Amorphous crystalline materials, disordered

The EXAFS technique is used primarily for investigations of disordered materials and amorphous solids. Figure 8.35(b) shows how interference occurs between the wave associated with a photoelectron generated on atom A and the waves scattered by nearest-neighbour atoms B in a crystalline material. 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

While interest in amorphous alloys was becoming vane over the time, the paradigm shift in materials science brought about by the discovery of amorphous metals and rapid solidification cannot be underestimated. The interest of physicists, chemists, materials scientists, and engineers became refocused from well-ordered crystalline materials to disordered and nanocrystalline phases. Shortly, substantial R D programs were initiated in the USA, Japan, and worldwide both at universities and national government laboratories. Foundations have been established for the advance of the science of nanomaterials. 

Consider the isothermal transformation of a disordered (amorphous) solid to an ordered (crystalline) solid. Obviously, there must be enough thermal energy to allow individual atoms to move around and reorient themselves, but assuming this is possible, it is generally found that at constant temperature, the amount of amorphous material transformed to crystalline material, dx (on a volume basis) per unit time, dt, is given by... 

With A U = 2 kcal/gmol we find 2°g = 200 K for x - 1 (complete state of disorder) and 400 K for x = 0.5. In the case of partially crystalline material, the glass transition temperature exists only for the amorphous part. 

Amorphous forms in many ways are even more complex to describe than crystalline materials. Amorphous forms are usually not completely disordered in that... 

With a Fourier transformation of (k) in the distance space, one obtains a separation of the contribution of the various coordination shells. This Fourier transform yields the structural parameters Rj, Nj and ah and thus the near range order of the specimen with respect to the absorbing atoms. The EXAFS analysis for the different absorber atoms within the material yields their specific near range order. Thus, one may get the structure seen form several kinds of absorbing atoms. EXAFS does not require highly crystalline materials. It is a suitable method to study disordered, or even amorphous, structures. The a values provide quantitative information about the thermal and structural disorder. 

The disorder of the atomic structure is the main feature which distinguishes amorphous from crystalline materials. It is of particular significance in semiconductors, because the periodicity of the atomic structure is central to the theory of crystalline semiconductors. Bloch s theorem is a direct consequence of the periodicity and describes the electrons and holes by wavefunctions which are extended in space with quantum states defined by the momentum. The theory of lattice vibrations has a similar basis in the lattice symmetry. The absence of an ordered atomic structure in amorphous semiconductors necessitates a different theoretical approach. The description of these materials is developed instead from the chemical bonding between the atom, with emphasis on the short range bonding interactions rather than the long range order. 

The glassy state of materials refers to a nonequilibrium, solid state, such as is typical of inorganic glasses, synthetic noncrystalline polymers and food components. Characteristics of the glassy state include transparency, solid appearance and brittleness (White and Cakebread 1966 Sperling 1992). In such systems, molecules have no ordered structure and the volume of the system is larger than that of crystalline systems with the same composition. These systems are often referred to as amorphous (i.e., disordered) solids (e.g., glass) or supercooled liquids (e.g., rubber, leather, syrup) (Slade and Levine 1991 Roos 1995 Slade and Levine 1995). 

Milling of crystalline materials introduces or increases amorphous character as the result of the significant mechanical activation that takes place during the process, including friction, deformation, attrition, and agglomeration. The extent of disorder, or... 

It is the heteropoiysaccharides of plants that bestow cellulosic composites with the ability to absorb impact, the ability to absorb moisture, and the ability to create pores in the form of free volume in amorphous (disordered or para-crystalline) materials [58,59]. Modification by reducing molecular regularity has the additional benefit of creating a transition from a focus on mechanical (structural) functions to an emphasis on energy storage and gel formation. Reduction in order translates into ease of hydrolysis, enzyme accessibility, rate of nutrient release for decay organisms, water absorption and swelling. Reduction in order is achieved by the introduction of monosaccharide units, and of bond types, which differ from those of cellulose. The principal monosaccharides involved in the heteropoiysaccharides of plants are shown in O Fig. 12. 

There are now many classes of problems that have been studied using total scattering analysis. Traditionally it was used for liquids and amorphous materials,more recently for the study of disorder in crystalline materials, and now with increasing popularity it is used to study nanostructured materials. Several recent reviews give examples of modern applications of the PDF method. 

The amorphous state, therefore, can be arrived at by methods other than melting and quenching and all such methods result in the loss of crystalline order. All these processes introduce additional enthalpy into the disordered material. Therefore amorphous materials crystallize irreversibly when heated to a temperature, below T of the parent crystalline material and the process is exothermic. The free energy of the amorphous state of a material is higher than that of its crystalline state. Thus the enthalpy addition (A//) during amorphization has to be generally... 

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