Anti-Frenkel type defects

Frenkel type in which metal atoms on regular sites move to interstitial sites, leaving metal vacancies, i.e. (M = MJ (Fig. 1.9(b)). Anti-Frenkel type defects, in which anion atoms on regular sites move to interstitial sites, are also possible, but are rarely observed because the ionic radii of anions are usually larger than those of the metals under consideration. Frenkel type is stoichiometric. 

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. 

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. 

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,... 

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. 

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. 

Let us next calculate the defect strucmre of a more general case, AaO-doped MO. Here we assume that A substitutes M and MO has the anti-Frenkel disorder as the majority type of ionic disorder. Then we may list the defects of the most concern as... 

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 a doped oxide M2O3 exhibiting anti-Frenkel disorder, Colomban and Novak present a sehematie Kroger-Vink diagram of the extrinsic and intrinsic point defects as a function of the partial water pressure. With regard to electrical properties, the proton conductivity in the binary metal oxides is usually much lower than in the perovskite-type oxides. ... 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

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