Defect anion vacancy

In general, the lattice distortion can be caused both by point and extended defects generated due to incorporation of modifying cations (Zr, Ca) or anions (fluorine, residual lattice hydroxyls). Extended defects differing from the surrounding lattice by the electron density can be detected by using SAXS [6], while point defects (anion vacancies etc) are usually probed by UV-Vis [7]. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

Defect lattice with ordered anion vacancies... 

In this case, we use 6 as a small fraction since the actual number of defects is small in relation to the overall number of ions actually present. For the F-Center, the brackets enclose the complex consisting of an electron captured at an anion vacancy. Note that these equations encompass all of the mechanisms that we have postulated for each of the individual reactions. That is, we show the presence of vacancies in the Schottlqr case and interstitial cations for the Frenkel case involving either the cation or anion. The latter, involving an interstitlcd anion is called, by convention, the "Anti-Frenkel" case. The defect reaction involving the "F-Center" is also given. 

This type of electronic defect, found only in heterogeneous solids, consists of two associated, negatively-charged anion vacancies, one on each plcme as shown. 

Intrinsic Defects The simplest crystalline defects involve single or pairs of atoms or ions and are therefore known as point defects. Two main types of point defect have been identified Schottky defects and Frenkel defects. A Schottky defect consists of a pair of vacant sites a cation vacancy and an anion vacancy. A Schottky defect is... 

The origin of the color is as follows. The electron trapped at an anion vacancy in an alkali halide crystal is an analog of a hydrogen atom. The electron can occupy one of a number of orbitals, and transitions between some of these levels absorb light and hence endow the solid with a characteristic color. F centers and related defects are discussed further in Chapter 9. 

Such changes in the defect population can be critical in device manufacture and operation. For example, a thin him of an oxide such as SiO laid down in a vacuum may have a large population of anion vacancy point defects present. Similarly, a him deposited by sputtering in an inert atmosphere may incorporate both vacancies and inert gas interstitial atoms into the structure. When these hlms are subsequently exposed to different conditions, for example, moist air at high temperatures, changes in the point defect population will result in dimensional changes that can cause the him to buckle or tear. 

In crystals of more complex formula, such as titanium dioxide, TiC>2, a Schottky defect will consist of two anion vacancies and one cation vacancy. This is because it is necessary to counterbalance the loss of one Ti4+ ion from the crystal by the absence of two O2- ions in order to maintain composition and electroneutrality. This ratio of two anion vacancies per one cation vacancy will hold in all ionic compounds of formula MX2. In crystals like A1203, two Al3+ vacancies must be balanced by three O2- vacancies. Thus, in crystals with a formula M2X3, a Schottky defect will consist of two vacancies on the cation sublattice and three vacancies on the anion sublattice. These vacancies are not considered to be clustered together but are distributed... 

A Schottky defect in a crystal consists of a cation and anion vacancy combination that ensures overall electroneutrality in the crystal (Section 1.9). The estimation of the configurational entropy change in creating a population of Schottky defects in a crystal can be obtained in the same way as that of a population of vacancies in a monatomic crystal. The method follows that given in Section 2.1 for the equilibrium concentration of vacancies in a monatomic crystal and is set out in detail in Supplementary Material S4. 

The ratio of cation to anion vacancies due to Schottky defects in a crystal of formula M2X3 is equal to ... 

Pure potassium bromide, KBr, which adopts the sodium chloride structure, has the fraction of empty cation sites due to Schottky defects, ncv/Nc, equal to 9.159xl0-21 at 20°C. (a) Estimate the enthalpy of formation of a Schottky defect, Ahs. (b) Calculate the number of anion vacancies per cubic meter of KBr at 730°C (just below the melting point of KBr). The unit cell of KBr is cubic with edge length a = 0.6600 nm and contains four formula units of KBr. 

When Schottky defects are present in a crystal, vacancies occur on both the cation and anion sublattices, allowing both cation and anion vacancy diffusion to occur (Fig. 5.12a). In the case of Frenkel defects interstitial, interstitialcy, and vacancy diffusion can take place in the same crystal with respect to the atoms forming the Frenkel defect population (Fig. 5.12b). 

Derive the polynomial expressions for the concentration dependence of electrons, metal vacancies, and anion vacancies for a compound MX showing Schottky equilibrium (Section 7.9.4). Insert values of the equilibrium constants to obtain polynomial expressions for the cases where electronic defects dominate. 

The acceptor defects can be compensated by anion vacancies or holes (Section 8.2.3). That is, the addition of acceptors to the left-hand side of Eq. (8.10) requires an increase in the number of anion vacancies ... 

Fig. 21. (a) The nature of the glide shear plane defects in three-dimensional projection and (b) in one layer of idealized structure, showing the novel glide shear process and the formation of glide shear plane defects. Filled circles are anion vacancies, (c) Schematic of glide shear. Glide defects accommodate the misfit at the interface between catalyst surface layers with anion vacancies (filled circles) and the underlying bulk (85,89). 

Conesa373 modeled the surfaces and defects on ceria, and based on computer simulations, determined the relative stabilities of surfaces (111) > (110) > (211) > (100). Although the formation of anion vacancy defects was suggested to be more difficult to form on the more stable (111) surface, he indicated that anion vacancy pairs, important for 02 uptake and release processes, were easiest to form on the ceria (111) surface. 

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... 

The dielectric constant and breakdown field of a material are not the only considerations. Because a capacitor is used for charge storage, the leakage properties of the film are also critical. These are largely controlled by the defects in the films which can include oxygen (anion) vacancies or mixed valence effects in the cations. It is important that films that are as fully oxidized as possible be studied. 

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