Anion Frenkel defect

A single anion Frenkel defect in an ionic crystal of formula MX2 needs to be balanced by ... 

The energy of formation of defects in PbF2 are anion Frenkel defect, 0.69 eV cation Frenkel defect, 4.53 eV Schottky defect, 1.96 eV. (a) What point defects do these consist of (b) What are (approximately) the relative numbers of these defects in a crystal at 300 K (Data from H. Jiang et al., 2000). 

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

The structure of the oxide Ba2In205 suggests that anion Frenkel defects will be preferred. Oxidation will add anions and reduction will remove anions. The four equilibria can now be written. 

It is less common to observe an anion Frenkel defect when an anion moves into an interstitial site. This is because anions are commonly larger than the cations in the structure and so it is more difficult for them to enter a crowded low-coordination interstitial site. 

When AX (e.g., KC1) is irradiated with X-rays (or electrons), pairs of anionic Frenkel defects (Le., Xf, V ) are formed. Most of them recombine, but a small fraction separates and becomes so-called H(X ) and F(Vx) centers. Depending on the tempera-... 

An example of the kinds of result obtainable can be seen in the work of Harding (1985) on calcium fluoride. The calculated defect parameters for the formation enthalpy and entropy of the anion Frenkel defect are 2.81 eV and 5.4k, respectively. This compares with the experimental values of Jacobs and... 

Frenkel defects are usually formed by displacing the smaller ion. In AI2O3, for example, the cation is smaller and we would expect to form cation Frenkel defects. However, anion Frenkel defects will form in UO2, Ce02, and Th02, which all have large cations. In contrast, we would expect to hnd Schottky defects in crystals with high coordination numbers such as MgO. 

The vacancy on an interstitial site is simply that there is no interstitial initially. Notice that Eq. 11.4 can be written for a single cation. We do not need to consider the number of sites, etc. The anion Frenkel defect reaction would be similar, but is unlikely to occur in a material such as AI2O3. 

Similar equations can be obtained as the Frenkel defects are formed at anion sites. However, anion Frenkel defects are rarely encountered, because anions have relatively large sizes, i.e., there are no interstitial sites for them to stay. Also, the formation of cation and anion Frenkel defects is not controlled by the requirement of electroneutraUty balance, so that the concentration of cation interstitial may not... 

Corresponding equations can be written for the formation of Frenkel defects on the anion sites. It should be noted that the formation of cation and anion Frenkel defects are not linked through an electroneutrality condition, so the cation interstitial concentration need not be equal to the anion interstitial concentration. 

A corresponding equation may be written for the formation of an anion Frenkel defect pair. This latter defect situation is also often termed an anti-Frenkel defect stmcture. 

Write a reaction for the formation of anion Frenkel defects in MO. 

In the case of the Frenkel defect, the "square" represents where the cation was supposed to reside in the lattice before it moved to its interstitial position in the cation sub-lattice. Additionally, "Anti-Frenkel" defects can exist in the anion sub-lattice. The substitutional defects axe shown as the same size as the cation or anion it displaced. Note that if they were not, the lattice structure would be disrupted from regularity at the points of ins tlon of the foreign ion. 

Draw a heterogeneous lattice, using circles and squares to indicate atom positions in a simple cubic lattice. Indicate both Schottky and Frenkel defects, plus the simple lattice defects. Hint- use both cation and anion sub-lattices. 

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 similar equation can be written for Frenkel defects on the anion positions ... 

Frenkel defects on the cation sublattice of a sodium chloride structure compound. Frenkel defects on the anion sublattice of a fluorite structure compound. 

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). 

Frenkel defects on the anion sublattice show only anion migration and hence have fa close to 1. The alkali halides NaF, NaCl, NaBr, and KC1 in which Schottky defects prevail and in which the cations and anions are of similar sizes have both cation and anion contributions to ionic conductivity and show intermediate values of both anion and cation transport number. 

It is theoretically possible for cations to occupy anion sites, and vice versa. Kroger-Vink notation, then, dictates that an M atom on an X site be designated as Mx and that an X atom on an M site be designated as Xm- Recall that we can have defect clusters, such as a Frenkel defect. Defect clusters are enclosed in parentheses—for example, (VmVx) or (X Xm)—to indicate that the individual defects are associated with one another. Impurity atoms are also coded as to lattice position. If we introduce a metal impurity atom L into our compound MX, it might occupy a metal cation site, and is thus designated as Lm- Similarly, Sj is an S impurity atom on an interstitial site. 

Point defects. Point defects (Fig. 5.1) are limited to a single point in the lattice, although the lattice will buckle locally so that the influence of point defects may spread quite far. A Frenkel defect consists of a misplaced interstitial atom and a lattice vacancy (the site the atom should have occupied). For example, silver bromide, which has the NaCl structure, has substantial numbers of Ag+ ions in tetrahedral holes in the ccp Br array, instead of in the expected octahedral holes. Frenkel defects are especially common in salts containing large, polarizable anions like bromide or iodide. 

Defects in which both a cation and sufficient anions to balance the charge (or vice versa) are completely missing from the lattice are called Schottky defects. Schottky defects result in a density that is lower than that calculated on the basis of unit cell dimensions, whereas Frenkel defects do not affect this density. Titanium(II) oxide, for example, also has the NaCl structure, but, even when its composition is TiOi.oo (which it rarely is see Section 5.4), about one-sixth of the Ti2+ and 02 sites are vacant. 

Irradiation of all kinds of solids (metals, semiconductors, insulators) is known to produce pairs of the point Frenkel defects - vacancies, v, and interstitial atoms, i, which are most often spatially well-correlated [1-9]. In many ionic crystals these Frenkel defects form the so-called F and H centres (anion vacancy with trapped electron and interstitial halide atom X° forming the chemical bonding in a form of quasimolecule X2 with some of the nearest regular anions, X-) - Fig. 3.1. In metals the analog of the latter is called the dumbbell interstitial. 

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. 

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. 

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. 

Generally, anion interstitials are rare, because the anionic radius is greater than the cationic radius. The rule of electrical neutrality in a material containing both Schottky and Frenkel defects requires that the positive and negative point defects must be balanced, that is... 

If the semiconductor is an ionic solid, then electrical conduction can be electronic and ionic, the latter being due to the existence of defects within the crystal that can undergo movement, especially Frenkel defects (an ion vacancy balanced by an interstitial ion of the same type) and Schottky defects (cation and anion vacancies with ion migration to the surface). This will be discussed further in Chapter 13, as ionic crystals are the sensing components of an important class of ion selective electrodes. 

In a Frenkel defect, an ion leaves its lattice position for an interstitial site, producing a vacancy. Since in well-packed structures the cation is normally smaller than the anion, the Frenkel defect is more probable for the cation. Crystal volume remains almost unaltered by defect formation. 

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