Defect aggregation

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. 

In the last decades, both experimental data [2, 51] and theoretical studies [52-56] revealed the effect of the statistical similar defect aggregation under defect accumulation (permanent particle source). It means that the initial random mixture of defects of two kinds A and B during bimolecular reaction is... 

Fig. 3.8. Qualitative illustration of the similar defect aggregation under irradiation, (a) Random distribution, mean distance between defects r exceeds the recombination radius R. (b) New pair is created near the pre-existing defects, (c) It disappears, (d) Similar defect aggregates could be established, if newly-created defects find themselves near defects of the same kind.

In the last several decades, both experimental data and theoretical studies [5, 9, 13-15] have revealed the effect of similar defect aggregation in the course of the bimolecular A+B —> 0 reaction under permanent particle source (irradiation) - the phenomenon similar to that discussed in previous Chapters for the diffusion-controlled concentration decay. Radiation-induced aggregation of similar defects being observed experimentally at 4 K after prolonged X-ray irradiation [16] via both anomalously high for random distribution concentration of dimer F2 centres (two nearest F centres) and directly in the electronic microscope [17], permits to accumulate defect concentrations whose saturation value exceed by several times that of the Poisson distribution. 

In order to study theoretically defect aggregation, several methods of physical and chemical kinetics were developed in recent years. Irrespective of the particular method used, the two basic approaches - a continuous and discrete-lattice ones - are used. In the former model intrinsic defect volume is ignored and thus a number of similar defects in any volume element is unlimited. In its turn, in the latter model any lattice site could be occupied by no more than a single particle (v or i) [15]. 

Note that equations (7.1.57) and (7.1.58) are of rather limited use since they are derived for large diffusion coefficients D when defect aggregation is not well pronounced. Moreover, equation (7.1.57) assumes existence of the steady-state for d = 2 whereas other methods discussed in [15] argue for the macroscopic defect segregation occuring here even for mobile defects. In this respect of great interest is the generalization of the more correct accumulation equations (7.1.50) to (7.1.52) presented below for the case of mobile 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. 

The rate at which the cluster formation occurs can be measured as a function of dopant concentration and temperature to obtain kinetic information about the defect aggregation mechanism. 

Defective aggregation in response ADP, TXA2, thrombin, collagen shape change normal (Offermans et al. 1997 Ohlmann et al. 2000). 

On this view, interaction between defects determines the concentration at which a phase becomes saturated with defects, and also the manner in which defects aggregate or order. It can be foreseen that stoichiometrically defined intermediate phases are likely to undergo an order-disorder transition at higher temperatures and that, in general, some detectable stoichiometric range is likely before the disordering temperature is reached. 

Taylor W. R., Jaques A. L., and Ridd M. (1990) Nitrogen-defect aggregation characteristics of some Australasian diamonds time-temperature constraints on the source regions of pipe and alluvial diamonds. Am. Min. 75, 1290-1310. 

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... 

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. 

The defect aggregates themselves, depending on the nature of the defect, can acquire a net charge on the surface by trapping either electrons or positive holes. This allows them to trap further defects to increase the aggregate size. The step in this reaction may be sym-bohzed as follows, using the simple case of aggregation of F-centre defects to produce metal M from an ionic solid MX ... 

Fig. 42.— Energy diagram for decomposition of metallic azid.es ia) defect aggregate before separation from azide lattice and (b) metallic nucleus after separation.

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