Defect cation-Frenkel pair

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

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... 

A) Shottky defects consist of paired cation and anion vacancies. (B) Frenkel defects consist of ion vacancy and ion interstitial pairs. (C) Anion vacancies may be neutralized by substitution of cations of higher valence. 

Similarly, in thermal equilibrium, some ionic crystals at a temperature above absolute zero enclose a certain number of Frenkel pair defects, that is, anion and cation interstitials in the structure. Since the concentration of Frenkel pair defects at equilibrium at an absolute temperature, T, obeys the mass action law, then [16]... 

Intrinsic point defects are deviations from the ideal structure caused by displacement or removal of lattice atoms [106,107], Possible intrinsic defects are vacancies, interstitials, and antisites. In ZnO these are denoted as Vzn and Vo, Zn and 0 , and as Zno and Ozn, respectively. There are also combinations of defects like neutral Schottky (cation and anion vacancy) and Frenkel (cation vacancy and cation interstitial) pairs, which are abundant in ionic compounds like alkali-metal halides [106,107], As a rule of thumb, the energy to create a defect depends on the difference in charge between the defect and the lattice site occupied by the defect, e.g., in ZnO a vacancy or an interstitial can carry a charge of 2 while an antisite can have a charge of 4. This makes vacancies and interstitials more likely in polar compounds and antisite defects less important [108-110]. On the contrary, antisite defects are more important in more covalently bonded compounds like the III-V semiconductors (see e.g., [Ill] and references therein). 

A population of vacancies on one subset of atoms created by displacing some atoms into normally unoccupied interstitial sites constitute a second arrangement of paired point defects, termed Frenkel defects (Figure 2(b), (c)). Because one species of atom or ion is simply being redistributed in the crystal, charge balance is not an issue. A Frenkel defect in a crystal of formula MX consists of one interstitial cation plus one cation vacancy, or one interstitial anion plus one anion vacancy. Equally, a Frenkel defect in a crystal of formula MX2 can consist of one interstitial cation plus one cation vacancy, or one interstitial anion plus one anion vacancy. As with the other point defects, it is found that the free energy of a crystal is lowered by the presence of Frenkel defects and so a popnlation of these intrinsic defects is to be expected at temperatures above 0 K. The calculation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects. The appropriate chemical equilibrium for cation defects is ... 

There are two types of lattice defects that occur in all real crystals and at very high concentration in irradiated crystals. These are known as point defects and line defects. Point defects occur as the result of displacements of atoms from their normal lattice sites. The displaced atoms usually occupy sites that are not in the lattice framework they are then known as interstitials. The empty lattice site left behind by the interstitial is called a vacancy. Avacancy produced by displacement of an anion or cation, along with its interstitial ion, is called a Frenkel pair, or simply a... 

Figure 12.8 Binary ionic crystal showing defects that can lead to lattice diffusion, (a) Frenkel defect vacancy-interstitial pair), (b) Schottky defect (anion-cation vacancy). (After Kingery ct a .. 1976.)...

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

Ceria Ceria (CeO2) is similar to zirconia and, in pure form, has the fluorite structure (see Chapters 2 and 9). The dominant point defects are anion Frenkel pairs and, like zirconia, ceria can be doped with rare earth cations to increase the concentration of anion vacancies and increase the oxygen ion conductivity. There is considerable interest in the application of ceria in SOFCs, as it has a higher conductivity than zirconia and can therefore operate at lower temperatures [127]. Unlike zirconia, ceria is readily reduced at elevated temperatures, resulting in the loss... 

Defect pairs Schottky pairs of anion and cation vacancies Frenkel pairs of a cation vacancy and the same cation as an interstitial Anti-Frenkel the same as Frenkel but for anions 0... 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

The migration of a lattice atom/ion into an available interstitial site will leave behind a vacancy (Figure 2.49) the formation of such an interstitial/vacancy pair is known as a Frenkel defect. In contrast, Schottky defects are formed through the migration of a cation-anion pair from the crystal lattice framework, leaving behind two vacant lattice sites. For ionic crystals, the overall charge of the crystal must be charge-balanced. That is, if trivalent ions such as La are substituted with divalent cations such as Ca, there must be concomitant placements of divalent anions... 

Figure 1-15. Cation Frenkel defect pair in AgCl. From Shriver and Atkins Inorganic Chemistry.

