Silver bromide Frenkel defects

In silver bromide, Frenkel-type defects predominate ... 

In this section we are concerned with the properties of intrinsic Schottky and Frenkel disorder in pure ionic conducting crystals and with the same systems doped with aliovalent cations. As already remarked in Section I, the properties of uni-univalent crystals, e.g. sodium choride and silver bromide which contain Schottky and cationic Frenkel disorder respectively, doped with divalent cation impurities are of particular interest. At low concentrations the impurity is incorporated substitutionally together with an additional cation vacancy to preserve electrical neutrality. At sufficiently low temperatures the concentration of intrinsic defects in a doped crystal is negligible compared with the concentration of added defects. We shall first mention briefly the theoretical methods used for such systems and then review the use of the cluster formalism. 

Point defects. Point defects (Fig. 5.1) are limited to a single point in the lattice, although the lattice will buckle locally so that the influence of point defects may spread quite far. A Frenkel defect consists of a misplaced interstitial atom and a lattice vacancy (the site the atom should have occupied). For example, silver bromide, which has the NaCl structure, has substantial numbers of Ag+ ions in tetrahedral holes in the ccp Br array, instead of in the expected octahedral holes. Frenkel defects are especially common in salts containing large, polarizable anions like bromide or iodide. 

Iron (II) sulphide never has the precise composition FeS—the sulphur is always present in excess. This could be due either to the inclusion in the lattice of extra, interstitial S atoms or to the omission from it of some of the Fe atoms. The second explanation is correct (Hagg and Sucksdorff, 1933), the phenomcon being an example of lattice defect (p. 152). There are two types of lattice defect. In Schottky defects, found in iron(Il) sulphide, holes are left at random through the crystal because of migration of ions to the surface. In Frenkel defects, holes are left at random by atoms which have moved to interstitial positions. Silver bromide has a perfect face-centred cubic arrangement of Br ions but the Ag+ ions are partly in interstitial positions. The effect is even more marked in silver iodide (p. 153). 

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.

The silver halide series of compounds have been extensively studied because of their usage in photographic film. In particular, it is known that if silver bromide is Incorporated into a photographic emulsion, any incident photon will create a Frenkel defect. When the film is developed, the Agi+ is reduced to Ag metal. These localized atoms act as nuclei to... 

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. 

At this point of the discussion it is worthwhile to distinguish between two different kinds of disorder. If the concentrations of the majority defect centers, which constitute the disorder type, are independent of the component activities and are only determined by P and 7, then we speak of thermal disorder or intrinsic disorder (e. g. Frenkel disorder in silver bromide). However, the concentrations of minority defect centers do depend upon the component activities even in the case of a crystal with thermal disorder. This will be discussed more explicitly later. On the other hand, if the concentrations of the majority defects are dependent upon the component activities, then we speak of activity-dependent disorder or extrinsic disorder (e. g. cation vacancies and electron holes in transition metal oxides). 

Defect relaxation times for homogeneous reactions in solids can be calculated essentially by the methods of homogeneous chemical kinetics [2, 3]. For the sake of illustration, let us consider more closely the equilibration of Frenkel defects in silver bromide following a sudden change in temperature. 

By introducing numerical values for silver bromide into eq. (6-5), we find that even at room temperature the relaxation time for the equilibration of Frenkel defects is of the order of milliseconds and less. Because of the paucity of available data [9], only such rough estimates can be made. Furthermore, it should be remembered that these estimates are dependent upon the assumption that the defect reaction is, in fact, a homogeneous reaction. 

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