The structure of quasicrystals

Since 1984, when Dan S. Shechtman and his colleagues at the National Institute of Standards and Technology (NIST) discovered the first quasicrystal, workers have fabricated many different species of quasicrystalline alloys. They have learned how to improve samples to the point that they can quantitatively study issues that were only ideal speculations seven years ago. The study of quasicrystals has advanced three theories about their structure: the Penrose, glass and random tiling models. The Penrose model - derived from the work of mathematician Roger Penrose of the University of Oxford - suggests that quasicrystals are composed of two or more unit cells that fit together according to specific rules. The model accurately describes some of the basic properties of quasicrystals, but it has difficulty explaining how these rules might be related to atomic growth processes. The glass model, in contrast, relies on local interactions to join clusters of atoms in a somewhat random way. According to the model, all the clusters have the same orientation, but because of random growth, the structure contains many defects. It now seems that the two models are converging toward a third, and random-tiling model, which combines some of the best features of its predecessors. In the past few years the structure of quasicrystals has been one of the most hotly debated topics in solid state physics. The resolution of this debate may lead to a theory of quasicrystalline structure and guide the development of materials with unusual structural and electrical properties