Defect zero-dimensional

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

Point defects (zero-dimensional defects) indicate a fault within one site of the crystal lattice. This can be either a vacant site (called a vacancy), or an atom (ion) in the interstitial site. The impurity species can be also treated as point defects. Often, electronic defects are also ascribed to this group, especially if the electronic charge carriers are localized. 

During crystal growth defects in the ideal crystal lattice can occur. They are characterized as zero-, one-, or two-dimensional. A vacancy or an interstitial atom is a zero-dimensional defect due to a missing atom on a lattice place or an additional atom on an interstitial (Figure 1.11). 

A zero-dimensional defect in the lattice creates varying distances between the neighboring atoms, which also generate tensions. 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

The defects in solids can be classified according to the dimensions of the region of translation symmetry disruption. When one or a few nearest host crystal sites are disturbed, we speak of point (zero-dimensional) defects, called also local defects. Also known are extended defects that introduce structural imperfections in lattice directions - linear (one-dimensional) defects or in the lattice planes planar or two-dimensional defects). The surface of a crystal and dislocations are the important examples of two-dimensional and linear defects, respectively. 

Point defect or zero-dimensional defect. This kind of defects include both the possible existence of vacancies and substituted impurity atoms on their sites of crystal lattice structure and include misplaced parts of atoms with each other in solid compound of AB, namely, A atom occupies the B atomic site, while inversely B atom occupies A, or to say there are misplaced atoms or variable valence ions on the sublattice sites. The interstitial atoms sited in the interstitials of lattice structure are also parts of those point defects. It can further be divided into Schottky defects and Frenkel defect. The former means a metal atomic defect and the original metal atoms are transformed to the metal surface and the latter is composed of an atomic defect and an interstitial atom, as presented in Fig. 3.23. It could be imagined that the existence of inner defects would bring the distortions of lattice, as shown in Fig. 3.24. The issue of point defect is the major subject and key problem for the studies of solid chemistry. 

Point-like (zero dimensional) defects are also present in polymeric crystals. They arise from the presence of chain ends, kinks (see example in Fig. 7.8) and jogs (molecular defects with collinear stems on each side of the defect). 

Figure 10.15. Illustration of Frank-Read source of dislocations under external stress the original dislocation (labeled 1) between two zero-dimensional defects is made to bow out. After sufficient bowing, two parts of the dislocation meet and annihilate (configuration 6), at which point the shorter portion shrinks to the original configuration and the larger portion moves away as a dislocation loop (configuration 7, which has two components).

We distingiiish between point defects (zero dimensional defects) — these are atomic and electronic imperfections line (one-dimensional) defects — these are essentially dislocations plane (two-dimensional) defects — i.e. surfaces and basically internal interfaces and pores or inclusions as three-dimensional defects. We will not discuss other variants of higher-dimensional disorder, which can be very compleot, particularly in multiphase systems. Since we concentrate on the equilibrium state in this chapter, we are primarily interested in point defects and surfaces. Point defects exist at equilibrium on accoimt of entropy surfaces are a necessary consequence of the requirement that the amoimt of substance is finite. Defects of other types are necessarily nonequilibrium phenomena", which will be demonstrated in Section 5.4. Nonetheless, the higher-dimensional defects will, as metastable structure elements, be important for us later (see Sections 5.4, 5.8). 

Zero dimensional defects, generally known as point defects, represent the substitution of one atom for another on a given lattice site in the structure, the absence of an atom, or atoms lying between sites in a crystalline material. 

Point defects can, for the sake of cataloging, be considered to be zero dimensional. Extended defects with higher dimensionality can also be described. One-dimensional defects extend along a line, two-dimensional defects extend along a plane, and three-dimensional defects occupy a volume. In this chapter these extended defects are introduced. 

Point defects are only notionally zero dimensional. It is apparent that the atoms around a point defect must relax (move) in response to the defect, and as such the defect occupies a volume of crystal. Atomistic simulations have shown that such volumes of disturbed matrix can be considerable. Moreover, these calculations show that the clustering of point defects is of equal importance. These defect clusters can be small, amounting to a few defects only, or extended over many atoms in non-stoichiometric materials (Section 4.4). 

Zero-dimensional point defects, such as Schottky and Frenkel defects. 

Defects can be further classified into point defects and extended defects. Unassociated point defects are associated with a single atomic site and are thus zero-dimensional. These include vacancies, interstitials, and impurities, which can be intrinsic or extrinsic in nature. Extended defects are multi-dimensional in space and include dislocations and stacking faults. These tend to be metastable, resulting from materials processing. The mechanical properties of solids are intimately related to the presence and dynamics of extended defects. A discussion of extended defects is deferred until Chapter 10. For now, only point defects are covered. Their importance in influencing the physical and chemical properties of materials cannot be overemphasized. 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

Point Defects These are zero dimensional consisting of atoms present in the spaces between the lattice positions, vacancies, and foreign atoms in lattice positions. Line defects are one dimensional consisting of edge dislocations and screw... 

Very few crystals are perfect. Indeed, in many cases they are not required to be, since lattice imperfections and other defects can confer some important chemical and mechanical properties on crystalline materials. Surface defects can also greatly influence the process of crystal growth. There are three main types of lattice imperfection point (zero-dimensional, line (one-dimensional) and surface (two-dimensional). 

Point defects are zero-dimensional (Figure 10.6) and they are the only defects that are thermodynamically stable. Line and plane defects are not thermodynamically stable and do not occur in equilibrium states. Point defects determine the extrinsic physical properties of solids such as electrical conductivity, work function, and color as well as the chemical properties such as dififusivity, stoichiometry, and sinter rate. Some examples of point defects are (a) vacancies, where atoms or ions that should be on lattice sites are missing (b) interstitials which are atoms or ions between the regular lattice sites of a solid (c) foreign atoms or... 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

The zero-dimensional or point defects were the major object of this review. They are much difieroit for polymer aystals when compared to small-molecule... 

Finally, there are zero-dimensional or point defects that could also be considered part of the microstructure of the material. These include vacancies or foreign atoms substituting at atomic positions in a crystal lattice as well as interstitial atoms residing in between the normal atomic sites. They are not discussed further in this chapter, partly due to limited space and partly because they are not amenable to observation by the same sorts of microscopic techniques typically used to define the other aspects of the material microstructure. More information can readily be found in the many existing treatises on point defects and crystal chemistry in the literature. ... 

Defects play a major role in the performance of materials, some wanted and some unwanted. Therefore, it is necessary to understand what they do, how they form, and how to control them. Defect are categorized by their dimensionality point defects (zero dimensional), line defects (1-D), planar defects (2-D), and volume defects (three dimensional [3-D]). 

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