Frenkel hopping

Interstitial sites are defined as those that would usually be empty in an ideal structure. Occasionally in real structures, ions may be displaced from their lattice sites into interstitial sites Frenkel defect formation). Once this happens, the ions in interstitial sites can often hop into adjacent interstitial sites. These hops may be one stage in a long range conduction process. A schematic example is shown in Fig. 2.1(h) a small number of Na ions are displaced into the tetrahedral interstitial sites and can subsequently hop into adjacent tetrahedral sites. It should be noted, however, that while a small number of Frenkel defects may form in NaCl, conduction is primarily by means of vacancies whereas in some other structures, e.g. AgCl, Frenkel defects do predominate. 

Emin D (2008) Generalized adiabatic polaron hopping Meyer-Neldel compensation and Poole-Frenkel behavior. Phys Rev Lett 100 166602... 

Photoconductivity of Kapton, (polypyromellitimide where R is oxygen) was investigated in detail [224-234]. Frenkel, Onsager, hopping and other models were used by different authors for explanation of the photoconductive properties. The photoconductivity spectra of Kapton film for various directions of the electric field are presented in Fig. 29 [230]. The high anisotropy depending on... 

The ionic charge carriers in ionic crystals are the point defects.1 2 23,24 They represent the ionic excitations in the same way as H30+ and OH-ions are the ionic excitations in water (see Fig. 1). They represent the chemical excitation upon the perfect crystallographic structure in the same way as conduction electrons and holes represent electronic excitations upon the perfect valence situation. The fact that the perfect structure, i.e., ground structure, of ionic solids is composed of charged ions, does not mean that it is ionically conductive. In AgCl regular silver and chloride ions sit in deep Coulomb wells and are hence immobile. The occurrence of ionic conductivity requires ions in interstitial sites, which are mobile, or vacant sites in which neighbors can hop. Hence a superionic dissociation is necessary, as, e.g. established by the Frenkel reaction ... 

Unlike the Poole-Frenkel effect, the dipole trap argument does not require high concentrations of charged traps. Further, the problem of small distances between the hopping sites relative to the position of the potential energy maxima, which is a major limitation of Poole-Frenkel arguments, is avoided. The model predicts field and temperature dependencies that are similar to the disorder formalism. The dipole trap model and the disorder formalism both lead to activation energies that are temperature dependent. 

Diffusion in solids occnrs as Schottky or Frenkel defects hop from one lattice site to another by a thermally activated process akin to chemical reactions. 

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)... 

In these relations the operator B (Bn) describes the creation (annihilation) of a molecular excitation at lattice site n. We assume below that n 1,2,. ..,Ar, where N is the number of molecules in the chain and we consider one electronically excited molecular state. Then E-p is the on-site energy of a Frenkel exciton and Mnni is the hopping integral for molecular excitation transfer from molecule n to molecule n. In the summation in HF the terms with n = n are omitted. The Hamiltonian HF describes the Frenkel excitons in the Heitler-London approximation. 

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