Point defect: also clusters

Apart from its function as a point defects trap, Ti diffuses towards structure dislocations to form Cottrell-type atmospheres that can block the restoration and the rise of the initial lattice. Weertman and Green [41] demonstrated that these dislocations, thus decorated by dense clusters of large solutes such as Ti, become neutral sinks that cause unbiased elimination of point defects and therefore an increase in the resistance to swelling. Furthermore, by screening dislocations from the arrival of point defects, these clusters are probably conducive to mutual recombinations close to the decorated dislocations which will also tend to increase the resistance to swelling ... 

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. 

As in the case of wiistite, one of the earliest applications of atomistic simulations was to explore the likely stability of this defect cluster. It was found that not only the 2 2 2 arrangement but also other cluster geometries were preferred over isolated point defects. 

The type and concentration of defects in solids determine or, at least, affect the transport properties. For instance, the -> ion conductivity in a crystal bulk is usually proportional to the -> concentration of -> ionic charge carriers, namely vacancies or interstitials (see also -> Nernst-Einstein equation). Clustering of the point defects may impede transport. The concentration and -> mobility of ionic charge carriers in the vicinity of extended defects may differ from ideal due to space-charge effects (see also - space charge region). 

The free electrons and holes are denoted as e and h, respectively. The simplest defect clusters are usually written by listing all point defects between parentheses, with subsequent superscript showing the cluster effective charge. Note that parentheses and brackets are sometimes used also to indicate local coordination in the lattice. 

The MX2+X phases contain interstitial anions. As with the anion-deficient phases, these interstitials are not random point defects, but ordered or clustered. The earliest cluster geometry to be postulated was the [2 2 2] cluster in UO2+J, the prototype anion-excess flnorite phase. The cluster is composed of 2 interstitial oxygen atoms displaced along (110), two interstitial oxygen atoms displaced along (111) in UO2+J (Figure 5). Other cluster geometries have also been proposed in this oxide, and the defect structure of this well studied phase is still not completely resolved. 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

It is not possible to give here a complete review of DMol applications, so only a non-systematic selection of applications is mentioned here. Applications to chemical reactions have been studied by Seminario, Grodzicki and Politzer [10]. Buckminster-fullerenes have been studied by various groups [11] including also nonlinear optical properties [8] and the geometrical structure of Cs4 [13]. Cluster model studies of surfaces with adsorbates are reported in [14-17]. Cluster models for point defects in solids, in particular spin density studies of interstitial muon can be found in [18,19]. Spin density studies of molecular magnetic materials are in ref [20]. Polymers have been studied by Ye et al [21]. 

In this respect, the cluster size, from which on the defect-induced perturbation on the electronic structure disappears, is a key quantity. The calculations showed [178] that effect of the surface defects on the adhesion energy decreases rapidly with cluster size. Thus, for particles of nanometer size, differences in the bonding to the substrate tend to vanish as the larger polarizability of the particle screens the effect of the defect and the relative effect of defect-related bonds become less important due to the larger number of metal-oxide bonds at the interface. However, because point defects are the most likely sites for the initial steps of nucleation, one has to expect that also large metal particles are still located at these sites unless the temperature is sufficiently high to permit diffusion of particles. 

Defects in ceramics can be charged, which are different from those in metais. For a simple pure ionic oxide, with a stoichiometric formula of MO, consisting of a metal (M) with valence of +2 and an oxygen (O) with valence of -2, the types of point defects could be vacancies and interstitials of both the M and O, which can be either charged or neutral. Besides the single defects, it is also possible for the defects to associate with one another to form defect clusters. Electronic defects or valence defects, consisting of quasi-free electrons or holes, are also observed in crystalline solids. If there are impurities, e.g., solute atoms Mf, substitutional or interstitial defects of Mf could be formed, which can also be either charged or neutral. 

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