Lattice defects vacancies, voids

The formation of hot spots is generally attributed to the presence of lattice defects [11,17,19-23], which could include vacancies, voids, dislocations, misalignments, cracks, impurities, etc. One explanation is that defects induce strain in the lattice, which is relieved, via structural relaxation, by the externally-introduced energy this results in a disproportionate localization of energy in the neighborhood of the defect, a portion of it being in lattice vibrations [21,22]. The thermal energy of hot spots must be efficiently transferred to appropriate molecular vibrational... 

The electrical resistivity is the summation of two contributions the contribution of the lattice or the thermal resistivity, i.e., the thermal scattering of conduction electrons due to atomic vibrations of the material crystal lattice (i.e., phonons), and the residual resistivity, which comes from the scattering of electrons by crystal lattice defects (e.g., vacancies, dislocations, and voids), solid solutes, and chemical impurities (i.e., interstitials). Therefore, the overall resistivity can be described by the Matthiessen s equation as follows ... 

In particular, the most powerful method for studing lattice defects, due to the high sensitivity of positrons to open volume defects such as vacancies, vacancy clusters, voids, dislocations, grain boundaries, etc., is positron annihilation spectroscopy (PAS). A diagram illustrating the applicability of PAS and other techniques as a function of defect size and density versus depth in material is shown in Figure 4.25. Thus, PAS represents a non-local experimental technique that is sensitive to microstructural defects at the atomic scale. A well-established theory of positron annihilation phenomena is currently available. Especially for metallic materials, it is possible to perform ab initio calculations of positron parameters for various defects and atomic arrangements [72,73]. 

There are certain unusual types of defects in metal systems that are noteworthy. It has been found (Taylor Doyle, 1972) that in NiAl alloys A1 atoms on the Al-rich side do not substitute on the Ni sublattice instead there are vacancies in the Ni sites. For example, at 55 at.% Al, 18% of Ni sites are vacant while the A1 sites are filled. Such vacancies determined by composition are referred to as constitutional vacancies. Other alloys have since been found to exhibit such vacancies, typical of these being NiGa and CoGA. Another rather curious aspect of defects is the formation of void lattices when metals such as Mo are irradiated with neutrons or more massive projectiles (Gleiter, 1983). Void lattices arise from agglomeration of vacancies and are akin to superlattices. Typically, neighbouring voids in Mo are separated by 200 A. An explanation for the stability of void lattices on the basis of the continuum theory of elasticity has been proposed (Stoneham, 1971 Tewary Bullough, 1972). 

Some of the defect equilibria which we have deduced by this type of analysis were not surprising—a parent lattice may dissociate into interstitials and vacancies in conformity with appropriate equilibrium constants defects may associate, again consistent with an equilibrium constant or the lattice may dissolve excess atoms in simple solubility. (When we speak of a solvent or parent lattice we mean the crystallographic lattice, as it would be determined by x-ray analysis, stoichiometri-cally perfect, and free of vacancies or interstitials. We call the process of vacancy and interstitial formation lattice dissociation. Simple solution adds interstitials or fills voids in the parent lattice). 

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). 

The large vacancy clusters are called voids. At higher temperatures these voids may collapse and form loops. These loops may be regarded as a special type of dislocation. Dislocations are present in every non-ideal material and determine its mechanical properties. The two main types are the edge and the screw dislocations. Defects are called edge dislocations when one plane of atoms in the lattice is missing or supernumerary screw dislocations are formed when a part of the crystal is displaced by an atomic layer. Fig. 14 illustrates the two types of dislocation. 

Long-range periodicity based on extended defects is not, however, confined to shear-plane structures. Indeed the occurrence of extended defect super-lattices is widespread. The adaptive structures discussed by Anderson have already been referred to in the Introduction. A further illustration of the phenomenon, which strikingly illustrates its generality, is provided by the void lattice observed in certain irradiated metals, e.g., Mo, where voids, typically of diameters 50 A, formed by the aggregation of irradiation induced vacancies, order to give a stable f.c.c. lattice in which the voids are separated by 300 A. 

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... 

Kirkendall Effect The Kirkendall effect is a phenomenon observed frequently in solid materials [38]. It refers to a vacancy counter diffusion process through an interface of two solid materials, metals in particular, to compensate the unequal material flow formation at the interface [38a]. In metals and metallic alloys, the vacancy is atomic defect, that is, empty lattice site. Combination of excess vacancies can lead to the formation of void within the fast-diffusion side of the interface [39]. While this phenomenon has been known for a very long time, synthesis of hollow nanostructures based on Kirkendall effect was realized fairly recently [40]. Ym studied the time evolution in the formation of hollow nanospheres and found that Kirkendall diffusion followed the Tick s law [41]. This means that the diffusion of atoms and vacancies is driven by the difference in atom concentration. Wu et al. synthesized hollow nanostructures of CoCuPt alloy catalyst by using Co nanoparticles as the sacrificial templates. For this trimetallic system, Co atoms diffused faster than those of Pt or Cu to form core-shell like Co CuPt hollow nanoparticles and then the CoCuPt hollow spheres (Fig. 2.10) [42]. 

A self-interstitial is an atom from the crystal that is crowded into an interstitial site—a small void space that under ordinary circumstances is not occupied. This kind of defect is also represented in Figure 4.1. In metals, a self-interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated. Consequently, the formation of this defect is not highly probable, and it exists in very small concentrations that are significantly lower than for vacancies. 

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