Defect structures Schottky type

In order to calculate the equilibrium defect structure of a compound whether intrinsic or extrinsic, one should first posmlate the most likely defects on the basis of the strucmre of MO. Let us suppose that our system MO has the Schottky disorder as the majority type of ionic... 

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. 

Density and X-ray measurements on TiO revealed that the intrinsic defects were Schottky defects (Fn -I- Vq) and the intrinsic defect concentration in a sample annealed at 1300°C was 0.140. TiO has the NaCl-type structure. Using Eq. (23) with s = 1, Kj is calculated to be 0.030. Since there are two tetrahedral interstices per metal atom, a = 2, and Kg = 0.080. 

All solids contain defects or imperfections of structure or composition. Defects are important because they influence properties, such as mechanical strength. Two common types of defects are a missing ion in an otherwise perfect lattice, and the slipping of an ion from its normal site to a hole in the lattice. The holes discussed in this chapter are often called interstitial sites, since the holes are in fact interstices in the array of spheres. The two types of defects described here are called point defects because they occur within specific sites. In the 1930s, two solid-state physicists, W. Schottky and J. Fraenkel, studied the two types of point defects A Schottky defect corresponds to a missing ion in a lattice, while a Fraenkel defect corresponds to an ion that is displaced into an interstitial site. 

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 same analysis can be applied to more complex situations. Suppose that cation vacancy diffusion is the predominant migration mechanism, in a sodium chloride structure crystal, of formula MX, which contains Schottky defects as the major type of intrinsic defects. The relevant defect concentration [ii] is [Eq. (2.11)]... 

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... 

For a 1 1 solid MX, a Schottky defect consists of a pair of vacant sites, a cation vacancy, and an anion vacancy. This is presented in Figure 5.1 (a) for an alkali halide type structure the number of cation vacancies and anion vacancies have to be equal to preserve electrical neutrality. A Schottky defect for an MX2 type structure will consist of the vacancy caused by the ion together with two X anion vacancies, thereby balancing the electrical charges. Schottky defects are more common in 1 1 stoichiometry and examples of crystals that contain them include rock salt (NaCl), wurtzite (ZnS), and CsCl. 

Light sensors made from a-Si H are either p-i-n or Schottky barrier structures. Unlike crystalline silicon, a p-n jimction is ineffective without the undoped layer, because of the high defect density in doped a-Si H. Illumination creates photoexcited carriers which move to the junction by diffusion or drift in the built-in potential of the depletion layer and are collected by the junction. A photovoltaic sensor (solar cell) operates without an externally applied voltage and collection of the carriers results from the internal field of the junction. When the sensor is operated with a reverse bias, the charge collection generally increases and the main role of the doped layers is to suppress the dark current. A Schottky device replaces the p-type layer with a metal which provides the built-in potential. 

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... 

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 Erenkel defects. Solid state defects are discussed further in Chapter... 

Most impurity and defect states in SiC can be considered as deep levels. Both capacitance and admittance spectroscopy provide data on these deep levels which can act as donor or acceptor traps. Bulk 6H-SiC contains intrinsic defects which are thermally stable, up to 1700 °C. In epitaxial films of 6H-SiC a deep acceptor level is seen in boron-implanted samples but not when other impurities are implanted. Other centres, acting as electron traps, are also seen in p-n junction and Schottky barrier structures. Irradiation of 6H-SiC produces 6 deep levels, reducing to 2 after annealing. Only limited studies have been carried out on the 3C-SiC polytype, in the form of epitaxial films on silicon substrates. No levels were seen in thick films but electron traps were seen in thin n-type films and a hole trap (structural defect) was found to be a mobility killer. Neutron irradiation produces defects most of which can be removed by annealing. Two levels were found in Al-implanted 4H-SiC. 

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. 

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

Titanium(ll) oxide is manufactured by heating Ti02 Ti in vacuo. It is a black solid and a metallic conductor which adopts a defect NaCl-type structure at room temperature one-sixth of both anion and cation sites are unoccupied, i.e. a Schottky defect. The oxide also exists as a non-stoichiometric compound with compositions in the range TiOo.82-TiOi.23. Conducting properties of the first row metal(II) oxides are compared in Section 28.2. 

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