Quasicrystalline Tetrahedra

Tetrahedra can be packed into highly dense phases that exhibit quasicrystalline order, according to a theoretical study by scientists at the University of Michigan, Ann Arbor, and their coworkers (Nature 2009, 462, 773). Both philosophers of old and modern scientists have studied close packing of spheres—a topic central to crystallography—but other shapes have drawn far less attention. The new study may enable researchers to understand packing of tetrahedral nanocrystals and other uniquely shaped solids synthesized recently. Michigan’s Sharon C. Glotzer and coworkers used thermodynamics-based computer simulations to examine the way a “fluid” of tetrahedra responds to increasing pressure. Among other observations, the group found that under some conditions, tetrahedra pack into a quasicrystalline phase, which can be recognized by its 12-fold rotational symmetry and a lack of three-dimensional periodicity. This theoretical crystal’s packing fraction—the fractional volume occupied by the tetrahedra—is roughly 0.83, significantly higher than the packing fraction exhibited by close-packed spheres.