Ionization of defects

The next question that arises is what is the charge state of these defects for a given Fermi level. This is easily determined, as occupation is set as usual by the Fermi 

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We will deal with the first two cases, namely 1) defects in the stoichiometric case and 2) ionization of defects in stoichiometric compounds. Since the case of non-stoichiometiic compounds can be very complicated, we will present treatment of the last two in the Appendix at the end of this Chapter. 

This presentation is presented for those who wish to examine the mathematics of both non-stoichiometric intrinsic- defect compounds and the ionization of defects in both stoichiometric and nonstoichiometric compounds as represented by ... 

In the non-stoichiometric case where ionization of defects is the norm, the mathematics become too complicated so that the equations are not solvable. However, we can use a thermodynamic method to obtain the results we want. We will present here the case of silver bromide whose use in photographic film highlights the use of defect chemistry for practical purposes. 

We have already covered, albeit briefly, non-ionized stoichiometric and non-ionlzed non-stoichlometric intrinsic-defect compounds. Let us now consider the ionization of defects in these compounds. In the MXs compound, if we remove some of the X-atoms to form Vx, the electrons from the removed X-atom (or from the bond holding the X-atom in the crystal) are left behind for charge compensation reasons. At low temperatures, these electrons are localized near the vacancy but become dissociated from the point defect at higher temperatures. They become free to move through the crystal, and we say that the intrinsic defect has become ionized. We can write the following equations for this mechanism ... 

A useful example for understanding the above equations, and the ionization of defects, is that of cobaltous oxide, CoO. External oxygen... 

Brouwer Plot for Schottky Defects in the Hypothetical Compound, MX, When Ionization of Defects is the Norm i.e. - I K > Ksh 1 ... 

The defect concentrations found in sulphides are so high that some interaction of defects is almost inevitable. In the case of iron sulphide, FeS, if there were localized electronic defects, the progressive ionization of defects could be expressed by Equations (6.3)-(6.5) ... 

The ionization of defects can take place but is not described here (see reference 1 for detailed analysis). 

This is the outermost lattice layer, which is essentially limited to the presence of the surface charge formed as a result of ionization of defects within this layer. In the first approximation, the thickness of this layer is limited to dimensions of the outer crystal layer (Figure 4.1a). 

The degree of ionization of defects frequently can be determined by measuring the defect concentration as a function of pressure of the more volatile component and using the mass action law. For example, for the case of cobalt vacancies in CoO, the equilibrium constant for Eq. (21) is... 

By introducing the relations for ionization of defects and for intrinsic ionization [Eq. (7)] and using the following reaction ... 

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