Simple internal defect equilibria

We have previously established (i) that, at finite temperatures, ionic and electronic point defects are required as local chemical excitations at equiUbrium, (ii) that we can write ideal mass action laws in all cases for low concentrations of defects, and (iii) that we know what parameters influence our mass action constants. We can now turn to a specific consideration of defect chemistry. Let us consider first internal defect reactions and pure single crystals By internal defect reactions in pure substances we mean processes that occur as a consequence of nonzero temperature in the otherwise perfect crystal without neighbouring phases being involved. (For two of these reaction tjrpes, however, we will need surfaces as sinks or sources of monomeric units, i.e. of lattice molecules.) In binary systems such processes leave the composition within the sohd undhanged. If we refer to the Dalton composition , we also speak of the intrinsic case. 

The first basic disorder type to be discussed is the Frenkel disorder. Here a few cations have left their regular positions, on accoimt of the favourable configurational entropy (thermal influence), thus leaving behind vacancies, and now occupy interstitial sites. Such defects typically occur in the cationic sublattice and preferentially in cases of high polarizabihty, such as in the Ag sublattices of the silver halides AgCl, AgBr and Agl (see Section 5.2). 

The old-fashioned charge designations which are exclusively used for the defects, indicate particles and indicate the relative charge with respect to the perfect lattice. According to the arguments detailed in Section 5.2 we know that there is, at equilibrium, a mass action law of the form (F indicates Frenkel reaction) 

Since the rest of this chapter is exclusively devoted to equilibrium concentrations, we can suppress the equilibrium arc (as done in Eq. (5.81)). Values for ApS and ApH are listed in Table 5.1 (on page 114). 

The building element formulation (5.80) evidently lacks vividness, even though it is thermodjmamically the most correct [166] In accordance with the treatment in 

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The purpose of the chapter dealing with equilibrium thermodynamics of the perfect solid (Chapter 4) is to elaborate, on the one hand, simple expressions for the thermodynamic functions of the chemical ground state and, on the other hand, to make the reader familiar with questions of internal and external equilibria, not least with the intention to provide the equipment to deal with the thermodynamics of defect formation. (The major portion of the free enthalpy at absolute zero consists of bonding energy, while the temperature dependence is largely determined by the vibration properties.)... 

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