





This pattern, called a Penrose tiling,
is a classic example of an aperiodic pattern that exhibits longrange
order. 


Crazy Quasicrystals
To understand the maddeningly paradoxical state of quasicrystals, first
consider kitchen floor tiles. Tiles can be arranged in patterns of squares,
hexagons, or octagons without leaving gaps. But cover the floor with pentagons
or decagons and you'll see a patchwork of empty space. These gaps mean
the pattern doesn't possess periodicity, meaning the tiles can't theoretically
stretch to infinity in a regularly repeating pattern. In periodic patterns,
if one tile is surrounded by six neighbors, then every tile is surrounded
by six neighbors.
But in aperiodic structures, this regular pattern breaks down. Until
the early 1980s, scientists believed all crystals were composed of atoms
arranged periodically much like four or sixsided tiles. They believed
this because light diffracted from crystals produces sharp, crisp patterns
indicative of periodicity. Then along came quasicrystals with five or
tenfold symmetry. These structures aren't periodic, yet they produce sharp
diffraction patterns. Something was wrong with the definition of crystals.
This discovery, in fact, spurred an international union of crystallographers
to redefine crystals as anything with a sharp diffraction pattern.
Further analysis revealed that like conventional crystals, quasicrystals
exhibit perfect longrange structural order, meaning once the location
of a single atom is known, the precise location of all other atoms can
be calculated. This newfound combination of aperiodic structure and longrange
order captured the imagination of many physicists.
"I think they're beautiful, and that's the main
reason why I'm studying them," Rotenberg says.
More about the
theory of quasicrystals.
