Defects Schottky defects

A point defect is a localized defect that consists of a mistake at a single atom site in a solid. The simplest point defects that can occur in pure crystals are missing atoms, called vacancies, or atoms displaced from the correct site into positions not normally occupied in the crystal, called self-interstitials. Additionally atoms of an impurity can occupy a normal atom site to form substitutional defects or can occupy a normally vacant position in the crystal structure to form an interstitial. Other point defects can be characterized in pure compounds that contain more than one atom. The best known of these are Frenkel defects, Schottky defects, and antisite defects. 

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. 

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... 

Schottky defect See defect structures. Schradan, octamethylpyrophosphoramide,... 

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. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

The vacant sites will be distributed among the N lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a conesponding number of vacancies on die N lattice sites. In the case of ionic species, it is necessaty to differentiate between cationic sites and anionic sites, because in any particular substance tire defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, tire random distribution of the n vacancies on the N lattice sites cair be achieved in... 

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... 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

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. 

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

Schottky defects (absence of both cation and anion)... 

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). 

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. 

Write a series of equations for the Frenkel defect, similar to those given for the Schottky defect, i.e.- Equations 3.7.2 to 3.7.3. 

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... 

FIGURE 25.1 Schematic representations of (a) a Schottky defect in NaCl and (b) a Frenkel defect in AgCl. (From Gelings and Bouwmeester, 1997, Fig. 3.36, with permission from CRC Press LLC via CCC.)... 

In some ionic crystals (primarily in halides of the alkali metals), there are vacancies in both the cationic and anionic positions (called Schottky defects—see Fig. 2.16). During transport, the ions (mostly of one sort) are shifted from a stable position to a neighbouring hole. The Schottky mechanism characterizes transport in important solid electrolytes such as Nernst mass (Zr02 doped with Y203 or with CaO). Thus, in the presence of 10 mol.% CaO, 5 per cent of the oxygen atoms in the lattice are replaced by vacancies. The presence of impurities also leads to the formation of Schottky defects. Most substances contain Frenkel and Schottky defects simultaneously, both influencing ion transport. 

For Schottky defects in an ionic crystal with a cubic lattice, the diffusion coefficient is given by the relationship, e.g. for a cation,... 

Crystals with Frenkel or Schottky defects are reasonably ion-conducting only at rather high temperatures. On the other hand, there exist several crystals (sometimes called soft framework crystals ), which show surprisingly high ionic conductivities even at the room or slightly elevated temperatures. This effect was revealed by G. Bruni in 1913 two well known examples are Agl and Cul. For instance, the ar-modification of Agl (stable above 146°C, sometimes denoted also as y-modification ) exhibits at this temperature an Ag+ conductivity (t+ = 1) comparable to that of a 0.1m aqueous solution. (The solid-state Ag+ conductivity of a-Agl at the melting point is actually higher than that of the melt.) This unusual behaviour can hardly be explained by the above-discussed defect mechanism. It has been anticipated that the conductivity of ar-Agl and similar crystals is described... 

Lanthanum fluoride (and fluorides of some other lanthanides) has an unusual type of defect (see Section 6.3.2), namely Schottky defects of the molecular hole type (whole LaF3 molecules are missing at certain sites). Charge carriers (F ) are formed as the result of interaction of LaF3 with this hole, leading to dissociation with formation of LaF2+ and F . 

Although this is a small fraction, for 1 mole of lattice sites, this amounts to 5.6 X1018 Schottky defects. The ability of ions to move from their sites into vacancies and by so doing creating new vacancies is largely responsible for the conductivity in ionic crystals. 

It is possible to create a population of Schottky defects that is much higher than the equilibrium population that is based on Eq. (7.32). If a crystal is heated to high temperature, lattice vibrations become more pronounced, and eventually ions begin to migrate from their lattice sites. If the crystal is quickly cooled, the extent of the motion of ions decreases rapidly so that ions that have moved from their lattice sites cannot return. As a result, the crystal will contain a population of Schottky defects that is much higher than the equilibrium population at the lower temperature. If a crystal of KC1 is prepared so that it contains some CaCl2 as an impurity, incorporating a Ca2+ ion in the crystal at a K+ site... 

FIGURE 7.16 An illustration of Schottky defects in an ionic crystal. 

For an ion to leave a lattice site in order to enter the coordination sphere of the metal would require the formation of a Schottky defect. The energy required to form this type of defect can be expressed by the equation... 

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