Lattice defects clusters

It is possible for one or more lattice defects to associate with one another, that is, to cluster together. These are indicated by enclosing the components of such a cluster in parentheses. As an example, (VMVX) would represent a defect in which a vacancy on a metal site and a vacancy on a nonmetal site are associated as a vacancy pair. 

The thermodynamic functions of non-stoichiometric solids at very high deviations from stoichiometry are strongly affected by defect clusters and molecularities. The detailed theoretical description of the interactions between defects and the lattice as well... 

It is theoretically possible for cations to occupy anion sites, and vice versa. Kroger-Vink notation, then, dictates that an M atom on an X site be designated as Mx and that an X atom on an M site be designated as Xm- Recall that we can have defect clusters, such as a Frenkel defect. Defect clusters are enclosed in parentheses—for example, (VmVx) or (X Xm)—to indicate that the individual defects are associated with one another. Impurity atoms are also coded as to lattice position. If we introduce a metal impurity atom L into our compound MX, it might occupy a metal cation site, and is thus designated as Lm- Similarly, Sj is an S impurity atom on an interstitial site. 

Regardless of whether the non-imaging of a species is due to preferential field evaporation or to preferential field ionization, the distinguisha-bility of alloy components in ordered alloys makes much easier the identification of lattice defects and of all types of domains, such as orientational and translational domains, and the discernment of order-disorder phase boundaries in ordered alloys, as well as facilitating the study of clustering and order-disorder phase transformation, etc.88 In most cases, image interpretations become self-obvious. For example in PtCo, which has the LI 0 structure, a Co layer can be distinguished from a... 

Fig. 5.19 A helium field ion image of a tungsten tip electroplated with a thick layer of platinum. Many lattice defects such as grain boundaries, twin boundaries, vacancies and vacancy clusters can be seen. From the work of Rendulic ...

The effects of damage by ion implantation on the low-temperature diffusion of dopant can also be studied by implanting Si+ or Ge+ ions into predeposited layers in Si. Recently, Servidori et al. (58) studied the influence of lattice defects induced by Si+ implantation. Using triple crystal X-ray diffraction and TEM, they confirmed (1) that below the original amorphous surface-crystal interface, interstitial dislocation loops and interstitial clusters exist and (2) that epitaxial regrowth leaves a vacancy-rich region in the surface. 

The catalytic behavior of solid materials is certainly largely governed by the nature of their few topmost atomic layers. However, it can be assumed that these layers are frequently related to the bulk properties of the materials. If one goes along with this preposition, catalytic performance should also be related at least partly to these properties. Then in turn, an expert system should not only incorporate surface but also bulk properties, such as crystallographic structure, lattice parameters, cluster sizes, electronic conductivity and concentration of ion defects. 

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. 

Glusker JP, Traeblood KN (1985) Crystal Stmctnre Analysis. 2nd edition. Oxford Univ Press, Oxford, UK Gnutzmaim V, Vogel W (1990) Surface oxidation and reduction of small platinum particles observed by in situ X-ray diffraction. Z PhysikD (Atoms, Molecules, Clusters) 12 597-600 Greenwood NN (1970) Ionic Crystals Lattice Defects and Norrstoichiometry. Butterworths, London Guinier A (1963) X-ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies. W H Freeman, San Francisco... 

Electron microscopic studies in the 1940s proved that supported catalysts possess a crystalline structure, dispelling earlier conjecture of amorphicity. However, practical catalysts are never uniform, exhibiting particle size distribution, lattice defects (Frenkel or Schottky), and dislocations. The following questions then arise Are all lattice surfaces equally active Do surface clusters of particles and surface atoms have comparable activity Does catalytic activity depend on particle size Is there an optimal particle size or distribution These questions remain, in general, still unanswered. However, in recent electrocatalytic studies concern about these effects is shown, following similar concern in conventional heterogeneous catalysis. 

Presence of these interstices provides to the fluorite stmcture extremely specific features. In UO2 particularly, it allows for placement of some radioactive decay products, these sites are responsible for existence of hyperstoichiometric UO2+X phase, where the extra oxygen ions fill the empty interstitial sites in the fluorite lattice etc. First case is extremely important in radiation damaged UO2. Second one is cmcial in oxidation of pure UO2 in atmospheric conditions. Diffusion of atmospheric oxygen into the bulk of crystal brings excess oxygens into empty interstices. These become filled more or less randomly only at low x, at higher concentration of extra anions they form different types of clusters, including so-called 2 2 2 Willis dimers Willis), tetra- and pentameric defects clusters of cuboctahedral symmetry Allen and Tempest). Last defects appear due to interaction of extra anions with intrinsic crystal FP defects (anion Frenkel pairs, i.e. anion vacancies and anion interstitials). 

Figure 4. Defects clusterings in UO2 after thermal shock, quenching and annealing periods. Dark spheres symbolize oxygen ions in interstitial positions, light grey spheres represent vacancies in oxygen sub-lattice. Two interstitial-centred CO(l3) and one CO(l2) self-assembled globular clusters are clearly seen. Uranium and oxygen ions in their lattice positions are not shown for the sake of clarity.

The interaction of lattice defects in fluorite-like solids under conditions when the thermal motion is restricted, leads to self-assembling of the long-living metastable globular clusters. The same effect was observed in hyper-stoichiometric and radiation-damaged UO2+X Yakub, 2008). At elevated... 

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