incommensurate structure, however, is surely the newly discovered icosahedral quasicrystal, observed in rapidly quenched aluminum-manganese alloys and in several other systems27 (see Cahn and Gratias, in this volume).
The subject of partially ordered systems is a particularly fascinating area of the study of structural order. It embraces the various liquid-crystal phases, superionic conductors, and so-called plastic crystals, all of which are intermediate between a liquid and a conventional solid.28–30 All these materials have some type of long-range structural order or broken symmetry, in contrast to the disorder of liquids, but the structural order is not enough to specify a unique equilibrium position for each of the constituent atoms.
One partially ordered system that illustrates the richness of this field is the hexatic phase of smectic liquid crystals. The existence of this phase was proposed by Birgeneau and Litster31 in 1978 on the basis of theoretical work that Nelson and I did on two-dimensional systems.32 In 1981, Pindak, and co-workers33 found the hexatic phase experimentally through x-ray studies of a material known as n-hexyl-4′-n-pentyloxybiphenyl-4-carboxylate (650BC). The molecules in the hexatic phase are arranged in layers, but in the plane of the layers there is no long-range translational order of the positions of the molecules. Nevertheless, there is long-range order in the orientation of the bonds between neighboring molecules in the layers so that the material possesses sixfold anisotropy in the plane. In other words the hexatic phase has the anisotropy characteristic of a hexagonal crystal but lacks the translational order in the plane of the layers. These properties are manifest in the x-ray diffraction pattern by the appearance of six diffuse spots in the x-y plane, where an ordinary hexagonal crystal would have infinitely sharp Bragg peaks.
Many interesting forms of order occur in phases that exist at surfaces or in very thin films, including suspended smectic films, adsorbates on crystal surfaces, and reconstructions of clean crystal surfaces.25,33 There are also forms of “induced order” that may be found at the surface of a bulk liquid or liquid crystal.34 These subjects interest condensed-matter physicists because of the problems posed by the greater importance of fluctuations in some two-dimensional systems than in the analogous three-dimensional systems. And, improvements in experimental techniques and in materials preparation have made many of these systems accessible for the first time. For example, the development of glancing-incidence x-ray diffraction, together with synchrotron x-ray sources, has given us a sensitive and powerful method to study order just inside the surface of a bulk material.34
Many types of nonequilibrium structures can also be properly characterized as novel forms of structural order, in particular, various macroscopic structures, such as dendrites and other complex forms of crystal growth, loose aggregate structures, and structures formed by spinodal decomposition.35–37 On the atomic level, the structure of glasses continues to be of great interest to condensed-matter physicists.38