Dislocations helical

Highly dislocated helical versions of the SmA and SmC phases, denoted twist grain... 

In making the edge dislocation of Fig. 9.3 we could, after making the cut, have displaced the lower part of the crystal under the upper part in a direction parallel to the bottom of the cut, instead of normal to it. Figure 9.7 shows the result it, too, is a dislocation, called a screw dislocation (because it converts the planes of atoms into a helical surface, or screw). Like an edge dislocation, it produces plastic strain when it... 

The electrocrystallization on an identical metal substrate is the slowest process of this type. Faster processes which are also much more frequent, are connected with ubiquitous defects in the crystal lattice, in particular with the screw dislocations (Fig. 5.25). As a result of the helical structure of the defect, a monoatomic step originates from the point where the new dislocation line intersects the surface of the crystal face. It can be seen in Fig. 5.48 that the wedge-shaped step gradually fills up during electrocrystallization after completion it slowly moves across the crystal face and winds up into a spiral. The resultant progressive spiral cannot disappear from the crystal surface and thus provides a sufficient number of growth... 

The climb of mixed dislocations possessing some screw character can proceed by basically the same jog-diffusion mechanism as that for the pure edge dislocation.10 On the other hand, a pure screw dislocation can climb if the excess vacancies convert it into a helix, as in Fig. 11.10. Here the turns of the helical dislocation possess... 

Figure 11.10 Formation of a helical segment on an initially straight screw dislocation...

Solution. The dislocation will tend to adopt a form for which the net force on it given by Eq. 11.12 is everywhere zero. We therefore want to show that a helical dislocation will possess a tangent vector ( that satisfies... 

When a metal crystal free of applied stress and containing screw dislocation segments is quenched so that supersaturated vacancies are produced, the screw segments are converted into helices by climb. Show that the converted helices can be at equilibrium with a certain concentration of supersaturated vacancies and find an expression for this critical concentration in terms of appropriate parameters of the system. Use the simple line-tension approximation leading to Eq. 11.12. We note that the helix will grow by climb if the vacancy concentration in the crystal exceeds this critical concentration and will contract if it falls below it. 

Solution. The helical dislocation may be regarded as equivalent to a stack of circular prismatic edge dislocation loops of radius a as illustrated in Fig, 11.16. This may be confirmed by realizing that the stack of loops can be converted into a helix in a conservative fashion by cutting each loop at its intersection with AB and then sliding... 

Edge dislocations result when atoms in one layer do not match up precisely with those of the next. As a result, the distances between the dislocated atoms and atoms in adjacent rows are larger than usual and the angles between atoms are distorted for a number of rows on either side of the dislocation. A screw dislocation is one that has part of one layer shifted a fraction of a cell dimension. This kind of dislocation frequently causes a rapidly growing site during crystal growth and forms a helical path, which leads to the name. Because they provide sites that allow atoms from the solution or melt to fit into a corner where attractions from three directions can hold them in place, screw dislocations are frequently growth sites for crystals. 

The twist grain boundary (TGB) phases predicted by Renn and Lubensky have been intensively studied in the few last years. The general structure of the TGB phase is shown schematically in Figure 5.4. Because the symmetry of the Sm A phase does not allow continuous helical twisting, the chiral superstructure is realized in a stepwise manner Small smectic grains rotate around a helical axis, while screw dislocations build the... 

There is a helical structure surrounding the screw dislocation line. The screw dislocation is perpendicular to the smectic layer and the deformation is... 

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

Often, in quenched crystals which have been subsequently annealed so as to favor climb processes, dislocations in the form of long spirals have been observed. These are known as helical dislocations and a convincing explanation for their occurrence has been given by Amelinckx et al. (19). In essence, the helix consists of a screw dislocation parallel to the axis of the helix and a set of prismatic loops similar to that shown in Fig. 15. 

Fig. 6. However, these two structures are incompatible with one another and cannot co-exist and the molecules still fill space uniformly without forming defects. The matter is resolved by the formation of a periodic ordering of screw dislocations which enables a quasi-helical structure to co-exist with a layered structure. This is achieved by having small blocks/sheets of molecules, which have a local smectic structure, being rotated with respect to one another by a set of screw dislocations, thereby forming a helical structure [15]. As the macroscopic helix is formed with the aid of screw dislocations, the dislocations themselves must be periodic. It is predicted that rows of screw dislocations in the lattice will form grain boundaries in the phase, see Fig. 7, and hence this structurally frustrated phase, which was theoretically predicted by Renn and Lubensky [15], was called the twist grain boundary (TGB).

Fig. 16. The helical arrangement of the twist grain boundaries showing the relationship between the block/sheet thickness of the smectic layers and the distance between the screw dislocations (after Renn and Lubensky)...

Fig. 33. a Concentric cylindrical twist walls separating different chiral smectic regions. Inside each region the layer surface adopts a helicoidal shape, b Each cylindrical twist wall is comparable to that found in a conventional TGB phase, a helical shape being given to the screw dislocations constituting them (after Gilli and Kamaye [43])... 

As or Ts of opposite signs occur in pairs to form dislocations and pincements (fig. 4.2.6). Such pairing can be observed directly in the fingerprint textures which are exhibited by cholesterics of large pitch when the helical axis is parallel to the plates (figs. 4.2.7 and 4.2.8). 

FIGURE 12.18 Forming a pair of kinks and a pair of jogs and how this leads to helical dislocations in MgO. 

Amelinckx, S., Bontinck, W., and Dekeyser, W. (1957) Helical dislocations and spiral etch-pits, Philos. Mag. 2, 1264. 

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