Amorphous materials order ranges

The formation of ordered two- and three-dimensional microstructuies in dispersions and in liquid systems has an influence on a broad range of products and processes. For example, microcapsules, vesicles, and liposomes can be used for controlled drug dehvery, for the contaimnent of inks and adhesives, and for the isolation of toxic wastes. In addition, surfactants continue to be important for enhanced oil recovery, ore beneficiation, and lubrication. Ceramic processing and sol-gel techniques for the fabrication of amorphous or ordered materials with special properties involve a rich variety of colloidal phenomena, ranging from the production of monodispersed particles with controlled surface chemistry to the thermodynamics and dynamics of formation of aggregates and microciystallites. 

In contrast to crystalline solids characterized by translational symmetry, the vibrational properties of liquid or amorphous materials are not easily described. There is no firm theoretical interpretation of the heat capacity of liquids and glasses since these non-crystalline states lack a periodic lattice. While this lack of long-range order distinguishes liquids from solids, short-range order, on the other hand, distinguishes a liquid from a gas. Overall, the vibrational density of state of a liquid or a glass is more diffuse, but is still expected to show the main characteristics of the vibrational density of states of a crystalline compound. 

When an amorphous material exists in a glassy state, it is hard and brittle. In a rubbery state, the material is soft and pliable. An amorphous material, at solid state (also referred to as glass), does not flow, but the molecules are randomly distributed as if they were in liquid state. When this "glass" is heated, it softens and eventually becomes a fluid. However, this is not a first-order transition and therefore occurs over a range of temperatures called the glass transition temperature (Tg). The state... 

The optical properties of amorphous solids are interesting. These solids are optically isotropic. Furthermore, the sharp features present in crystal spectra are absent in the spectra of amorphous solids even at low temperatures. The overall features in the electronic spectra of amorphous solids (broad band maxima) are, however, not unlike those of crystals, reflecting the importance of short-range order in determining these characteristics. The optical absorption edges of amorphous materials are not sharp and there is an exponential tail in the absorption coefficient (Fig. 7.13) associated with the intrinsic disorder. 

For many years, during and after the development of the modem band theory of electronic conduction in crystalline solids, it was not considered that amorphous materials could behave as semiconductors. The occurrence of bands of allowed electronic energy states, separated by forbidden ranges of energy, to become firmly identified with the interaction of an electronic waveform with a periodic lattice. Thus, it proved difficult for physicists to contemplate the existence of similar features in materials lacking such long-range order. 

The degree of short-range order in an amorphous material can be characterized by a hard sphere model if the basic structure of an amorphous material is approximated by spheres. The density of packing of atoms around a reference atom is described by the number of atom centers per volume that lie in a spherical shell of thickness, dr, and radius about the reference atom. In a hard sphere model, the number, n, of neighboring spheres with centers between r and dr is measured as a function of r. 

Amorphous materials have no long-range structural order, so there is no continuous lattice in which atoms can vibrate in concert in order for phonons to propagate. As a result, phonon mean free paths are restricted to distances corresponding to interatomic spacing, and the (effective) thermal conductivity of (oxide) glasses remains low and increases only with photon conduction (Figure 8.2). 

All of these different types of amorphous materials posses short-range order, usually in the form of local coordination environments around individual atoms (Voronoi polyhedra). For example, the local tetrahedral coordination of silicon... 

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