Defect structures Frenkel type

The difference in catalytic activity between the La- and the Ba-based hexa-aluminates results from the following reasons the first difference is the valence of cation in the mirror pleuie between tri-valent lanthanum ion and di-valent barium ion. The second is the crystal structure between magnetoplumbite and P-alumina, which are different in the coordination of ions and concentration of Frenkel-type defect in mirror plane. The redox cycle of transition metal in hexa-aluminate lattice, which closely related with catalytic activity, is affected sensitively with these two factors. 

Undoped PbS is an -type semiconductor and crystallizes in the NaCl structure. The predominant defects are Frenkel defect pairs on the Pb sublattice. 

It should be noted that recently in nano-scale powders of Ce02 Frenkel type defects have been found. Prom a neutron diffraction study interstitial oxygen defects have been proofed to exist depending on the fomation conditions of the ceria material [13]. The interstitial oxygen was revealed on the octahedral sites of the structure which is the center of the anion cube. These interstitials are charge compensated by oxygen vacancies in the structure. 

Cobalt forms two oxides, CoO and C03O4, of NaCl and spinel structures, respectively CoO is a p-type cation-deficit semiconductor through which cations and electrons migrate over cation vacancies and electron holes. In addition to the usual extrinsic defects, due to deviations from stoichiometry above 1050 °C, intrinsic Frenkel-type defects are also present. The variations of oxidation-rate constant with oxygen partial pressure and with temperature are, therefore, expected to be relatively complex. Consequently, it is important to ensure that very accurate data are obtained for the oxidation reactions, over a wide range of oxygen pressure and temperature. 

Fig. 4.2. (a) Schematic representation of electrolytic domain, i.e. relative electronic (for instance n and p type for ZrOj Ca) and ionic conductivity as a function of partial pressure pXj of the more volatile element (e.g. Oj or Ij). Dotted zone corresponds to a mixed conduction domain where the ionic transport number (tj) goes from 0 to 1 (with permission). The Agl area is limited by the a-p transition and by melting on the low and high temperature sides, respectively, (b) Schematic defect structure of an oxide M2O3 as a function of the water pressure. The oxide is dominated by anti-Frenkel defects and protons ([H ]) and doped with cations, concentration of which is assumed to be constant ([MI ]). Metal vacancies are shown as examples of minority defects. 

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 ... 

In view of the many types of point defects that may be formed in inorganic compounds and that each type of defect may have varying effective charge, numerous defect reactions may in principle be formulated. In the following, a few simple cases will be treated as examples. First, we will consider defect stmcture situations in stoichiometric compounds (Schottky, Frenkel and intrinsic electronic disorders) and then defect structure situations in nonstoichiometric oxides will be illustrated. Finally, examples of defect reactions involving foreign elements will be considered. 

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). 

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. 

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

Fluorite type oxides are particularly prone to nonstoichio-metric effects. This most commonly occurs in the form of cation nonstoichiometry induced by partial reduction of the cation or by replacement of a portion of the oxide by flnoride. Anion excess phases can occur as a result of cation oxidation or by replacement with higher valence impurities. The dominant defect in this structure involves the migration of oxygen to the large cuboidal interstice resulting in the formation of a vacancy at a normal lattice site. A vacancy of this type is called a Frenkel defect. 

Schottky defects occur when sites that are normally occupied by atoms or ions are left vacant. In order that the crystal structure maintain its electrical neutrality, for every cation-site vacancy there must be an anion-site vacancy. At room temperatures, one in 10 sites is typically vacant, but this adds up to 10 Schottky defects in a 1 mg crystal. A less commonly observed defect is a Frenkel defect, in which an atom or ion is displaced from its site to an interstitial site that is normally unoccupied. In so doing the number of nearest neighbors of one component of the crystal is changed. This type of defect is seen in... 

First approaches to the quantitative understanding of defects in stoichiometric crystals were published in the early years of the last century by Frenkel in Russia and Schottky in Germany. These workers described the statistical thermodynamics of solids in terms of the atomic occupancies of the various crystallographic sites available in the structure. Two noninteracting defect types were envisaged. Interstitial defects consisted of atoms that had been displaced from their correct positions into normally unoccupied positions, namely, interstitial sites. Vacancies were positions that should have been occupied but were not. 

The actual type of defect found in the crystal will depend on the energy of formation. There may be either more Frenkel defects or more Schottky defects depending on which has the smaller energy of formation. As we have already mentioned, Frenkel defects are more likely to be important in crystals with open structures that can accommodate the interstitials without much lattice distortion. 

So far in this chapter, we have assumed implicitly that all the pure substances considered have ideal lattices in which every site is occupied by the correct type of atom or ion. This state appertains only at OK, and above this temperature, lattice defects are always present. The energy required to create a defect is more than compensated for by the resulting increase in entropy of the structure. There are various types of lattice defects, but we shall introduce only the Schottky and Frenkel defects. Solid state defects are discussed further in Chapter 28. Spinels and defect spinels are introduced in Box 13.6. 

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... 

Explain what is meant by Frenkel and Schottky defects in an NaCl structure type. 

Anti-Frenkel disorder similar to Frenkel disorder except that the interstitials are anions and vacancies are therefore in the anion sublattice. In Zr02 the reaction is 0 kS + 0[ and the anti-Frenkel equilibrium constant is K p = [ko ][On- This type of thermal defect is found in lattices that have a fluorite structure (CaF2, Zr02), which means that there are many large interstitial sites where the anions can be accommodated, but not the cations because their charge is larger, and they are less well screened from each other. 

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