Point defects clustering

Three-dimensional (volume) defects—point defect clusters, voids, precipitates. 

Figure 1.11. Schematic diagrams of (a) and (b) Fei j O point defect clusters (after Koch and Cohen 1969) (c) clustering in fluorite-type structures and (d) the Cap2 structure.

The superlattice can be indexed as the (101) -phase. The HRTEM in figure 3.18(a) shows a contrast (circled and arrowed) indicative of cation point defect clusters. 

Fig. 2. Etch pits produced by point-defect clusters. (A) pits beginning to form at small precipitates (B) pits become flat-bottomed when precipitates are gone (C) small pits caused by precipitates in LiF (D) same as (C) after more etching (large pits are at dislocations).

The point defect clusters described in earlier sections can be legitimately termed extended defects. In this section, defects that are less easily considered in terms of point defects will be described. Perhaps the best known of these are the planar boundaries, the most abrupt example being the crystal surface itself (see Surfaces Semiconductor Interfaces). 

We can finally conclude that the number of chemical systems which appear to reject point-defect populations as a mode of accommodating their non-stoicheiometric behaviour is large and varied and here we have touched upon only a few which make use of planar faults or parallel lamellar or foliar intergrowth structures. The results presented show that physical terms, such as elastic strain, are of importance in controlling the microstructures of such phases, but whether they form or whether they coexist with some form of point-defect clusters may well depend in a sensitive way to the anion-cation bonding within the individual co-ordination polyhedra which made up the structure. The continuing research in this area is certain to produce new and unexpected results before complete answers to the problems posed here are found. 

Figure 4 Point defect clusters in Fe i 0. The open circles represent cation vacancies and the shaded circles Fe + interstitials. The unmarked cube vertices are occupied by oxide ions, (a) 4 1 cluster (b) 6 2 cluster, (c) 8 3 cluster, (d) 16 5 cluster. In (d), four 4 1 clusters are arranged tetrahedrally around a central cluster, drawn with heavy outline...

Defect structure of neutron-irradiated Fe-Cr alloys contains free vacancies, SIA, VC, pure dislocation loops, dislocation loops decorated by Cr atoms, and vacancy-Cr complexes as well as Cr precipitates depending on the irradiation regime (Malerba et al. 2008). The CD model in our study is close to the model proposed by Christien and Barbu (2004), where the CD simulations are first performed for the free vacancies, SIAC, and point defect clusters and then for the precipitates, taking into account the steady state values of the free point defects concentrations obtained in the first step. In addition, we take into account the Cr-effect on the SIA diffusivity according to the density functional theory (DFT) calculations (Terentyev et al. 2008). 

Since the details of these equations are explained elsewhere, only key ideas are briefly described here. One of these is to classify the solute atom clusters into irradiation-induced clusters and irradiation-enhanced clusters. Irradiation-induced clusters correspond to solute atom clusters with or without Cu atoms, whose formation mechanism is assumed to be the segregation of solute atoms based on point defect cluster or matrix damage (heterogeneous nucleation). On the other hand, the irradiation-enhanced clusters correspond to so-called CRPs (Cu-rich precipitates) or CELs (Cu-enriched clusters), and the formation mechanism is the clustering of Cu atoms above the solubility limit enhanced by the excess vacancies introduced by irradiation. This model also assumes that the formation of solute atom clusters and matrix damage is not independent to each other, which is a very different model from the conventional two-feature models as described in the previous sections. Another key idea is the introduction of a concept of a thermal vacancy contribution in the diffusivity model. This idea is essentially identical to that shown in Rg. 11.11. This is a direct modeling of the results of atomic-level computer simulations. ... 

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