Frenkel-type process

Despite the fact that not all details of the photographic process are completely understood, the overall mechanism for the production of the latent image is well known. Silver chloride, AgBr, crystallizes with the sodium chloride structure. While Schottky defects are the major structural point defect type present in most crystals with this structure, it is found that the silver halides, including AgBr, favor Frenkel defects (Fig. 2.5). 

An intrinsic defect is one that is in thermodynamic equilibrium in the crystal. This means that a population of these defects cannot be removed by any forms of physical or chemical processing. Schottky, Frenkel, and antisite defects are the best characterized intrinsic defects. A totally defect-free crystal, if warmed to a temperature that allows a certain degree of atom movement, will adjust to allow for the generation of intrinsic defects. The type of intrinsic defects that form will depend upon the relative formation energies of all of the possibilities. The defect with the lowest formation energy will be present in the greatest numbers. This can change with temperature. 

In studying processes of accumulation of the Frenkel defects, one uses three different types of simple models the box, continuum, and discrete (lattice) models. In the simplest, box model, which was proposed first in [22], one studies the accumulation of complementary particles in boxes having a certain capacity, with walls impenetrable for diffusion of particles among the boxes. The continuum model treats respectively a continuous medium the intrinsic volume of similar defects at any point of the space is not bounded. In the model of a discrete medium a single cell (e.g., crystalline lattice site) cannot contain more than one defect (v or i). 

A simulation has been carried out [105, 106, 119] of the process of accumulation of the immobile Frenkel defects restricted by tunnelling recombination of dissimilar defects, as it is observed in many solid insulators. As follows from Chapter 3, in contrast to the ionic process of instant annihilation of close pairs of the vacancy-atom type, it is characterized by a broad spectrum of recombination times. Thus, the probability for a pair of chosen defects that lie at the relative distance r to survive for r seconds is... 

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 ... 

Despite the reservations set down above, to carry out a molecular dynamics study of the diffusion process itself one resorts to a computational cell of the type described earlier. The temperature is assigned and maintained via some scheme such as the Nose thermostat (Frenkel and Smit, 1996), and the atomic-level trajectories are obtained via a direct integration of the equations of motion. In fig. 3.22, we showed the type of resuiting trajectories in the case of surface... 

Becker was the first to suggest, in 1925, [2] that the deformation rate could be expressed by an Arrhenius-type equation. His concept was developed from the recognition of an identity between deformation and chemical reactions. The rate theory of thermally activated processes and, in general, the principles of deformation and fracture were established by Eyring [3], Orowan [4], and J. Frenkel [S]. In the latter part of the 20th century, these principles were further developed for polymers by Krausz and Eyring [6], Dorn [7], Zhurkov [8] and his collaborators [9], Kausch [10], and many others [11-14]. 

Frenkel [5] classifies raw water supplies into several types with different characteristics (Table 12.1). Other authors propose similar classifications and often add hardness to the list of characteristics. Arden and Forrest [6] take a modular proach to treatment. Silted river water, for example, considered suitable only for irrigation, is improved by sedimentation to a quality comparable to that of most other surface waters. The clarified water then becomes suitable for crude industrial applications. Coagulation and filtration then virtually eliminate suspended solids and make the water suitable for general purposes. These include plant utility use without necessarily qualifying the water for process application. Beyond this point, the intended application determines the extent of treatment required. 

Fig. 5 Schematic representation of photo excitation processes in an n-type oxide film (a) localized state to localized state, (b) localized state to conduction band, (c) valence band to localized state, (d) excitation to localized state followed by escape to conduction band by Poole-Frenkel effect, (e) excitation to localized state followed by electron tunneling into the electrolyte.

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