Lattice dislocation model

Elsewhere (22) a model for the highly acidic sites is discussed that is supported by electrostatic potential calculations. According to that model the activity is due to generation of protons coordinated to oxygen ions that connect the silicon-containing tetrahedra with aluminium-containing octrahedra. Such sites, however, can only contribute to catalysis at lateral planes, at lattice dislocations in the basal plane or at the edges of the lateral and basal planes. 

In the case of high-angle grain boundaries (see Fig. 5.21) both the extended dislocation models and coincidence site lattice models have proven worthwhile. The... 

Very recently, people who engage in computer simulation of crystals that contain dislocations have begun attempts to bridge the continuum/atomistic divide, now that extremely powerful computers have become available. It is now possible to model a variety of aspects of dislocation mechanics in terms of the atomic structure of the lattice around dislocations, instead of simply treating them as lines with macroscopic properties (Schiotz et al. 1998, Gumbsch 1998). What this amounts to is linking computational methods across different length scales (Bulatov et al. 1996). We will return to this briefly in Chapter 12. 

The diSuse scatter arises because dislocations are defects which rotate the lattice locally in either direction. This gives rise to scatter, from near-core regions, which is not travelling in quite the same direction as the diffraction from the bulk of the crystal. This adds kinematically (i.e. in intensity not amplitude) and gives a broad, shallow peak that mnst be centred on the Bragg peak of the dislocated layer or substrate since all the local rotations are centred on the lattice itself. We can model the diffuse scatter quite well by a Gaussian or a Lorentzian function of the form ... 

By modeling r in this way, we have tacitly assumed that the atomic oxygen has free access to the vacancy sinks which are the internal sites of repeatable growth for the lattice molecules. Properly spaced dislocations with fast oxygen diffusion could be a prototype of those sinks. 

The notion of nonuniformity of catalytic surfaces has been originally advanced by Langmuir (20) and particularly by Taylor. The physical nature of nonuniformity is insufficiently clarified. To some extent, it results from the difference in properties of crystal faces, from dislocations, and other disturbances of crystal lattice. It is possible that admixtures of some foreign substances is of greater importance. The particles of admixtures change adsorption energy on adjacent surface sites. The model of nonuniform surface probably describes the overall result of the effect of particles of admixtures on adsorbed particles and of the mutual influence of adsorbed particles (i.e., to an approximation the model takes into account not only biographical, but also induced nonuniformity). 

In fig.4 (lower panel) it is schematically presented the structure of the SC vortex in the SDW/CDW + SC state. Since arising of the CDW results in the lattice modulation so that wave of dislocation walls is formed (fig.4 (middle panel)). As known, such dislocation walls are effective centers for pinning of SC vortices. Note that in such a structure every fifth wall is equivalent to first one ( cn+4 - c ). In this a model a vortex core has AF SDW structure which is also outside a core too. Because of equivalence of c and c +4 dislocation walls vortex core becames to be two part in form fluctuating in space (cf. with [14]). 

Ball (31) studied the solid-state hydrolysis of single crystals of aspirin, and also observed S-shaped plots of fraction decomposed vs. time, but found that the kinetic data fit an Avrami-Erofeyev model involving nucleation at dislocations in the crystal lattice. 

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