Where are the atoms? Per Bak posed this question about the positions of atoms in icosahedral quasicrystals 1 two years after their discovery in 1984. But despite thousands of papers published during the subsequent two decades, not one quasicrystal structure is known with the detail and accuracy that crystallographers can claim for normal crystals. The strange nature of quasicrystals accounts for the difficulty. 2 Judging by the sharp Bragg peaks in their diffraction patterns, quasicrystals can possess a long-range order comparable to the most perfectly crystalline material. But unlike normal crystals, quasicrystals also possess a rotational symmetry that forbids packing into a repeated array of unit cells. Consequently, they lack periodic translational order and a straightforward path from Bragg peaks to structure.
The sensitive interaction of x rays with atomic electrons makes x-ray diffraction foremost among the methods available to determine the arrangement of atoms in a crystal. X rays...