Dislocations mixed

The edge dislocation on the 011 plane is again widely spread on the glide plane w = 2.9 6) and moves with similar ease. In contrast, the edge dislocation on the 001 plane is more compact w = 1.8 6) and significantly more difficult to move (see table 1). Mixed dislocations on the 011 plane have somewhat higher Peierls stresses than either edge or screw dislocations. 

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.

As a consequence edge and mixed (111) dislocations move with relative ease, whereas the Peierls barrier for screw dislocations is as high as 2 GPa. These results are in contrast to previous calculations [6], which have shown a splitting for the screw dislocations and also a much lower Peierls barrier. However, our results can perfectly explain most of the experimental results concerning (111) dislocations which will be discussed in the following section. 

Fig. 20.32 Schematic illustration of a mixed dislocation as the boundary between slippted and unslipped crystal. The arrow shows the Burgers vector...

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 Burgers vector of most dislocations is neither perpendicular nor parallel to the dislocation line. Such a dislocation has an intermediate character and is called a mixed dislocation. In this case the atom displacements in the region of the dislocation are a complicated combination of edge and screw components. The mixed edge and screw nature of a dislocation can be illustrated by the structure of a dislocation loop,... 

Figure 3.9 Part of a dislocation loop (a) pure edge, pure screw, and mixed dislocation character (b) glide is perpendicular to the Burgers vector, b, for the edge component, parallel to b for the screw component and at an angle to b for the mixed component and (c) continued glide results in removal of the dislocation from the crystal, leaving a step of height b on the surface.

The effect of dislocations has also been studied by Bloembergen and Rowland 106) in cold-worked copper (Cu and Cu resonances), and also the effect of alloying in Al-Zn alloys (Al resonance) by Rowland 107). Otsuka and Kawamura 108) have studied the NMR of 1" in KI, Na in NaCl-NaBr mixed crystals, and Br in KBr-NaBr mixed crystals and have estimated dislocation densities in these materials. 

Mixed Neither nor J. to dislocation Neither nor J. to dislocation line. 

Figure 1.34 Representation of propagation modes for (a) edge, (b) screw, and (c) mixed dislocations.

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. 

Figure 3.8. Explanation of dislocations in relation to glide. The solid arrow, b, corresponds to the Burgers vector of the dislocation. SV is the screw dislocation, WE is the edge dislocation, and VW is a mixed dislocation. The shaded area represents a glide plane.

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

Dislocations are line defects. They bound slipped areas in a crystal and their motion produces plastic deformation. They are characterized by two geometrical parameters 1) the elementary slip displacement vector b (Burgers vector) and 2) the unit vector that defines the direction of the dislocation line at some point in the crystal, s. Figures 3-1 and 3-2 show the two limiting cases of a dislocation. If b is perpendicular to s, the dislocation is named an edge dislocation. The screw dislocation has b parallel to v. Often one Finds mixed dislocations. Dislocation lines close upon themselves or they end at inner or outer surfaces of a solid. 

Since screw and edge components of a mixed dislocation have no common stress components, one can add the respective strain energies in order to obtain the line energy of a mixed dislocation. The strain and stress fields of a screw dislocation (in direction 5) are respectively... 

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