Silver halides, Frenkel defects

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

A somewhat different situation is found in the type of point defect known as a Frenkel defect. In this case, an atom or ion is found in an interstitial position rather than in a normal lattice site as is shown in Figure 7.17. In order to position an atom or ion in an interstitial position, it must be possible for it to be close to other lattice members. This is facilitated when there is some degree of covalence in the bonding as is the case for silver halides and metals. Accordingly, Frenkel defects are the dominant type of defect in these types of solids. 

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). 

Photochromic behavior depends critically upon the interaction of two point defect types with light Frenkel defects in the silver halide together with substitutional Cu+ impurity point defects in the silver halide matrix. It is these two defects together that constitute the photochromic phase. 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

In densely packed solids without obvious open channels, the transport number depends upon the defects present, a feature well illustrated by the mostly ionic halides. Lithium halides are characterized by small mobile Li+ ions that usually migrate via vacancies due to Schottky defects and have tc for Li+ close to 1. Similarly, silver halides with Frenkel defects on the cation sublattice have lc for Ag+ close to 1. Barium and lead halides, with very large cations and that contain... 

The first reaction is a site exchange reaction and so does not alter the number of lattice sites. The second reaction describes the formation of a complete lattice molecule M. An example of the first type of reaction (exchange reaction, Eqn. (2.59)) is the so-called Frenkel defect formation reaction in AX (e.g., in silver halides, see Fig. 1-2)... 

Let us finally estimate the relaxation times of homogeneous defect reactions. To this end, we analyze the equilibration course of a silver halide crystal, AX, with predominantly intrinsic cation Frenkel disorder. The Frenkel reaction is... 

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... 

The silver halide crystals show ionic conductivity by Frenkel defects (interstitial silver ions, Ag"t). 

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. 

Frenkel defects and impurity ions can diffuse through the silver halide lattice by a number of mechanisms. Silver ions can diffuse by a vacancy mechanism or by replacement processes such as collinear or noncollinear interstitialcy jump mechanisms [18]. The collinear interstitial mechanism is one in which an interstitial silver ion moves in a [111] direction, forcing an adjacent lattice silver ion into an interstitial position and replacing it The enthalpies and entropies derived from temperature-dependent ionic conductivity measurements for these processes are included in Table 4. The collinear interstitial mechanism is the most facile process at room temperature, but the other mechanisms are thought to contribute at higher temperatures. 

Silver halides are used in photography to capture light and form an image. The action of light on the halide produces silver which forms the black areas of the negative (Figure 2.2). The formation of silver depends on the presence of Frenkel defects in the crystal. 

The dominant defect in silver halides is a Frenkel defect, in which a silver ion moves to an interstitial site. To calculate the energy required to form this defect we simply remove a silver ion from one position, put it in its new position and compare the energy of the crystal lattice with that of the perfect lattice. 

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. 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. 

For higher concentrations of defects the equation must be written in terms of activities instead of concentrations. Frenkel disorder occurs in the silver halides, for example, in AgCl. 

The Frenkel disorder is the simultaneous presence of vacancies and atoms in interstitial positions of the same element, for exattple, Va and A . This is an asymmetrical disorder one will thus have two possible Frenkel disorders for a binary sohd the disorder on the A atoms and the disorder on the B atoms. As we will see in section 2.5.2.2.2, the well and the source of the Frenkel disorder are purely local its formation does not require displacement of atoms with long distance. The defects that constitute the disorder can be ionized or not, respecting the electric neutrality. It is for the atom of smaller volume that the Frenkel disorder is most probable because it is easiest to place it in an interstitial position. We will quote, as an example, the Frenkel disorder on silver in silver halides. 

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). 

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