Lattice defects Frenkel

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. 

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. 

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... 

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. 

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... 

Intrinsic defects fall into two categories Schottky defects which consist of vacancies in the lattice, and Frenkel defects, where a vacancy is created by an atom or ion moving into an interstitial position. 

However, in the last two decades it has been shown experimentally [1,7, 8,12-14] and theoretically [15-18] that in many wide-gap insulators including alkali halides the primary mechanism of the Frenkel defect formation is subthreshold, i.e., lattice defects arise from the non-radiative decay of excitons whose formation energy is less than the forbidden gap of solids, typically 10 eV. These excitons are created easily by X-rays and UV light. Under ionic or electron beam irradiations the main portion of the incident particle... 

Conduction of electricity in ionic crystals is due to the motion of lattice defects, cither of the Schollky or Frenkel type. The mobility is given hy... 

Fig. 13.5. Defects in crystal lattices (a) Frenkel defect (b) Schottky defect.

For a classical SEI electrode such as lithium, the surface films formed on it in most of the commonly used polar aprotic systems conduct Li ions, with a transference number (t+) close to unity. As stated earlier the surface films on active metals are reduction products of atmospheric and solution species by the active metal. Hence, these layers comprise ionic species that are inorganic and/or organic salts of the active metal. Conducting mechanisms in solid state ionics have been dealt with thoroughly in the past [36-44], Conductance in solid ionics is based on defects in the medium s lattice. Figure 8 illustrates the two common defects in ionic lattices interstitial (Frenkel-type) defects [37] and hole (Schottky-type) defects [38],... 

Figure 8 Schematic presentation of Frenkel- and Schottky-type lattice defects.

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... 

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... 

Iron (II) sulphide never has the precise composition FeS—the sulphur is always present in excess. This could be due either to the inclusion in the lattice of extra, interstitial S atoms or to the omission from it of some of the Fe atoms. The second explanation is correct (Hagg and Sucksdorff, 1933), the phenomcon being an example of lattice defect (p. 152). There are two types of lattice defect. In Schottky defects, found in iron(Il) sulphide, holes are left at random through the crystal because of migration of ions to the surface. In Frenkel defects, holes are left at random by atoms which have moved to interstitial positions. Silver bromide has a perfect face-centred cubic arrangement of Br ions but the Ag+ ions are partly in interstitial positions. The effect is even more marked in silver iodide (p. 153). 

Crystals of the inert gases can develop only positional defects with respect to the ideal crystal lattice. Well known types of defects include lattice vacancies (Schottky defects) and the occupation of interstitial lattice sites (Frenkel defects). As long as the concentration of such defects remains small, as is the case in most well known crystals, their energy of formation can be regarded as independent of the neighbouring sites. But when the... 

Defect - Any departure from the regular structure of a crystal lattice. A Frenkel defect results when an atom or ion moves to an interstitial position and leaves behind a vacancy. A Schottky defect involves either a vacancy where the atom has moved to the surface or a structure where a surface atom has moved to an interstitial position. 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

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. 

The low molecular weight fractions of polymers contain many chain ends, which serve as lattice defects in the large crystal to lower their melting points. The Flory-Vrij equation has also been well verified by the experiments (Mandelkem 2002) and simulations (Hu and Frenkel 2005). 

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... 

Figure 4-10 Conceptual diagram of lattice defects (a) Frenkel disorder, (b) Schottky disorder.

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