Point defects in solids

A crystalline solid is never perfect in that all of the lattice sites are occupied in a regular manner, except, possibly, at the absolute zero of temperature in a perfect crystal. Point defects occur at temperatures above zero, of which the principal two forms are a vacant lattice site, and an interstitial atom which 

The vacant sites will be distributed among the Ni lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a corresponding number of vacancies on the N lattice sites. In the case of ionic species, it is necessary to differentiate between cationic sites and anionic sites, because in any particular substance the defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, the random distribution of the n vacancies on the N lattice sites can be achieved in 

When there are tii interstitial defects distributed on N sites each requiring Ei energy of formation, the equilibrium number of these at temperature T is given by 

In the hypothesis of a perfect crystal lattice defined by a single pattern present on all of the lattice s nodes, it is difficnlt to imagine an atom or ion moving aroimd in the structure of the solid. Yet, experience shows scattering of chemical species in most materials. To explain this movement and to conceptualize some heterogenous reactions involving solid compoimds, it was necessary to imagine the existence of point defects in solids. 

In the case of metallic solids, these defects consist either of the presence of metallic atoms in interstitial positions of the lattice or the absence of a few atoms from the nodes of the lattice. 

In the case of ionic solids and according to the Wagner classificatiorr, there are four kinds of point defects, that is to say  

To make sttre the electroneutrality principle is respected in the lattice, these defects have to be associated with charge carriers electrorrs or electron holes. These carriers can be trapped in the defects or free to move arotmd in the lattice. The release of a charge carrier by a defect is identifted with an ionization of the defect (see Figirre 2.6). 

The denotation suggested by F.A. Krbger and HJ. Vink is now used by all seientists. Thus, in binary ionic crystal AB (A B ) where each site of the ideal lattice carries a +n or -n charge, we will have structural member X for each lattice  

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Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

Point defects can have a profound effect upon the optical properties of solids. The most important of these in everyday life is color,3 and the transformation of transparent ionic solids into richly colored materials by F centers, described below, provided one of the first demonstrations of the existence of point defects in solids. 

This article is concerned with the statistical mechanics of interactions between point defects in solids at thermodynamic equilibrium. The review is made entirely from the point of view of the... 

The motion of ions through solids results in both charge as well as mass transport. Whereas charge transport manifests itself as ionic conductivity in the presence of an applied electric field, macroscopic mass transport (diffusion) occurs in a concentration gradient. Both ionic conductivity and diffusion arise from the presence of point defects in solids (Section 5.2). For a solid showing exclusive ionic conduction, conductivity is written as... 

Up to now we have been discussing in this Chapter many-particle effects in bimolecular reactions between non-interacting particles. However, it is well known that point defects in solids interact with each other even if they are not charged with respect to the crystalline lattice, as it was discussed in Section 3.1. It should be reminded here that this elastic interaction arises due to overlap of displacement fields of the two close defects and falls off with a distance r between them as U(r) = — Ar 6 for two symmetric (isotropic) defects in an isotropic crystal or as U(r) = -Afaqjr-3, if the crystal is weakly anisotropic [50, 51] ([0 4] is an angular dependent cubic harmonic with l = 4). In the latter case, due to the presence of the cubic harmonic 0 4 an interaction is attractive in some directions but turns out to be repulsive in other directions. Finally, if one or both defects are anisotropic, the angular dependence of U(f) cannot be presented in an analytic form [52]. The role of the elastic interaction within pairs of the complementary radiation the Frenkel defects in metals (vacancy-interstitial atom) was studied in [53-55] it was shown to have considerable impact on the kinetics of their recombination, A + B -> 0. 

A. D. Franklin in Point Defects in Solids Volume 1, editors J. H. Crawford and L. M. Slifkin, Plenum Press, New York, p.l (1972). 

J.-M. Spaeth, J.R. Niklas, R.H. Baitram [ Structural Analysis of Point Defects in Solids (Springer-Verlag, Berlin, 1992) ]... 

Kroger-Vink notation — is a conventional method to denote point -> defects in solids and their associates. This method proposed by F.A. Kroger and H.J. Vink [i, ii] is now commonly accepted in solid-state electrochemistry, chemistry, and physics, with adaptation to various specific cases [iii, iv]. 

The observed uptake of water by quartz under conditions of high temperature, pressure, and water fugacity indicates that the diffusivity and/or solubility of water-related point defects in solid solution are much lower than are required by the Griggs model (Gerretsen et al. 1989 Kronenberg, Kirby, and Rossman 1986 Rovetta, Holloway, and Blacic 1986). 

In the above equation, Al i represents the normal aluminum ion in the regular site of the oxide film and Vai" represents the negatively charged aluminum vacancy in the oxide film. Here, the Krbger-Vink notation for representing point defects in solids is used (for a more detailed view, see Chapter 9). In alkaline media, generation of aluminum vacancies can be explained by the occurrence of a process involving water molecules adsorbed on the oxide film ... 

Kroger-Vink Notation for Representing Point Defects in Solids Point Defect Symbol... 

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