AgBr Frenkel defects

Some experimental values for the formation enthalpy of Frenkel defects are given in Table 2.2. As with Schottky defects, it is not easy to determine these values experimentally and there is a large scatter in the values found in the literature. (Calculated values of the defect formation energies for AgCl and AgBr, which differ a little from those in Table 2.2, can be found in Fig. 2.5.)... 

Despite the fact that not all details of the photographic process are completely understood, the overall mechanism for the production of the latent image is well known. Silver chloride, AgBr, crystallizes with the sodium chloride structure. While Schottky defects are the major structural point defect type present in most crystals with this structure, it is found that the silver halides, including AgBr, favor Frenkel defects (Fig. 2.5). 

Figure 2.5 Calculated variation of the formation energy of Schottky and Frenkel defects in the halides AgCl and AgBr as a function of temperature. [Redrawn from data in C. R. A. Catlow, Mat. Res. Soc. Bull., XIV, 23 (1989).]...

The enthalpy of formation of Frenkel defects (kJ mol-1) is AgCl, 140, AgBr, 109, Agl, 58. The compound with the greatest number of Ag+ interstitials is ... 

Figure 1-2. Two-dimensional schematic representation of the formation of Frenkel defect pairs in AgBr AgAg+V = Ag +VAg. = vacant cation site.

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

Frenkel Defect In Frenkel defect atom or ion in normal site is displaced to an interstitial site thus creating a vacancy. In this defect ion is not completely missing but only shifted to interstitial site from its normal site. This defect is found in AgBr. 

Figure 43. The mobility of the Frenkel defects in AgBr as a function of the temperature (according to Eq. 113). From Ref.186. (Reprinted from P. Muller, Ionenleitfahig-keit von reinen und dotierten AgBr- und AgCl-Einkristallen. Phys. Stat. Sol. 12, 775-794. Copyright 1965 with permission from WILEY-VCH Verlag GmbH.)...

Crystals in which particles have migrated to nonstandard positions are said to exhibit Frenkel defects [see Fig. 16.43(b)]. One group of compounds where Frenkel defects are present to the extreme is the silver halides—AgCl, AgBr, and Agl. In these compounds the anion positions are mostly those expected from closest packing ideas however, the silver ions are distributed almost randomly in the various holes and can easily travel within the solid structure. This property is a major reason that the silver halides are so useful in photographic films. 

For strongly ionic solids where cation and anion sizes are comparable, e.g. NaCf, KBr, etc., Schottky defects will predominate and both transport numbers and are greater than zero t = 0, no current is carried by electron migration). When the size of the cation is considerably smaller than the anion, eg. AgBr, AgCf, etc., Frenkel defects occur and the interstitial cations are the dominant current carriers 1). 

Frenkel Defects These defects arise when an ion occupies an interstial position between the lattice points. It appear in crystals in which the negative ions are much larger than the positive ions, example AgBr and ZnS crystals. 

Silver vacancies and interstitials are formed in pairs in a pure, perfect, single crystal so that njny = 1. This ratio can be altered by doping with polyvalent impurities that require charge compensation by Frenkel defects in order to maintain charge neutrality in the host lattice. At room temperature, (CF)1/2 is approximately 1012/cm3 in AgCl and 1014/cm3 in AgBr(10) and,... 

Fig. 5.27 Silver bromide adopts an NaCl lattice, (a) An ideal lattice can be described in terms of Ag ions occupying octahedral holes in a cubic close-packed array of bromide ions, (b) A Frenkel defect in AgBr involves the migration of Ag ions into tetrahedral holes in the diagram, one Ag+ ion occupies a tetrahedral hole which was originally vacant in (a), leaving the central octahedral hole empty. Colour code Ag, pale grey Br, gold.

Frenkel defects illustrated by the structure of AgBr (Section 5.17). 

In ionic lattices in which there is a significant difference in size between the cation and anion (e.g. AgBr), the smaller ion may occupy a site that is vacant in the ideal lattice. This is a Frenkel defect Figure 5.27) and does not affect the stoichiometry or electrical neutrality of the compound. 

When an ion occupies a normally vacant interstitial site, leaving its proper site vacant, the defect is termed a Frenkel defect. Frenkel defects are most common in crystals where the cation is much smaller than the anion, for instance, in AgBr, as illustrated schematically in Fig. 2-14(b). 

Estimate the number of Frenkel defects in AgBr (NaCl structure) at 500°C. The enthalpy of formation of the defect is 110 kJ/mol, and the entropy of formation is 6.6/ . The density and molecular weights are 6.5g/cm and 187.8 g mol. respectively. State all necessary assumptions. 

Frenkel defects occur in silver bromide, AgBr. In this compound some of the silver ions (Ag ) move from the normal positions to sit at usually empty places to generate interstitial silver ions and leave behind vacancies on some of the usually occupied silver sites. The bromide ions (Br ) are not involved in the defects. (Frenkel defects in AgBr make possible black and white and colour photography on photographic film.)... 

A Frenkel defect in a crystal of silver bromide, AgBr, consists of ... 

The enthalpy of formation of a Frenkel defect in silver bromide, AgBr, is 1.81 x 10 J. Estimate the fraction of interstitial silver atoms owing to Frenkel defect formation in a crystal of AgBr at 300 K. 

Frenkel defects. The case where only the cation is mobile can be explained by assuming that the anion lattice is perfect but that the cation lattice contains cation vacancies and interstitials in equivalent concentrations to maintain electroneutrality for the wholecrystal. This type of defect is found in the silver halides and is shown for AgBr in Figure 3.2. The cation in this case is free to migrate over both vacancy and interstitial sites. 

Interstitials If an atom is present on any site that would be unoccupied in a perfect crystal then that atom is an interstitial. A Frenkel defect is a vacancy -i- interstitial pair formed by removing an atom from its site in the crystal structure and putting it into an interstice as illustrated in Figure 11.2. Frenkel defects formed in iodine-containing AgBr are essential to the photographic process. 

Express using Krbger-Vink notation the formation of Frenkel defects in AgBr and explain why you think these are more numerous than Schottky defects. How might you increase the concentration of Schottky defects in AgBr ... 

In a Frenkel defect, an atom or ion occupies a normally vacant site, leaving its own lattice site vacant. Figure 6.27 illustrates this for AgBr, which adopts an NaCl structure type. In Figure 6.27a, the central Ag+ ion is in an octahedral hole with respect to the fee arrangement of Br ions. Migration of the Ag ion to one of the previously unoccupied... 

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