Aggregation of defects

In their turn, the equations (4) and (5) correspond to taking account of two more terms of this expansion respectively. (It was erroneously stated in [41] that the coefficient of the cubic term of equation (5) equals -0.01, which was then copied in all the experimental studies that used this approximation.) However, it is not always acknowledged that these two equations also assume the absence of aggregation of defects the authors [41] propose using of equation (5) up to the saturation concentration. Therefore it is not justified to extrapolate the rate of accumulation of defects to a zero value for obtaining n0 from equations (3)-(5) (cf. [43,44,46]). Actually the saturation concentration can exceed several times the value predicted by these equations. 

Fig. 24.— Development of new energy bands in large aggregate of defects (F-centres).

If the technique of X-ray crystallography had attained sufficient refinement, it would be possible to determine by sin e-crystal analysis the nature of the defects present and their distribution over the possible sites in a structure, even for small defect concentrations. As it is, intensity measurements have been used in a few instances of grossly defective structure. The study of the structure of aggregates of defects is one which is of the utmost importance in the chemistry of the solid state refinement of the technique of X-ray or electron diffraction to the point where this is possible would be a significant advance. 

We will present a model which provides a self-consistent answer to the above questions based on the transport and aggregation of defects in glassy systems. 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

Graphite is commonly produced by CVD and is often referred to as pyrolytic graphite. It is an aggregate of graphite crystallites, which have dimensions (L ) that may reach several hundred nm. It has a turbostratic structure, usually with many warped basal planes, lattice defects, and crystallite imperfections. Within the aggregate, the crystallites have various degrees of orientation. When they are essentially parallel to each other, the nature and the properties of the deposit closely match that of the ideal graphite crystal. 

Changes in density, unit cell dimensions, and macroscopic volume have serious effects. In an environment where point defects (or aggregates of point defects) are generated, such as in the components of nuclear reactors, or in vessels used for the storage of nuclear waste, where point defects are produced as a result of irradiation, dimensional changes can cause components to seize or rupture. 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

Figure 3.1 Electron micrograph showing a dislocation in silver, imaged as a dark line. The small triangular features that decorate the dislocation are stacking faults formed by the aggregation of point defects. [From W. Sigle, M. L. Jenkins, and J. L. Hutchison, Phil. Mag. Lett., 57 267 (1988). Reproduced by permission of Taylor and Francis, http //www.informa world.com.]...

Even when the composition range of a nonstoichiometric phase remains small, complex defect structures can occur. Both atomistic simulations and quantum mechanical calculations suggest that point defects tend to cluster. In many systems isolated point defects have been replaced by aggregates of point defects with a well-defined structure. These materials therefore contain a population of volume defects. 

Although this is correct in one sense, isolated iron vacancies appear not to occur over much of the composition range. Instead, small groups of atoms and vacancies aggregate into a variety of defect clusters, which are distributed throughout the wustite matrix (Fig. 4.6). The confirmation of the stability of these clusters compared to isolated point defects was one of the early successes of atomistic simulation techniques. 

Most reported zeolite/polymer mixed-matrix membranes, however, have issues of aggregation of the zeolite particles in the polymer matrix and poor adhesion at the interface of zeolite particles and the polymer matrix. These issues resulted in mixed-matrix membranes with poor mechanical and processing properties and poor separation performance. Poor compatibility and poor adhesion between the polymer matrix and the zeolite particles in the mixed-matrix membranes resulted in voids and defects around the zeolite particles that are larger than the micropores of the zeolites. Mixed-matrix membranes with these voids and defects exhibited selectivity similar to or even lower than that of the continuous polymer matrix and could not match that predicted by Maxwell model [59, 60]. 

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