Frenkel and Schottky Defects

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. 

BALANCED POPULATIONS OF POINT DEFECTS SCHOTTKY AND FRENKEL DEFECTS... 

Figure 2.5 Calculated variation of the formation energy of Schottky and Frenkel defects in the halides AgCl and AgBr as a function of temperature. [Redrawn from data in C. R. A. Catlow, Mat. Res. Soc. Bull., XIV, 23 (1989).]...

Equation 4.75 finds its application in the region of intrinsic disorder (a similar equation can be developed for Frenkel defects), where Schottky and Frenkel defects are dominant with respect to point impurities and nonstoichiometry. 

Table 5.1 lists some enthalpy-of-formation values for Schottky and Frenkel defects in various crystals. 

TABLE 5.1 The formation enthalpy of Schottky and Frenkel defects in selected compounds... 

Zero-dimensional point defects, such as Schottky and Frenkel defects. 

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... 

A variety of defect formation mechanisms (lattice disorder) are known. Classical cases include the - Schottky and -> Frenkel mechanisms. For the Schottky defects, an anion vacancy and a cation vacancy are formed in an ionic crystal due to replacing two atoms at the surface. The Frenkel defect involves one atom displaced from its lattice site into an interstitial position, which is normally empty. The Schottky and Frenkel defects are both stoichiometric, i.e., can be formed without a change in the crystal composition. The structural disorder, characteristic of -> superionics (fast -> ion conductors), relates to crystals where the stoichiometric number of mobile ions is significantly lower than the number of positions available for these ions. Examples of structurally disordered solids are -> f-alumina, -> NASICON, and d-phase of - bismuth oxide. The antistructural disorder, typical for - intermetallic and essentially covalent phases, appears due to mixing of atoms between their regular sites. In many cases important for practice, the defects are formed to compensate charge of dopant ions due to the crystal electroneutrality rule (doping-induced disorder) (see also -> electroneutrality condition). 

The examples discussed here are the simplest possible and real systems are usually more complicated. Moreover, we have used simplified models for example, v is the characteristic frequency of the interstitial ion or an ion adjacent to a vacant lattice position it will be diflerent from the characteristic lattice frequency and will not be the same for Schottky and Frenkel defects. However, the general principles of the transfer of matter through a crystalline solid are as they have been given here. 

Schottky and Frenkel defects do not alter the stoichiometry of the material as they are intrinsic. In non-stoichiometric materials, both types of point defect occur, but ... 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

The mole fractions of Schottky and Frenkel defects in a NaCI crystal at 1000 K estimated. The energies offormation of these defects are 2 eV and 3 eV respectively given ... 

There are several methods that may be used to study the occurrence of Schottky and Frenkel defects in stoichiometric crystals, but the simplest, in principle, is to measure the... 

These are defined as ones in which the crystal chemistry, i.e., the ratio of the cations to anions, does not change, and they include, among others. Schottky and Frenkel defects (Fig. 6.3). 

Note that these equations are simply the Combinatorial Equation as applied to these two sets of defects. We can set up a partition function(see the above definition), using equation 2.5.3. We apply this to the Schottky and Frenkel defects as examples ... 

It is clear without a doubt that both Schottky and Frenkel defects are thermal in ori n. 

So far in this chapter, we have assumed implicitly that all the pure substances considered have ideal lattices in which every site is occupied by the correct type of atom or ion. This state appertains only at OK, and above this temperature, lattice defects are always present. The energy required to create a defect is more than compensated for by the resulting increase in entropy of the structure. There are various types of lattice defects, but we shall introduce only the Schottky and Frenkel defects. Solid state defects are discussed further in Chapter 28. Spinels and defect spinels are introduced in Box 13.6. 

Figure 13.4. Effect of non-stoichiometry on effective diffusion coefficient in an MO oxide where both the Schottky and Frenkel defects are considerable.

Show the change in defect concentrations in AI2O3 with an increased addition of Zr02. Assume that the major and minor defects in AI2O3 are Schottky and Frenkel defects, respectively, and that all Zr cations go into A1 sites. 

R. F. Davis. Point (atomic) defects in stoichiometric ceramic materials. Part I Solid solutions Part II Schottky and Frenkel defects. J. Mater. Educ. 2, 809, 837 (1980). 

It is known that ionic compounds have appreciable electrical conductivity, which is inseparable from diffusion, due to atomic defects, such as Schottky and Frenkel defects to an extent, and ionic migration and diffusion. For instance, Schottky defects are combinations of cation and anion vacancies necessary to maintain ionic electrical neutrality and stoichiometric ionic structure. In general, ions (cations and anions) diffuse into adjacent sites. 

Let us consider a stoichiometric crystal with composition MX. If a charged point defect is formed in such a crystal, a complimentary point defect with opposite effective charge must be formed to conserve the electroneutrality of the stoichiometric crystal. Two types of defect stractures have been found to be important in stoichiometric metal oxides and these are termed Schottky and Frenkel defects, respectively, honouring early contributions of two of the many German scientists who pioneered the development of defect chemistry (Schottky (1935), Frenkel (1926)). 

Various imperfections in solid-state structures include the Schottky and Frenkel defects. The latter can lead to nonstoichiometric compounds. Edge dislocations can make a metal more malleable. Examples include lead, white tin, and the iron of horseshoes. 

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