The researchers used lasers to steer tiny plastic beads, creating interference patterns with lots of five-fold symmetry similar to that of quasicrystals. The red spots show the most intense light. The pentagons show the five-fold symmetry.
Jules Mikhael and his colleagues didn’t set out to make a
material with a structure that had never been seen before, much less one that
combines order and irregularity in a whole new way, one that Archimedes hinted
at 2,000 years ago, one bound together by the Fibonacci sequence. They just
wanted to understand a quasicrystal.
Even that wasn’t such a modest goal,
because quasicrystals are pretty odd critters. Slice one in half, and there is
a sort of mosaic with repeating shapes like tiles, much like a crystal. But
here’s the bizarre part: Spin the resulting mosaic a fifth of a turn and often
its tiles will line up exactly as they were before you spun it.
But that kind of five-fold symmetry is “forbidden,” because
mathematicians have shown that no repeating flat pattern has it. That’s why
you’ve never seen a bathroom tiled with regular pentagons—it’d be impossible to cover
the whole surface with no gaps.
The secret of a quasicrystal is that its
patterns never repeat. The tile shapes within the quasicrystal combine and
recombine, with one area perhaps looking similar to another but then skipping
off in its own unique formation. This eternal irregularity also gives
quasicrystals remarkable, intriguing properties. For example, they tend to be
slippery like Teflon, and even when made from metals, they’re good insulators.
Physicists have never really
quasicrystals have these properties, though. “This is the one million dollar
question,” says Clemens Bechinger, one of the Mikhael’s colleagues at the University of Stuttgart.
Part of the difficulty is that
quasicrystals are frustratingly complicated. They’ve generally been made from
mixtures of several different metals, and this chemical complexity on top of
the inherent structural complexity confuses matters.
To simplify matters, the team set out to create a quasicrystal from
micron-sized plastic beads called colloidal particles. This approach would make
the chemistry simple. Furthermore, they’d be able to see the quasicrystal
structure with a microscope. In metal alloys, the structure is so tiny — on the
scale of atoms — that physicists have been stuck inferring the structure from
X-ray diffraction techniques.
Colloidal particles are negatively
charged, so when poured into a flat pan of water, they naturally form a grid of
triangles as they try to get as far as possible from one another. This
structure is like a crystal: repeating, perfectly orderly, rather dull.
Then the team switched on five lasers,
arranged so that the light beams would interfere with one another and create a
complex pattern with lots of five-fold symmetry. The plastic beads were
attracted to the spots where the laser was most intense, creating the
quasicrystal the team had been hoping for.
Bechinger and Mikhael’s team had accomplished
their goal of creating a quasicrystal that would help explain quasicrystal
properties, but their most important discovery was still ahead of them. They
tried lowering the intensity of the lasers. When the lasers were very low, the
beads ignored the lasers entirely and formed a triangular grid. But at an
intermediate stage, the beads formed a pattern very close to an Archimedean
tiling, one of the repeating patterns that had long been believed to be the
only type possible. The beads formed rows of repeating triangles or repeating
squares, but the rows didn’t alternate evenly the way they would in an ordinary
Archimedean tiling. Like a quasicrystal, they formed an overall pattern that
But that isn’t to say that there was no
order. The pattern of triangular rows and square rows, the team realized, was
derived from another ancient piece of mathematics: the Fibonacci sequence. This
is the sequence that begins 1, 1, 2, 3, 5, 8 … , with each subsequent number
being the sum of the previous two.
The poor beads, the team deduced, were
torn in their loyalties, repelled from one another but also attracted to the
intense laser spots. So they had split the difference. The irregular pattern in
the vertical direction made the beads line up as close as possible to the
quasicrystalline shape the laser beams demanded, while the repeating horizontal
patterns aligned them as close as possible to the grid pattern their mutual
repulsion pushed them toward.
“We are absolutely sure that this
structure should have properties that are not usual,” Mikhael says, because
materials with odd structures almost always do. Now they just have to figure
out what those properties are.