Spiral dislocations

In the case of TiCl2 the number of propagation centers do not exceed 0.5% of the number of surface titanium ions this shows that the formation of the propagation centers proceeds at specific points on the surface of the crystalline catalyst (e.g. lateral faces, outlets of the spiral dislocations). 

This type of volume defect in the crystal is known as a "screw dislocation", so-called because of its topography. Note that the spiral dislocation of the growing lattice deposits around the Une defect at right angles to the line defect. 

Another common surface incorporation model is based on regeneration of spiral dislocations in the lattice at the crystal surface. Such spirals have been clearly identified in many growing crystal systems and mate an attractive incorporation site for growth units. The spiral growth model developed by Burton et al. (1951) predicts a second-order dependence of growth rate on supersaturation at low levels of supersaturation, but a linear dependence at higher supersaturations (Mullin 1993). 

Samples of a-TiCls, prepared by reduction of TiCIa with hydrogen, contain a low number of propagation centers. The Cp value of these well crystallized samples (the specific surface area according to BET is 3 m /g) is several per cent of the number of surface titanium ions. The low number of ACs is in agreement with the Cossee and Arlman concept and the experimental data of Rodrigues et al. on the localization of the ACg on the lateral faces and outlets of spiral dislocations on TiCls crystals. 

Fig. 6 Weak-beam DF imaging. Weak-beam DF images of (A) lamellar titanium aluminide showing thickness contours and (B) a spiral dislocation in Al-3 at% Ag, the white speckling is caused by silver-rich Guinier—Preston zones. (View this art in color at www.dekker.com.)...

A step dislocation can be understood as a slippage of part of the crystal relative to the rest. The boundary between the slipped and the unslipped regions is the dislocation line (Fig. 4.3). A step dislocation can also be considered to be an extra lattice plane inserted into the undisturbed crystal. The dislocation line is a line along this step (the edge of the plane). The neighbourhood of a dislocation line is strained. In the case of spiral dislocations, a section of the crystal lattice is rotated by one lattice constant through a slippage (Fig. 4.4). 

Fig. 4.4 Schematic representation of a spiral dislocation. The line of dislocations A runs parallel to the shear strain. This line of dislocations is surrounded by distorted material.

The synthesis of spiral PANl nanostructures (2-D ordered spirals comprised of singlestrand PANI-NFs) by chemical oxidative polymerization using a hydrated surfactant sodium dodecylsulfonate crystallite template was recently described [406]. It was found that a spiral dislocation structure on the surface of a hydrated sodium dodecylsulfonate crystallite was responsible for the growth of the spiral PANl nanoarchitecture. It was revealed that APS has a strong tendency to induce the formation of a spiral dislocation stmcture in hydrated sodium dodecylsulfonate crystallites. A mechanism of adsorption of oligoanilines on the steps of dislocation has been proposed for the growth of PANl spirals. 

Figure 5 15. Single crystals of poly(ethylene) obtained from dilute solution, A spiral dislocation can be observed in lower center crystal (after A. J. Pennings and A. M. Kiel).

Some authors have observed that the growth rate at very small supersatirration is greater than predicted by the nucleation models. This can be explained by the so-called BCF model (Bruton et al. 1951). The authors assume that the presence of spiral dislocations which end somewhere on the crystal surface creates steps, which are thus a continuous soirrce of favorable integration sites. The soirrce of such screw dislocations is a lattice imperfection which prevents an ideally smooth crystal surface. The steps of these spiral dislocations are remote from the centers and considered to be parallel and the same distance apart from each other. The linear displacement rate of a face is controlled by surface diffusion. With the siuface diffusion coefficient the growth rate Vg p according to Burton, Cabrera, and Frank is... 

For crystalline materials especially, it must be kept in mind that a crystal surface may contain any or all of the defects already mentioned, as well as missing layers, and screw and spiral dislocations. All such defects will alter the surface energy of the crystal and comphcate the analysis of phenomena related to it. Obviously, sohd surfaces are more difficult to analyze and understand not only because of their inherent anisotropic nature but also because of the potential role of history in determining the exact nature of the surface produced at formation. 

Another possibility to increase the dislocation density is a spiral dislocation, pinned at the centre. Similar to a dislocation loop, the spiral dislocation extends when shear stresses are acting on it. As its centre is pinned, the length of the spiral grows (figure 6.20). This process does not increase the number of dislocations, but their density. 

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