Point Defect Aggregations

Non-stoichiometric oxides with high levels of disorder may adopt two modes of stabilization aggregation or elimination of point defects. Point defect aggregates forming clusters are examples of the former and extended defect structures like crystallographic shear-plane structures are examples of the latter. 

Shear Plane-Point Defect Equilibria.—The question of the existence of point defects in compounds where extended defects are known to occur has been controversial. Indeed, it has occasionally been claimed that point defects cannot form in such phases and that they will always be eliminated with the formation of extended structures. We reject these latter arguments as thermodynamically unsound. From a thermodynamic standpoint, the formation of extended defects can be viewed as a special mode of point defect aggregation as such, shear planes will be in equilibrium with point defects, with the position of the equilibrium depending on both temperature and the extent of the deviation from stoicheiometry. Thus, if we assume, as is suggested by our calculations, that anion vacancies are the predominant point defects in reduced rutile (a further point of controversy as mentioned above) then there will exist an equilibrium of the type... 

It seems therefore that little or no stability is to be expected for the point defect aggregates which provide the necessary shear-plane precursors in the homogeneous shear-plane formation mechanisms. These homogeneous nucleation mechanisms are therefore unlikely to operate, and we turn our attention now to a heterogeneous mechanism, in which point defects aggregate at pre-existing planar-defect sites. 

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. 

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. 

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.]...

An exactly similar situation can be envisaged if the crystal contains a high population of interstitial point defects. Should these aggregate onto a single plane, a dislocation loop will once again form (Fig. 3.14c). 

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. 

At sufficiently high temperatures, the radiation damage will recover by recombination of the point defects and their aggregates. The various annealing steps have been... 

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). 

More information about these approaches and their advantages readers could find in [14, 15, 64, 65] in this Section 7.2 we focus on the further improvement of the microscopic approach to the defect aggregation via taking into account elastic attraction between point defects. 

Observe the aggregation kinetics as point defects coalesce to form clusters or other phases. 

The existence of free interstitial point defects forming the complements to the vacancy centers is generally not observed following irradiation at room temperature. At these temperatures the interstitials cluster together to form interstitial aggregates and dislocation loops. However, lattice disorder can slow down or prevent the aggregation process due to interstitial trapping. 

The predominance in non-stoicheiometric compounds of structures based on point defects or defect aggregates indicates that in most compounds > Ep the repulsion energy outweighs the defect elimination term. This suggests that in those materials where shear planes form we should look for some special factor which... 

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