Defect in solids

Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

Lattice Vacancies and Interstitials Defects such as lattice vacancies and interstitials fall into two main categories intrinsic defects, which are present in pure crystal at thermodynamic equilibrium, and extrinsic defects, which are created when a foreign atom is inserted into the lattice. 

Intrinsic Defects The simplest crystalline defects involve single or pairs of atoms or ions and are therefore known as point defects. Two main types of point defect have been identified Schottky defects and Frenkel defects. A Schottky defect consists of a pair of vacant sites a cation vacancy and an anion vacancy. A Schottky defect is 

Fundamentals of Electrochemistry, Second Edition, By V. S. Bagotsky Copyright 2006 John Wiley Sons, Inc. 

FIGURE 25.1 Schematic representations of (a) a Schottky defect in NaCl and (b) a Frenkel defect in AgCl. (From Gelings and Bouwmeester, 1997, Fig. 3.36, with permission from CRC Press LLC via CCC.) 

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An atom or a molecule with the total spin of the electrons S = 1 is said to be in a triplet state. The multiplicity of such a state is (2.S +1)=3. Triplet systems occur in both excited and ground state molecules, in some compounds containing transition metal ions, in radical pair systems, and in some defects in solids. 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

Catlow C R A1994. Molecular Dynamics Studies of Defects in Solids. In NATO ASI Series C 418 (Defects and Disorder in Crystalline and Amorphous Solids), pp. 357-373. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

In principle, such propositions resemble the bipolaron model, which presents the physicist s view of the electronic properties of doped conducting polymers 53-159) The model was originally constructed to characterize defects in solids. In chemical terminology, bipolarons are equivalent to diionic spinfree states of a system (S = 0)... 

Whether you recdize it or not, we have already developed our own symbolism for defects and defect reactions based on the Plane Net. It might be well to compeu e our system to those of other authors, who have also considered the same problem in the past. It was Rees (1930) who wrote the first monograph on defects in solids. Rees used a box to represent the cation vacancy, as did Libowitz (1974). This has certain advantages since we can write equation 3.3.5. as shown in the following ... 

According to our nomenclature, as used in the table, Vm is a vacancy at an M cation site, etc. The first five pairs of defects given above have been observed experimentally in solids, whereas the last four have not. This answers the question posed above, namely that defects in solids occur in pairs. 

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. 

A formalism similar to that used for partially adiabatic proton transfer reactions was applied in the calculation of the transition probability. This model of the diffusion jump is similar to the model of the diffusion of light defects in solids which was first considered in Ref. 62. 

James W. Corbett, Institute for the Study of Defects in Solids, Department of Physics, The University at Albany, 1400 Washington Avenue, Albany, New York 12222 (49)... 

INSTITUTE FOR THE STUDY OF DEFECTS IN SOLIDS, PHYSICS DEPARTMENT THE UNIVERSITY AT ALBANY, ALBANY, NEW YORK... 

Defects in Solids, by Richard J. D. Tilley Copyright 2008 John Wiley Sons, Inc. 

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. 

A. M. Stoneham, The Theory of Defects in Solids, Oxford University Press, Oxford, United Kingdom, 1985. 

Many aspects of the study and importance of defects in solids presented from a historical and materials perspective are to be found in ... 

These limitations are largely eliminated in sophisticated defect calculations described in the following section. This approach can also include more sophisticated site exclusion rules, which allow defects to either cluster or keep apart from each other. Nevertheless, the formulas quoted are a very good starting point for an exploration of the role of defects in solids and do apply well when defect concentrations are small and at temperatures that are not too high. 

From these early beginnings, computer studies have developed into sophisticated tools for the understanding of defects in solids. There are two principal methods used in routine investigations atomistic simulation and quantum mechanics. In simulation, the properties of a solid are calculated using theories such as classical electrostatics, which are applied to arrays of atoms. On the other hand, the calculation of the properties of a solid via quantum mechanics essentially involves solving the Schrodinger equation for the electrons in the material. 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

Figure 3.20 Planar defects in solids (a) boundaries between slightly misaligned regions or domains b) stacking mistakes in solids built of layers, such as the micas or clays (c) ordered planar faults assimilated into a crystal to give a new structure and unit cell (shaded).

In this chapter, to keep the material compact, only the relationship between diffusion and defects in solids will be discussed. Moreover, the diffusion coefficient will be considered as a constant at a fixed temperature, and attention is focused upon the movement of atoms and ions rather than the equally important diffusion of gases or liquids through a solid. Discussion of diffusion per se, the extensive literature on classical theories of diffusion, and diffusion when the diffusion coefficient is not a constant will be found in the Further Reading section at the end of this chapter. 

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