Long-Range and Short-Range Order

orderliness in the arrangement of atoms and molecules in solids and liquids. Orderliness over distances comparable to interatomic distances is called short-range order, whereas orderliness repeated over infinitely great distances is called long-range order. In an ideal gas. the arrangement of an atom at any point in space is independent of the arrangement of other atoms. Thus, both long-range and short-range order are absent in the ideal gas, but liquids and amorphous solids exhibit short-range order—a certain regularity in the arrangement of the neighboring atoms. At great distances the order becomes “blurred” and gradually gives way to “disorder.” which means that long-range order does not exist in liquids and amorphous solids.

In crystals, the atoms are arranged in regular rows or networks (in three-dimensional lattices), and a regular alternation of atoms separated by the same distances is repeated for atoms separated by any distance—that is, both long-range and short-range order exist. The basic criteria of long-range order are the symmetry and regularity of arrangement of particles, which repeat at any distance from a given atom. The presence of long-range and short-range order is due to the interaction between the particles. A completely ordered state, however, is only possible at absolute zero, since order is disturbed by thermal motion.

The concepts of long-range and short-range order are important in the theory of alloys, in which they characterize the degree of ordering of an alloy—for example. in an alloy consisting of two components, complete ordering leads to alternation of the two types of atoms; in other words, the nearest neighbors of each atom are only atoms of the other type. Incomplete order is reflected by the fact that atoms of the same type appear among the nearest neighbors. Depending on the thermal and mechanical treatment, various degrees of ordering may be attained in an alloy; in this case. the physical properties of the alloy are also changed.

Long-range and short-range order exist in terms other than the mutual arrangement of the particles (coordination order). For example, a liquid consisting of asymmetric molecules exhibits short-range order (in the case of liquid crystals, long-range order) in the orientation of molecules (orienta-tional order). Ferromagnetic and antiferromagnetic materials exhibit short-range and long-range order in the orientation of magnetic moments.