Frenkel-defect

Subsequent findings that even conventional ionic solids, such as sodium chloride, have measurable conductivities that are not electronic stimulated the development of theories for ionic motion in solids. Early in this century, Ioffe introduced the concept of interstitial ions and vacancies (see Defects in Solids), which was the starting point of the theory of defects. Frenkel and Schottky used these theories to develop their classic mechanisms to explain how electricity can be conducted through ionic solids by the flow of ions (see Frenkel Defects, Schottky Defects) They proposed that ionic solids are not perfect, with every lattice site occupied by its appropriate ions, but contain defects in which either ions... 

Frenkel defect. In some cases, the displaced ions are removed so far from their vacancies that they form a new layer at the crystal surface. The vacancies left behind in this case are called Schottky defects. Frenkel and Schottky defects play very important roles in the properties of solids altered by radiation damage. 

Electron microscopic studies in the 1940s proved that supported catalysts possess a crystalline structure, dispelling earlier conjecture of amorphicity. However, practical catalysts are never uniform, exhibiting particle size distribution, lattice defects (Frenkel or Schottky), and dislocations. The following questions then arise Are all lattice surfaces equally active Do surface clusters of particles and surface atoms have comparable activity Does catalytic activity depend on particle size Is there an optimal particle size or distribution These questions remain, in general, still unanswered. However, in recent electrocatalytic studies concern about these effects is shown, following similar concern in conventional heterogeneous catalysis. 

When an ion occupies a normally vacant interstitial site, leaving its proper site vacant, the defect is termed a Frenkel defect. Frenkel defects are most common in crystals where the cation is much smaller than the anion, for instance, in AgBr, as illustrated schematically in Fig. 2-14(b). 

Stoichiometric reaction is one in which no mass is transferred across the crystal boundaries. The three most common stoichiometric defects are Schottky defects, Frenkel defects, and antistructure disorder or misplaced atoms. 

Frenkel defects occur in silver bromide, AgBr. In this compound some of the silver ions (Ag ) move from the normal positions to sit at usually empty places to generate interstitial silver ions and leave behind vacancies on some of the usually occupied silver sites. The bromide ions (Br ) are not involved in the defects. (Frenkel defects in AgBr make possible black and white and colour photography on photographic film.)... 

A second common type of defect in crystals is known as a Frenkel defect Frenkel defects occur when one of the ions (usually the smaller ion) becomes displaced from its normal position and occupies an interstitial site in the crystalline lattice. This occurs more frequently when there is a large difference in size between the cations and the anions. For example, the Ag+ ions in AgBr usually sit in the octahedral holes formed by a face-centered cubic lattice of Br ions. However, every so often, one of these Ag+ ions might find itself displaced to one of the smaller tetrahedral holes in the lattice. In the zinc blende ionic lattice, where every other tetrahedral hole is... 

A stoichiometric crystal with Frenkel disorder contains the same concentrations of metal vacancies and metal interstitial ions. Contrary to the Schottky defects, Frenkel defect pairs can be formed directly inside the crystal. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Fig. 1.6 Poinl defects (a) vacancies (Schotlky defects) (6) interstitials (Frenkel defects) (c) ideal crystal.

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

By analogy with similar materials in which free elecU ons and electron holes are formed, NiO is called a p-type compound having vacant site Schottky defects, and ZnO is an n-type compound having interstitial Frenkel defects. The concentrations of these defects and their relation to the oxygen pressure in the suiTounding atmosphere can be calculated, for a dilute solution of defects by the application of a mass action equation. The two reactions shown above are represented by the equations... 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

The equilibrium concentration of defects is obtained by applying the law of mass action to Eq. (7) or (8). This leads in the case of Frenkel disorder to... 

Point defects (Schottky, Frenkel, unoccupied lattice sites, misplaced units)... 

Frenkel defects (Cation vacancy plus same cation as interstitial)... 

Note that, in general, anions are larger in size than cations due to the extra electrons present in the former. A hexagonal lattice is shown in 3.1.6. with both Frenkel and Schottky defects, as well as substitutional defects. Thus, if a cation is missing (cation vacancy) in the cation sublattice, a like anion will be missing in the anion sub-lattice. This is known as a Schottky defect (after the first investigator to note its existence). 

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. 

In this case, we use 6 as a small fraction since the actual number of defects is small in relation to the overall number of ions actually present. For the F-Center, the brackets enclose the complex consisting of an electron captured at an anion vacancy. Note that these equations encompass all of the mechanisms that we have postulated for each of the individual reactions. That is, we show the presence of vacancies in the Schottlqr case and interstitial cations for the Frenkel case involving either the cation or anion. The latter, involving an interstitlcd anion is called, by convention, the "Anti-Frenkel" case. The defect reaction involving the "F-Center" is also given. 

Thus, if Frenkel Defects predominate in a given solid, other defects are usually not present. Likewise, for the Schottky Defect. Note that this applies for associated defects. If these are not present, there will still be 2 types of defects present, each having an opposite effect upon stoichiometry. 

CeHot. From thermodsmamic measurements, it was found that the intrinsic defects were Anti-Frenkel in nature, i.e.- (H + Vh). An equilibrium constant was calculated as ... 

---