Anti Schottky disorder

The considerations presented up to this point can be easily extended to higher ionic crystals and compounds with more than two or three components [4]. Again, quite generally, the energetically favourable defects constitute the disorder type. For a binary ionic crystal without electronic majority defects there are, in principle, only four disorder types. These are the previously described Schottky and Frenkel types and their corresponding anti-types namely, cations and an equivalent number of anions in the interstices (anti-Schottky disorder), and anion vacancies with an equal number of anions in the interstices (anti-Frenkel disorder). However, for higher ionic crystals the number of possible disorder types increases considerably because of the greater number of components and sublattices. Therefore, in such crystals, it is much more difficult to uniquely determine the disorder type. 

Besides the Frenkel and the Schottky disorders, also the anti-Frenkel and anti-Schottky disorders exist. But more important are the Frenkel and Schottky types. In the case of sodium sulfate, sodium ions on the normal lattice position (the notation of Krbger-Vink is used see entry Kroger-Vinks Notation of Point Defects ) go into free space of ions (interstitials) and sodium vacancies remain (Frenkel defects) ... 

For Schottky-disorder in alkali halides [114], Frenkel-disorder in silver halides and anti-Frenkel-disorder in alkaline earth halides it is found that const 1.5...2 [115]. Anti-Schottky disorder, i.e. the interstitial incorporation of both cation md anion, is extremely rare, primarily on account of the high energy of large anions in the interstices and is only possible in loose structures. It has, for instance, been postulated for orthorhombic PbO [116,117]. A detailed description of these disorder types is given in Section 5.5. Table 5.1 lists formation data for a series of halides. 

Natmally, the counterpart of the Schottky reaction exists as the last possibility, namely, the additional introduction of a monomeric unit (lattice molecule) into cationic and anionic interstitial positions. This anti-Schottky reaction requires an adequately flexible structure and is usually not a dominant disorder reaction. One exception might be yellow PbO, for which we then formulate ... 

PbO is a material displaying the I region. There is no anti-Prenkel disorder, but probably an anti-Schottky disorder is present. Nevertheless, on account of [Pbf] = [Of] = /K here, too, we expect... 

The composition of these oxides normally departs from the precise stoichiometry, expressed in their chemical formulae. For example, in the case of a stoichiometric oxide, such as A05, where 8 = 0, we will have only thermal disorder, where the concentration of vacancies, and interstitials will be determined by the Schottky, Frenkel, and anti-Frenkel mechanisms [40-42] (these defects are explained in more detail in Chapter 5). In the case of the Schotky mechanism, the following equilibrium, described with the help of the Kroger-Vink notation, [43] develops [40]... 

In Section 2.3, the structure of oxides were studied. For a stoichiometric oxide, such as AOs, where 5 = 0, we will have thermal disorder, and the concentration of vacancies and interstitials will be determined by the Frenkel, anti-Frenkel [40,41], and Schottky [40,42] mechanisms (see Figures 5.21 through 5.23). 

There are different types of formation reactions and equilibria, depending on the type of lattice and the type of defect. The types of disorders are known as Schottky, Frenkel, and anti-Frenkel,... 

A disorder is symmetrical if one of the two defects which make it up involves the lattice of the element A and the other the lattice of the element B. In practice, we find Schottky disorder and the anti-stmcture disorder. 

While intrinsic disorder of the Schottky, Frenkel, or anti-Frenkel type frequently occurs in binaiy metal oxides and metal halides, i.e., Equations (5.1), (5.3), and (5.5), Schottky disorder is seldomly encountered in temaiy compounds. However, in several studies Schottky disorder has been proposed to occur in perovskite oxides. Cation and anion vacancies or interstitials can occur in ternary compounds, but such defect stractures are usually to be related with deviations from molecularity (viz. Sections II.B.2 and II.B.3), which in fact represent extrinsic disorder and not intrinsic Schottky disorder. From Figures 5.3 and 5.4 it is apparent that deviations from molecularity always influence ionic point defect concentrations, while deviations from stoichiometry always lead to combinations of ionic and electronic point defects, as can be seen from Figures 5.2 and 5.5. 

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