Dislocations mixed-type

Table 1 Summary of the calculated properties of the various dislocations in NiAl. Dislocations are grouped together for different glide planes. The dislocation character, edge (E), screw (S) or mixed type (M) is indicated together with Burgers vector and line direction. The Peierls stresses for the (111) dislocations on the 211 plane correspond to the asymmetry in twinning and antitwinning sense respectively.

Figure 8.2 Plan-view transmission electron micrograph of misfit dislocation network formed at the GaN/SiC interface. The network consists mostly of edge dislocations. A step on the SiC surface can interact with the network to form mixed-type dislocations. Some mixed-type threading dislocations, emerging from the interface, are visible through their characteristic image contrast, as indicated by arrows...

Figure 8.13 Plan-view transmission electron micrograph of GaN grown on a TiN interlayer [16]. Screw- or mixed-type threading dislocations (s) exhibit a characteristic black/white image contrast aligned with the scattering vector (g). Contrast from edge dislocations (e) is much weaker. Reproduced from [16] with permission from the American Institute of Physics...

Line imperfections are called dislocations and occur in crystalline materials only. Dislocations can be an edge type, screw type, or mixed type, depending on how they distort the lattice, as shown in Figure 8. It is important to note that dislocations cannot end inside a crystal. They must end at a crystal edge or other dislocation, or they must close back on themselves. 

There are several approaches for dislocation density reduction [35]. It was shown [36, 37, 38] that the number of dislocations decreases with layer thickness, which results from dislocation reactions. The experimental behavior of dislocation density versus layer thickness h was found to be proportional to 1/h", where n = 0.66 [39]. This means that to obtain dislocation density in GaN in the mid 10 " cm , the thickness of the layer should be in submillimeter range. However, cracking can appear in thick layers due to difference in thermal expansion coefficients between the substrate and the layer. Experimental [40] and theoretical calculations [41] show that screw and edge TDs in GaN are parallel to the [0001] direction and only mixed type... 

Structurally, plastomers straddle the property range between elastomers and plastics. Plastomers inherently contain some level of crystallinity due to the predominant monomer in a crystalline sequence within the polymer chains. The most common type of this residual crystallinity is ethylene (for ethylene-predominant plastomers or E-plastomers) or isotactic propylene in meso (or m) sequences (for propylene-predominant plastomers or P-plastomers). Uninterrupted sequences of these monomers crystallize into periodic strucmres, which form crystalline lamellae. Plastomers contain in addition at least one monomer, which interrupts this sequencing of crystalline mers. This may be a monomer too large to fit into the crystal lattice. An example is the incorporation of 1-octene into a polyethylene chain. The residual hexyl side chain provides a site for the dislocation of the periodic structure required for crystals to be formed. Another example would be the incorporation of a stereo error in the insertion of propylene. Thus, a propylene insertion with an r dyad leads similarly to a dislocation in the periodic structure required for the formation of an iPP crystal. In uniformly back-mixed polymerization processes, with a single discrete polymerization catalyst, the incorporation of these intermptions is statistical and controlled by the kinetics of the polymerization process. These statistics are known as reactivity ratios. 

The primary consideration we are missing is that of crystal imperfections. Recall from Section 1.1.4 that virtually all crystals contain some concentration of defects. In particular, the presence of dislocations causes the actual critical shear stress to be much smaller than that predicted by Eq. (5.17). Recall also that there are three primary types of dislocations edge, screw, and mixed. Althongh all three types of dislocations can propagate through a crystal and result in plastic deformation, we concentrate here on the most common and conceptually most simple of the dislocations, the edge dislocation. 

This result is easily generalized for mixed dislocations which are partly screw-type and partly edge-type, and also for cases having subsaturated vacancies. For a mixed dislocation, 6 must be replaced by the edge component of its Burgers vector... 

We begin by examining the types of mixed atomistic/continuum strategies discussed earlier (see section 12.3.4) with special emphasis on how these methods have addressed the factors that determine whether an atomically sharp crack tip will cleave or emit dislocations. As shown in fig. 12.34, the lattice Green function... 

The slip of a mixed dislocation follows from the cases already discussed. If we consider the example of a dislocation loop (figure 6.10), the loop increases or decreases its diameter when a shear stress is applied because the edge dislocation moves in the direction of the shear stress and the screw dislocation moves perpendicular to it. A dislocation loop changes its shape uniformly if both types of dislocation have the same mobility. 

---