Defects hierarchy

Defects are often classified in terms of a dimensionality. This is known as the defect hierarchy. The classifications are given in Table 11.1. In spite of this table, remember that all these defects are three-dimensional. We will first summarize the different types of point defect that can occur in crystalline materials. To provide some idea of the importance of point defects, we will consider some specific examples. 

In view of the reported growing importance ascribed to folic acid deficiency in the prevention of various disease conditions, such as neural tube defects, megaloblastic anemia, colon cancer, and colorectal cancer, a dissolution requirement is specified for folic acid when it is present in multivitamin-mineral combination products. Currently, the dissolution standard required in the official articles of dietary supplements (including vitamin-mineral combination products) places folic acid outside the index vitamin hierarchy. Therefore, a mandatory dissolution test for folic acid is required that is independent of and in addition to the mandatory index vitamin test for multivitamin preparations containing folic acid. 

The kinetics of the diffusion-controlled reaction A + B —> 0 under study is defined by the initial conditions imposed on the kinetic equations. Let us discuss this point using the production of geminate particles (defects) as an example. Neglecting for the sake of simplicity diffusion and recombination (note that even the kinetics of immobile particle accumulation under steady-state source is not a simple problem - see Chapter 7), let us consider several equations from the infinite hierarchy of equations (2.3.43) ... 

Of special interest in the recent years was the kinetics of defect radiation-induced aggregation in a form of colloids-, in alkali halides MeX irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles with several nanometers in size were observed [58] more than once. Several theoretical formalisms were developed for describing this phenomenon, which could be classified as three general categories (i) macroscopic theory [59-62], which is based on the rate equations for macroscopic defect concentrations (ii) mesoscopic theory [63-65] operating with space-dependent local concentrations of point defects, and lastly (iii) discussed in Section 7.1 microscopic theory based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of defects). 

It is not an easy task to define inhomogeneities in the structure of a polymer network. Every system will exhibit the presence of defects and fluctuations of composition in space when the scale of observation becomes smaller and smaller. A hierarchy of structures exists, from atomic dimensions to the macroscopic material. A scheme of different scale levels used to describe linear and crosslinked polymer structures is shown in Fig. 7.2. Inhomogeneities described in the literature for polymer networks are ascribed to permanent fluctuations of crosslink density and composition, with sizes varying from 10 nm up to 200 nm. This means that their size lies in the range of the macromolecular scale. 

At each magnification starting from low to high we observe more and more detailed information until atoms are observed. It is possible to describe a hierarchy of defects since they are embedded in the material - they are merely members of a set of discrete objects which represent deviations from the ideal structure. The analyst is faced with the task of describing the sets of defects and conditions under which they are detrimental to the operation of the device. 

In 1990, Canham observed intense visible photoluminescence (PL) from PSi at room temperature. Visible luminescence ranging from green to red in color was soon reported for other PSi samples and ascribed to quantum size effects in wires of width 3 nm (Ossicini et al, 2003). Several models of the origin of PL have been developed, from which we chose two. In the first (the defect model), the luminescence originates from carriers localized at extrinsic centers that are defects in the silicon or silicon oxide that covers the surface (Prokes, 1993). In the second model (Koch et al., 1996), absorption occurs in quantum-confined structures, but radiative recombination involves localized surface states. Either the electron, the hole, both or neither can be localized. Hence, a hierarchy of transitions is possible that explains the various emission bands of PSi. The energy difference between absorption and emission peaks is explained well in this model, because photoexcited carriers relax into surface states. The dependence of the luminescence on external factors or on the variation of the PSi chemistry is naturally accounted for by surface state changes. 

There is a lack of atomistic-scale understanding of the role of various specific chemical species in the initiation of corrosion processes. Eor example, the role of ions on the precise atomic scale in processes such as pitting or cracking represents one opportunity for research. Moreover, the hierarchy of important defects across the length scales has been established only in a rudimentary way, and understand-... 

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