Defects in solid state lattices

So far in this chapter, we have assumed implicitly that all the pure substances considered have ideal lattices in which every site is occupied by the correct type of atom or ion. This state appertains only at OK, and above this temperature, lattice defects are always present The energy required to create a defect is more than compensated for by the resulting increase in entropy of the stmcture. In this section, we introduce some common types of defect Electrical conductivity that arises as a result of defects in ionic solids is detailed in Section 28.2. 

Intrinsic defects occur in lattices of pure compounds. 

Extrinsic defects result from the addition of dopants. 

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Chapter 6 Defects in solid state lattices an introduction 177... 

Eshelby J. D., The Continuum Theory of Lattice Defects, in Solid State Physics Vol. 3, edited by F. Seitz and D. Turnbull, Academic Press, New York New York, 1956. 

Packing of spheres Polymorphism Alloys and intermetallic compounds Band theory Semiconductors Sizes of ions Prototype structures Lattice energy Born-Haber cycle Defects in solid state structures... 

The lattice imperfections play an important role in reactions in solid state. The reactivity of solids are due to the defect or fault in the lattice. The more perfect a crystal is, the smaller is its reactivity. The defect may be point defect, dislocations, stacking faults, bulk defects etc. 

In solid state physics, it is well known that many inorganic solids, e.g., the oxides and sulfides, can dissolve metals and nonmetals in excess, and that by this process electron and ion defects in the lattice will be formed. Wagner and co-workers (1) have developed the basic theory of... 

After the formulation of defect thermodynamics, it is necessary to understand the nature of rate constants and transport coefficients in order to make practical use of irreversible thermodynamics in solid state kinetics. Even the individual jump of a vacancy is a complicated many-body problem involving, in principle, the lattice dynamics of the whole crystal and the coupling with the motion of all other atomic structure elements. Predictions can be made by simulations, but the relevant methods (e.g., molecular dynamics, MD, calculations) can still be applied only in very simple situations. What are the limits of linear transport theory and under what conditions do the (local) rate constants and transport coefficients cease to be functions of state When do they begin to depend not only on local thermodynamic parameters, but on driving forces (potential gradients) as well Various relaxation processes give the answer to these questions and are treated in depth later. 

For a classical SEI electrode such as lithium, the surface films formed on it in most of the commonly used polar aprotic systems conduct Li ions, with a transference number (t+) close to unity. As stated earlier the surface films on active metals are reduction products of atmospheric and solution species by the active metal. Hence, these layers comprise ionic species that are inorganic and/or organic salts of the active metal. Conducting mechanisms in solid state ionics have been dealt with thoroughly in the past [36-44], Conductance in solid ionics is based on defects in the medium s lattice. Figure 8 illustrates the two common defects in ionic lattices interstitial (Frenkel-type) defects [37] and hole (Schottky-type) defects [38],... 

Wang, J.A., R. Limas-Ballesteros, T. Lopez, A. Moreno, R. Gomez, O. Novaro and X. Bokhimi (2001b). Quantitative determination of titanium lattice defects and solid-state reaction mechanism in iron-doped Ti02 photocatalysts. Journal of Physical Chemistry B, 105(40), 9692-9698. 

In the shell model, as mentioned above, the short-range repulsion and van der Waals interactions are taken to act between the shell particles. This finding has the effect of coupling the electrostatic and steric interactions in the system in a solid-state system where the nuclei are fixed at the lattice positions, polarization can occur not only from the electric field generated by neighboring atoms, but also from the short-range interactions with close neighbors (as, e.g., in the case of defects, substitutions, or surfaces). This ability to model both electrical and mechanical polarizability is one reason for the success of shell models in solid-state ionic materials. 

A variety of related structures can be identified with 6,8, and 12-fold coordination of the A cation and four or sixfold coordination of the anion. In fact, the chemistry of ABO4 temarys is extremely complicated with solid solutions and phase transitions being common. Lattice defects may be introduced easily by appropriate dopings. Scheelites and its relatives have been studied intensively for their properties as heterogeneous catalysts, as host materials for impurity activated luminescent materials, and for specialized optical uses see Oxide Catalysts in Solid-state Chemistry and Section 4.4). 

The study of the electronic structure of impurities and defects in solids has a long tradition, both because of its own intrinsic theoretical interest and because of the technological importance in improving the performance of solid state devices. Lattice defects can be point defects (such as substitutional or interstital foreign atoms, vacancies, antisite defects in composite lattices), line defects (such as dislocations), planar defects (such as boundaries, adatom surfaces, stacking faults corresponding to misplaced planes of atoms), and so on. 

The solid state chemist approaches the problem in a different way(2). His main interest focus on the phase composition of the solid, type of crystal planes exposed, presence of additives and impurities, oxidation states of the cations and their changes in the course of the reaction, type of defects in the oxide lattice, etc. Correlation is sought between these parameters and the activity and selectivity of the oxide system in the given reaction, but little attention is usually paid to the type of interactions between the hydrocarbon molecule and the surface and to the possible transition states. When these two approaches are integrated, several general conclusions may be formulated, but also a number of important yet unanswered questions emerge. 

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