Frenkel mechanism

J. P. K. Doye, D. Frenkel. Mechanism of thickness determination in polymer crystals. Phys Rev Lett 57 2160-2163, 1998. 

Silver halides have the character of solid electrolytes, where the silver ion acts as the charge carrier (see [125, 204, 266] for AgCl) which moves according to the Frenkel mechanism in the crystal. This type of transport is depicted schematically in fig. 6.1. As the halide ions are located in fixed sites, no diffusion potential is formed within the membrane and (3.4.9) to (3.4.13) are valid for the membrane potential As mentioned in chapter 3, they can be used for determining either halide ions or silver. 

The results of several studies were interpreted by the Poole-Frenkel mechanism of field-assisted release of electrons from traps in the bulk of the oxide. In other studies, the Schottky mechanism of electron flow controlled by a thermionic emission over a field-lowered barrier at the counter electrode oxide interface was used to explain the conduction process. Some results suggested a space charge-limited conduction mechanism operates. The general lack of agreement between the results of various studies has been summarized (57). 

Fig, 7.15 Mechanisms of ionic conduction in crystals with defect structures (a) vacancy (Schoilky defect) mechanism, (b) interstitial (Frenkel defect) mechanism, (c) inlcrsthialcy (concerted Schottky-Frenkel) mechanism. 

The composition of these oxides normally departs from the precise stoichiometry, expressed in their chemical formulae. For example, in the case of a stoichiometric oxide, such as A05, where 8 = 0, we will have only thermal disorder, where the concentration of vacancies, and interstitials will be determined by the Schottky, Frenkel, and anti-Frenkel mechanisms [40-42] (these defects are explained in more detail in Chapter 5). In the case of the Schotky mechanism, the following equilibrium, described with the help of the Kroger-Vink notation, [43] develops [40]... 

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). 

In this structure there are perovskite layers of ABO3 separated by AO rock salt layers. It is this layered structure that allows great flexibility in the oxygen stoichiometry of these materials. It is possible to incorporate excess oxygen (5 > 0) in the unusual form of interstitial oxygens, which provide an alternative to the vacancy-based conduction mechanism present in the perovskite and fluorite oxides, where the dopant-vacancy interactions can limit the observed conductivity. The mobility of the oxide ions in these materials occurs mainly through an interstitialcy mechanism in the aZ)-plane, although evidence of low Ea for the conduction in the c-direction via a Frenkel mechanism has also been reported. ... 

Table II. The values of coefficients B obtained from e )q)eriments and calculated according to Schottky and Poole-Frenkel mechanisms.

A more searching analysis of the Poole-Frenkel mechanism performed for polysiloxane on the basis of the Hill model ( ) showed that charge carrier emission should proceed from the isolated Coulomb centre and should take place in the hemisphere related to that centre. The depth of the centres, determined form the activation dependence of the temperature, was =... 

Besides its temperature dependence, hopping transport is also characterized by an electric field-dependent mobility. This dependence becomes measurable at high field (namely, for a field in excess of ca. 10" V/cm). Such a behavior was first reported in 1970 in polyvinylcarbazole (PVK) [48]. The phenomenon was explained through a Poole-Frenkel mechanism [49], in which the Coulomb potential near a charged localized level is modified by the applied field in such a way that the tunnel transfer rate between sites increases. The general dependence of the mobility is then given by Eq. (14.69)... 

According to the Frenkel mechanism, an atom moves from its regular site into the nearest interstitial position hence, two types of defect are formed in the crystal, namely the vacancy and the interstitial atom. If the Frenkel defects form in the A-sublattice of AB2 crystal, this process and the corresponding equilibrium constant can be written as ... 

Kajihara, K., Hirano, M., Skuja, L., and Hosono, H., Intrinsic defect formation in amorphous SiOj by electronic excitation Bond dissociation versus Frenkel mechanisms, Phys. Rev. B 78, 094201 (2008a). 

At high fields and low temperatures, where the thermal activation Schottky and Poole-Frenkel mechanisms are frozen out, and for films too thick for tunneling from metal to metal, a Fowler-Nordheim law is expected. Mead has observed this relationship for Ta205 films, it could be due either to tunneling from the metal into the conduction band or from localized states to the conduction band. Mead favored the latter case. 

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