IS THERE any order in a pile of sand? A team of physicists thinks so. They
told the American Physical Society meeting in Seattle last week that apparently
jumbled-up grains of sand are actually trying to arrange themselves into a
four-dimensional sphere.
Physicists have been playing with sand piles for years. They hope that their
piles 鈥攁ctually large collections of hard spheres鈥攚ill provide a
window into disordered systems, such as the arrangement of molecules in glass.
Physicists would like to know if the apparent disorder in sand piles masks some
deeper structure. In particular, they would like to know if there is a 鈥渞andom
closest-packed鈥� state: an arrangement that fits the most spheres into the least
space.
Gerry Seidler and his colleagues at the University of Washington in Seattle
set out to answer this question by finding the exact location of every sphere in
a 鈥渟and pile鈥� of 12,000 glass beads. They poured the beads into a glass cylinder
and then shone X-rays through it to capture a 鈥渢ransmission image鈥濃�攖he
beads鈥� shadows. They then took another 559 X-ray images, each from a slightly
different angle, and used them to reconstruct the pile on a computer.
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Seidler and his colleagues knew that the beads would be 鈥渇rustrated鈥� between
two extremes. The entire collection could minimise its energy by falling into a
cubic lattice with an extra bead at the centre of each square鈥攁
face-centred cubic lattice. On the other hand, any four beads could minimise the
distances between them even better by forming a tetrahedron.
But on a larger scale, tetrahedra do not fit together to make a regular
lattice. 鈥淭he system is trying to minimise energy locally,鈥� Seidler says. 鈥淚t
doesn鈥檛 know what the global low-energy state should be.鈥� So disorder
reigns.
Or does it? A collection of tetrahedra can be fitted together into a regular
shape鈥攁 spherical shell鈥攂ut only in four dimensions. Space isn鈥檛
four-dimensional, but a four-dimensional sphere can be unwrapped and 鈥渇lattened鈥�
into three-dimensional space, just as a globe can be sliced and stretched into a
flat map of the world. And just as with the map, the shell may become distorted
when it is projected onto three dimensions, making the beads in it appear to be
randomly distributed.
Seidler says that the distances between beads seem to correlate with what
such a flattened-out four-dimensional sphere would look like. But more data is
needed to see if the angles between the beads also support this idea. 鈥淭o figure
out where every bead is in three dimensions and non-invasively is a great boon,鈥�
says James Kakalios of the University of Minnesota in Minneapolis.