The effects of higher valent cation impurities on Frenkel equilibria are analogous to those described for the Schottky equilibria. When divalent Mf impurities/dopants are dissolved in MX with predominating cation Frenkel defect pairs (and M ) the electroneutrality condition is given by... 

In an ionic solid, a cation may move into an interstitial site leaving a cation vacancy. This is known as a Frenkel defect and the cation interstitial-cation vacancy is known as a Frenkel pair (Figure 8.1). An anion could also move into an interstitial to form an anion interstitial-anion vacancy, but since anions are generally larger than cations, the former is more probable. 

Frenkel defect In an ionic solid, a cation-vacancy and cation-interstitial pair. 

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... 

We now introduce a Fourier transform procedure analogous to that employed in the solution theory, s 62 For the purposes of the present section a more detailed specification of defect positions than that so far employed must be introduced. Thus, defects i and j are in unit cells l and m respectively, the origins of the unit cells being specified by vectors R and Rm relative to the origin of the space lattice. The vectors from the origin of the unit cell to the defects i and j, which occupy positions number x and y within the cell, will be denoted X 0 and X for example, the sodium chloride lattice is built from a unit cell containing one cation site (0, 0, 0) and one anion site (a/2, 0, 0), and the translation group is that of the face-centred-cubic lattice. However, if we wish to specify the interstitial sites of the lattice, e.g. for a discussion of Frenkel disorder, then we must add two interstitial sites to the basis at (a/4, a/4, a]4) and (3a/4, a/4, a/4). (Note that there are twice as many interstitial sites as anion-cation pairs but that all interstitial sites have an identical environment.) In our present notation the distance between defects i and j is... 

Lattice defects in ionic crystals are interstitial ions and ion vacancies. In crystalline sodium chloride NaCl a cation vacancy Vn - is formed by producing a surface cation NaJ, (Nal - NaJ + Vua ) this is called the Schottky defect. On the other hand, in crystalline silver chloride AgCl a pair of cation vacancy Va,. and interstitial cation Ag is formed, (Ag - Agj + ) this is called the Frenkel... 

Figure 1-2. Two-dimensional schematic representation of the formation of Frenkel defect pairs in AgBr AgAg+V = Ag +VAg. = vacant cation site.

One of the causes of point defects is a temperature increase which results in an increased thermal movement of the atoms which can subsequently lead to the atoms escaping from their place in the lattice. Other causes are the effects of radiation and inbuilt, foreign atoms. In an atomic lattice a vacancy can occur due to the movement of an atom, an absence of an atom or molecule from a point which it would normally occupy in a crystal. In addition to this vacancy an atomic will form elsewhere. This combination of an atomic pair and a vacancy is called the Frenkel defect. In ionic crystals an anion and a cation have to leave the lattice simultaneously due to the charge balance. As a result a vacancy pair remains and this is called the Schottky defect. Both defects can be seen in figure 4.8. 

Various kinds of packing defects exist in the ionic crystals of NaCl type. A pair of cation and anion may be shifted from their stable positions toward the surface of the crystal, thus leaving behind a pair of vacancies. This is called the Schottky defect. The cation may leave its stable position and enter into an interstitial site. The formation of an interstitial cation and a vacancy is called the Frenkel defect. In addition to these two common kinds of defects, the presence of impurity atoms, atoms of varied valence, vacancies, and/or interstitial atoms is also possible. Some other important defects are discussed below. 

Intrinsic defects can form by the loss of pairs of cations and anions (Schottky) or by the movement of anions or cations on to interstitial sites (Frenkel). Both mechanisms can occur simultaneously. 

In compound crystals, balanced-defect reactions must conserve mass, charge neutrality, and the ratio of the regular lattice sites. In pure compounds, the point defects that form can be classified as either stoichiometric or nonstoichiometric. By definition, stoichiometric defects do not result in a change in chemistry of the crystal. Examples are Schottky (simultaneous formation of vacancies on the cation and anion sublattices) and Frenkel (vacancy-interstitial pair). 

Frenkel disorder a pair of defects involving only cations, with the pair... 

For the Frenkel disorder the predominant defects are either limited to the cations and anions, and the disorder involves the presence of equal numbers of vacancies and interstitial ions in a sublattice in a crystal. In the formation of a Frenkel defect pair, a cation on a normal site is transferred to an interstitial site, and no new lattice sites are created in the process. If, for the sake of illustration, the interstitial ion and the resulting vacancy are assumed to be doubly charged, the formation of a Frenkel defect pair may be written... 

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