Content area
Full Text
INTRODUCTION Since the time of Rene Just Hauy (1743-1822) it has been generally recognized that the wonderful polyhedral shapes of crystals and their naturally occurring planar faces are a manifestation of their internal atomic order. On the other hand, amorphous solids (glasses) such as obsidian have a very disordered internal structure, and do not naturally occur in the polyhedral shapes we so readily identify with crystals. Until the recent discovery of "quasicrystals," solids have been identified as being either crystalline or amorphous. Quasicrystals, however, are less ordered than crystals but are more ordered than glasses. Perhaps their most striking feature is their appearance as certain polyhedral shapes that are not allowed in crystals. For examples, the shape of the Al-Li-Cu quasicrystals in Figure 1 is called a triacontahedron, possessing 30 equivalent faces and six axes of 5-fold rotational symmetry (Fig. 2), a symmetry forbidden in crystals. (Figures 1 and 2 omitted)
BACKGROUND
In his works, Hauy championed the theory that for a given mineral, any of its varied crystal shapes could be constructed by the appropriate stacking of many identical building blocks or integrant molecules (molecules integrantes) of the same orientation (Fig. 3). (Fig. 3 omitted) Based on such constructions, Hauy proved that the regular icosahedron and dodecahedron (Platonic solids which possess 5-fold symmetry) violated his law of rational intercepts, and thus are impossible shapes for crystals (Hauy, 1801).(1) Subsequently, the existence of flat faces on crystals has become intimately associated with their being composed of a regular stacking of a single type of building block for a given crystal. Hauy's concept of an integrant molecule has since developed into what is known today as the unit cell--a hypothetical volume decorated with atoms, which when many are stacked together in the same orientation, make up the entire crystal structure. In an infinite crystal, each unit cell has the same surroundings as every other unit cell. One can then imagine a point (say at the center of each cell) as representing the position of each unit cell. This set of regularly spaced points is known as a lattice. If one imagines moving from one lattice point to another by going a certain distance in a certain direction, one will always come to another lattice point by...
