Cation Frenkel defect

It is important that the copper is in the monovalent state and incorporated into the silver hahde crystals as an impurity. Because the Cu+ has the same valence as the Ag+, some Cu+ will replace Ag+ in the AgX crystal, to form a dilute solid solution Cu Agi- X (Fig. 2.6d). The defects in this material are substitutional CuAg point defects and cation Frenkel defects. These crystallites are precipitated in the complete absence of light, after which a finished glass blank will look clear because the silver hahde grains are so small that they do not scatter light. 

The energy of formation of defects in PbF2 are anion Frenkel defect, 0.69 eV cation Frenkel defect, 4.53 eV Schottky defect, 1.96 eV. (a) What point defects do these consist of (b) What are (approximately) the relative numbers of these defects in a crystal at 300 K (Data from H. Jiang et al., 2000). 

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

For an estimate of the actual numbers of defects we need to know the Gibbs energy of formation, but the major contribution comes from the internal energy. Calculated values for the energy of formation of cation Frenkel defects in NaCl and AgCl are 308 kJ mol-1 and 154 kj mol-1, respectively. 

Frenkel defects are usually formed by displacing the smaller ion. In AI2O3, for example, the cation is smaller and we would expect to form cation Frenkel defects. However, anion Frenkel defects will form in UO2, Ce02, and Th02, which all have large cations. In contrast, we would expect to hnd Schottky defects in crystals with high coordination numbers such as MgO. 

We will illustrate how to formulate the Schottky and cation Frenkel defect reactions using Kroger-Vink notation for the model oxide M2O3. For the Schottky defect reaction... 

Whereas an additive can alter each of the diffusion coefficients for matter transport (A, Dgb, A, and Dg), historically the major emphasis has been placed on the ability of the additive to alter Di through its effect on the defect chemistry of the host. To determine how an additive will influence A, the defect chemistry of the host must be known. Specifically, we must know the nature of the ratecontrolling species (anion or cation), the type of defect (vacancy or interstitial), and the state of charge of the defect. In practice, this information is known in only a very few cases. To illustrate the approach, let us consider AI2O3, a system that has been widely studied. According to Kroger (62), the intrinsic defect structure consists of cationic Frenkel defects ... 

Figure 1-15. Cation Frenkel defect pair in AgCl. From Shriver and Atkins Inorganic Chemistry.

In the case of cation Frenkel defects in MO we assumed in the text that we had one interstitial site per MO. Derive the expression for the defect concentrations if the stmcture consists of fee close-packed O ions, with M ions on each octahedral hole, and with interstitial sites on all tetrahedral holes (Hint consult Chapter 1). 

The effects of higher valent cation impurities on Frenkel equilibria are analogous to those described for the Schottky equilibria. When divalent Mf impurities/dopants are dissolved in MX with predominating cation Frenkel defect pairs (and M ) the electroneutrality condition is given by... 

From studies of the effect of Cd-dopants on the ionic conductivity it could be concluded that cationic Frenkel defects predominate in AgBr. Thus the diffusion was therefore expected to involve both vacancy diffusion and transport of interstitial ions. The experimentally measured ratios of Dt/Dr varied from 0.46 at 150 °C to 0.67 at 350°C. For vacancy diffusion a constant ratio of 0.78 (=f) would have been expected, and the diffusion mechanism could thus be ruled out. For interstitial diffusion f=l, and this mechanism could also be excluded. 

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