such extended electronic states.

"One might imagine that from an electron's point of view the material appears disordered. If so, the electronic states would be confined to localized clusters," Rotenberg says, and indeed, theoretical considerations suggested electronic states confined to the quasicrystal's many different local structures.

IN THE PLANE, THE AlNiCo QUASICRYSTAL, WHICH CONSISTS OF OVERLAPPING DECAGONS, IS APERIODIC.  BUT THE STACKED PLANES HAVE PERIODIC STRUCTURE. Images by Steinhardt and Jeong, Nature 382, 433-5

Rotenberg, Horn, and their colleagues decided to test the prediction with a special kind of quasicrystal, an AlNiCo alloy consisting of stacked planes of atoms exhibiting ten-fold symmetry. By looking at the behavior of electrons in the plane, they could observe the effects of this quasicrystalline ordering; by looking at right angles to the planes, they could observe the effects of the periodic, crystalline-like ordering of the stack.

Peter Gille of the Ludwig-Maximilians-University, Munich, grew the quasicrystal, and the samples were prepared and characterized by Horn and by Wolfgang Theis of the Free University of Berlin. At the ALS, Rotenberg, Horn, and Theis examined the samples by means of low-energy electron diffraction and by angle-resolved photoemission at beamline endstation 7.0.1.2.

"We measure the emission angles and the kinetic energy of electrons scattered from near the surface of the material by soft x rays," says Rotenberg. "These are the valence electrons, not as tightly bound as electrons near the atomic cores."

The sample is rotated to get a complete distribution of electron angles and energies. The eventual result is a plot of the electronic states of AlNiCo's valence electrons in "momentum space," the mathematical space in which such fundamental concepts as Fermi surfaces and Brillouin zones are constructed and on which much of the band theory of solids is based.

"Our principal findings were that the distribution of the electronic states in momentum space correlates with the electron diffraction pattern, just like in an ordinary crystal. The electrons aren't localized to clusters, instead they feel the long-range quasicrystal potential," Rotenberg says.

"We found that the electrons propagate nearly freely, like conduction electrons in an ordinary metal," he continues, "and we found there is a Fermi surface, crossed by nickel and cobalt d-electrons; its topology should determine some of the material's fundamental properties."

The discoveries open many new avenues for inquiry, Rotenberg says. "How can we relate our observations to unusual properties such as high resistivity? And are there any localized electrons in addition to the delocalized electrons we found that look so 'ordinary?'"

"Quasicrystalline valence bands in decagonal AlNiCo," by Eli Rotenberg, Wolfgang Theis, Karsten Horn, and Peter Gille appears in Nature, 10 August 2000.

The Berkeley Lab is a U.S. Department of Energy national laboratory located in Berkeley, California. It conducts unclassified scientific research and is managed by the University of California.