Kinks and Jogs

Our treatment thus far has centered on idealized geometries in which the dislocation is presumed to adopt highly symmetric configurations which allow for immediate insights from the linear elastic perspective. From the phenomenological standpoint, it is clear that we must go beyond such idealized geometries and our first such example will be the consideration of kinks. The formation of kink-antikink pairs plays a role in the interpretation of phenomena ranging from plastic deformation itself, to the analysis of internal friction. 

As seen in the figure, the function u(x) characterizes the displacement of the line from the well at the origin. The boundary condition of interest here is that m(—oo) = 0 and u oo) = b. 

Our ambition is to find the energy minimizing disposition of the dislocation as described by the function u (x). This function in the present context is a complete 

If we further assume that u 1, then the equation simplifies to 

Upon multiplication by u, we are immediately led to a first integral of the problem, which implies in turn that the profile satisfies 

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Miyashita et al. [102] have proposed a possible model for the hexagonal-orthorhombic phase transition (Fig. 10). They proposed that since the hexagonal crystal contains many defects along the chain axis, such as kinks and jogs, on its phase transition to the orthorhombic phase, these defects are excluded from the crystal... 

Figure 5-12. Some lattice defects in poly (ethylene). From left to right aW-trans conformation (defect-free), Reneker defect, kink, and jog.

TTTTG TG TTTT. . . ). If, on the other hand, the displacement is larger than the interchain distance (e.g.,.. . TTTTG TTTTG TTTT. . . ), then the defect is called a jog. Kinks and jogs shorten planar chains and twist helices. 

Surface Diffusion RT High Energy Sites (Kinks and Jogs) allow dissolution of less noble metal Mathematical simulation Au-Cu, Au-Ag, Cu-Zn, others... 

The nature of the critical potential has been debated as part of the mechanistic studies of deallo5dng. Authors such as Forty [45], who subscribe to a rearrangement model for dealloying, suggest that the critical potential is the potential at which dissolution fix)m kinks and jogs on the surface is activated, while authors who ar e for a diffusion-related mechanism suggest that the critical potential relates to the unblocking of p ath-ways for the transport of the less noble metal to the surface [48-50,98-100]. Probably the most comprehensive discussion... 

Third Street winds downhill—past Leo s Pizza and Pasta, past life-size holograms of Clinton, Reagan, and Carter—following the kinks and bends of the Potomac River. The buildings are set well back from the streets and it isn t until you get nearer to the water that you see a considerable number of people. Hundreds. The nearby avenues are themselves very busy with endless streams of noisy taxis. A few joggers pass—no matter how swiftly they run, they are constrained to the asphalt and concrete and probably always would be. Would they want to experience, as you do, a jog into the fourth dimension ... 

Kinks Jogs, and Reneker defects are conformational defects (see Figure 5-12). With kinks and j ogs, a part of the chain is displaced perpendicular to the long axis by false conformations. This kind of defect is called a kink when the displacement is smaller than the interchain distance (example ... 

Dislocations glide by the movement of kinks and climb by the movement of jogs. Since climb requires changing the number of point defects (reacting or absorbing them), we call it nonconservative motion. 

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

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

In general, however, identification of the crystal cell is only part of the problem of characterizing the structure of crystalline polymers. Crystals are never perfect and the units cells do not infinitely duplicate through space even when they are grown very carefully from dilute solution using low molecular mass materials. As with the organic crystals considered in Chapter 3, a variety of defects can be observed and are associated with chain ends, kinks in the chain and jogs (defects where the chains do not lie exactly parallel). The presence of molecular (point) defects in polymer crystals is indicated by an expansion of the unit cell as has been shown by comparison of branched and linear chain polyethylene. The c parameter remains constant, but the a and b directions are expanded for the branched polymer crystals. Both methyl and... 

Fig. 6.32. Cutting of dislocations of various types and orientations (after [40]). The type and orientation of the moving dislocation is not determined, here. Depending on its type and orientation, a kink or jog is created in the immobile dislocation...

Point-like (zero dimensional) defects are also present in polymeric crystals. They arise from the presence of chain ends, kinks (see example in Fig. 7.8) and jogs (molecular defects with collinear stems on each side of the defect). 

Figure 3-1. a) Edge dislocation model b) Burgers vector h with Burgers circuit and glide plane indicated. Dislocation motion during plastic deformation under the action of force F. Jog and kink. 

Of particular interest in kinetics is the non-conservative dislocation motion (climb). The net force on a dislocation line in the climb direction (per unit length) consists of two parts Kei is the force due to elastic interactions (Peach-Koehler force), Kcbcm is the force due to the deviation from SE equilibrium in the dislocation-free bulk relative to the established equilibrium at the dislocation line. Sites of repeatable growth (kinks, jogs) allow fast equilibration at the dislocation. For example, if cv is the supersaturated concentration and c is the equilibrium concentration of vacancies, (in the sense of an osmotic pressure) is... 

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