Defect vacancy

We have shown that by stacking atoms or propagation units together, a solid with specific symmetry results. If we have done this properly, a perfect solid should result with no holes or defects in it. Yet, the 2nd law of thermod5mamics demands that a certain number of point defects (vacancies) appear in the lattice. It is impossible to obtain a solid without some sort of defects. A perfect solid would violate this law. The 2nd law states that zero entropy is only possible at absolute zero temperature. Since most solids exist at temperatures far from absolute zero, those that we encounter are defect-solids. It is natural to ask what the nature of these defects might be. 

Cairns-Smith is careful enough to concede that the first hypothetical informationcarrying material was not of necessity a clay mineral however, the basic features of the model can best be demonstrated using different clay species. Thus, for example, clays could have crystallized out in sandstone pores from solutions containing products derived from weathering. The result would have been clay layers, which could have been separated and transported further by external influences replication under similar conditions would have followed. Such crystallization processes would have also involved errors, such as defects, vacancies, and the incorporation of other ions or atoms these inorganic mutations would have been passed on, i.e., they would have been incorporated into the next sheet to be formed. 

Figure 1.1 Defects in crystalline solids (a) point defects (interstitials) (b) a linear defect (edge dislocation) (c) a planar defect (antiphase boundary) (d) a volume defect (precipitate) (e) unit cell (filled) of a structure containing point defects (vacancies) and (/) unit cell (filled) of a defect-free structure containing ordered vacancies. ...

Associated defects (vacancy pair) (VMVr) Associated defects with positive effective charge (VmVp) ... 

Fcaj, coexist with vacancies on Fe sites, VFe (Section 1.10). The iron sites, therefore, contain populations of two defects, vacancies and aluminum atoms. 

Defects in MWCNTs are always present. We can briefly differentiate between topological defects which lead to rehybridization (C5 and C7 rings instead of C6 lead to rehybridization between sp2 and sp3) and incomplete bonding defects (vacancies, dislocation) (Fig. 16.2). Functionalization or doping with heteroelements may add further modifications with respect to the ideal ordered structure, but are also the sites which allow for anchoring supported metals or metal oxides, or to functionalize the CNTs with organic groups. 

The term surface of a metal usually means the top layer of atoms (ions). However, in this book the term surface means the top few (two or three) atomic layers of a metal. Surfaces can be divided into ideal and real. Ideal surfaces exhibit no lattice defects (vacancies, impurities, grain boundaries, dislocations, etc.). Real surfaces have all types of defects. For example, the density of metal surface atoms is about 10 and the density of dislocations is on the order of magnitude 10 cm . ... 

Introduction of defects (vacancies or interstitials) in a perfect lattice determines a variation in the free energy G of the lattice which may be written as ... 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

Figure 5.1 Point defects in ionic solids Schottky defect, vacancy pair, Frenkel defect and aliovalent impurity (for definitions see Section 5.2).

Convince yourself that if there were nu defect vacancies m the 1-2-3 superconducting slab, its empirical formula would be Ba Cu Oi. ... 

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

Figure 2-5. Relative defect (vacancy) fraction as a function of alloy composition rVB (see Eqn. (2.78)), if defects interact differently with nearest neighbors A and B. (I) Ah = 0 (2) Ah — 0.6 R T (for definition of Ah see text).

Irradiation of all kinds of solids (metals, semiconductors, insulators) is known to produce pairs of the point Frenkel defects - vacancies, v, and interstitial atoms, i, which are most often spatially well-correlated [1-9]. In many ionic crystals these Frenkel defects form the so-called F and H centres (anion vacancy with trapped electron and interstitial halide atom X° forming the chemical bonding in a form of quasimolecule X2 with some of the nearest regular anions, X-) - Fig. 3.1. In metals the analog of the latter is called the dumbbell interstitial. 

It should be remembered that even for isotropic defects their elastic interaction is anisotropic, due to crystalline anisotropy, equation (3.1.4). A pair of the simplest Frenkel defects - vacancy and an interstitial atom - attract each other in the direction (100), but their interaction becomes repulsive, e.g., along (111) and (101) axes. 

It should be noted in conclusion of this Section that preliminary results obtained by means of the discrete lattice formalism are presented in [85], This study demonstrates clearly the cooperative nature of the aggregation of two kinds of the Frenkel defects, vacancies and interstitials. 

Alan Allnatt s research interests at Western Ontario have been concerned with the statistical mechanics of the transport of matter through crystals. His earliest work centered on obtaining methods for calculating the equilibrium distributions and thermodynamic properties of the point defects (vacancies, interstitials, solutes) that make transport possible. He first studied dilute systems, so the methods could be largely analytical. The methods for ionic crystals,... 

An extension of the kinetic theory on cases when a mechanical pressure interacts with kinetic processes inside solid volume and on interfaces has wide application interests. The elastic deformations in solid are presented from influence of external forces and from presence of internal defects of crystal structure point defects (vacancy, intersite atoms, complexes of atoms, etc.), extended defects (dislocations and inner interfaces in polycrystals), and three-dimensional defects (heterophases crystals, polycrystals). 

In addition to mechanical properties, other physical properties of polycrystaUine materials, such as electrical and thermal conduction, are also affected by microstmcture. Although polycrystals are mechanicaUy superior to single crystals, they have inferior transport properties. Point defects (vacancies, impurities) and extended defects (grain boundaries) scatter electrons and phonons, shortening their mean free paths. Owing to... 

Therefore, the related defect concentration depends on the impurity level and or temperature. When we consider the thermodynamics for the formation of point defects, vacancies are important, i.e., = N (T). 

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