Dislocations, edge

Fig. VII-7. Motion of an edge dislocation in a crystal undeigoing slip deformation (a) the undeformed crystal (b, c) successive stages in the motion of the dislocation from right to left (d) the undeformed crystal. (From Ref. 113 with permission.)...

One type of dislocation is the edge dislocation, illustrated in Fig. VII-7. We imagine that the upper half of the crystal is pushed relative to the lower half, and the sequence shown is that of successive positions of the dislocation. An extra plane, marked as full circles, moves through the crystal until it emerges at the left. The process is much like moving a rug by pushing a crease in it. 

Dislocations are characterized by the Burgers vector, which is the exua distance covered in traversing a closed loop around die core of the dislocation, compared with the conesponding distance traversed in a normal lattice, and is equal to about one lattice spacing. This circuit is made at right angles to the dislocation core of an edge dislocation, but parallel to the core of a screw dislocation. 

The interface between the substrate and the fully developed film will be coherent if the conditions of epitaxy are met. If there is a small difference between the lattice parameter of the film material and the substrate, die interface is found to contain a number of equally spaced edge dislocations which tend to eliminate the stress effects arising from the difference in the atomic spacings (Figure 1.13). 

Interface mismatch between two solids compensated with an edge dislocation... 

Figure 7.1. Atomic positions during the passage of an edge dislocation (after G.I. Taylor [4]).

How many atoms must be included in a three-dimensional molecular dynamics (MD) calculation for a simple cubic lattice (lattice spacing a = 3 x 10 ° m) such that ten edge dislocations emerge from one face of the cubic sample Assume a dislocation density of N = 10 m . ... 

Assume the edge dislocation density to be divided into positive and negative populations, N+ and N, moving only on slip planes at 45° (maximum shear stress) to the planar shock front. For a dislocation multiplication (annihilation) rate M, show that conservation of dislocations requires that... 

Fig. 9.3. An edge dislocation, (a) viewed from a continuum standpoint (i.e. ignoring the atoms) and (b) showing the positions of the atoms near the dislocation.

Fig. 9.4. How on edge dislocation moves through o crystal, (a) Shows how the atomic bonds at the centre of the dislocation break and reform to allow the dislocation to move, (b) Shows a complete sequence for the introduction of a dislocation into a crystal from the left-hand side, its migration through the crystal, and its expulsion on the right-hand side this process causes the lower half of the crystal to slip by a distance b under the upper half.

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... 

Explain briefly what is meant by a dislocation. Show with diagrams how the motion of (a) an edge dislocation and (b) a screw dislocation can lead to the plastic deformation of a crystal under an applied shear stress. Show how dislocations can account for the following observations ... 

The papers which introduced the concept of a dislocation all appeared in 1934 (Polanyi 1934, Taylor 1934, Orowan 1934). Figure 3.20 shows Orowan s original sketch of an edge dislocation and Taylor s schematic picture of a dislocation moving. It was known to all three of the co-inventors that plastic deformation took place by slip on lattice planes subjected to a higher shear stress than any of the other symmetrically equivalent planes (see Chapter 4, Section 4.2.1). Taylor and his collaborator Quinney had also undertaken some quite remarkably precise calorimetric research to determine how much of the work done to deform a piece of metal... 

Figure, ,20, An edge dislocation, as delincalcd by Orowan (a) and Taylor (b).

The other major defeets in erystalline solids oeeupy mueh more of the volume in the lattiee. They are known as line defeets. There are two types viz. edge dislocations and screw dislocations (Figure 1.4). Line defeets play an important role in determining erystal growth and seeondary nueleation proeess (Chapter 5). 

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. 

Comparing to the previous atomistic studies of (110) dislocations in NiAl [7, 6], there are differences in many details but all studies clearly show that the edge dislocations are limiting the mobility. 

Figure 1 Core configuration of the (110) 001 edge dislocation (Ni-core)...

Figure 2 Core configuration and Burgers vector distribution of the (111) 211 edge dislocation display separation into two superpartials.

Second-order stress is difficult to observe and much less extensively studied. The causes of internal stress are still a matter for investigation. There are broad generalisations, e.g. frozen-in excess surface energy and a combination of edge dislocations of similar orientation , and more detailed mechanisms advanced to explain specific examples. 

The simplest type of line defect is the edge dislocation, which consists of an extra half plane of atoms in the crystal, as illustrated schematically in Fig. 20.30a edge dislocations are often denoted by 1 if the extra half plane ab is above the plane sp, or by T if it is below. 

As with vacancies, the importance of dislocations derives from the fact that they are readily mobile, in this case under the influence of applied stresses. Figures 20.3Ia to c illustrate the slip or glide of an edge dislocation through... 

Fig. 20.31 Three stages in plastic deformation by the motion of an edge dislocation through...

A line or edge dislocation in the Solid. On one side of the Lattice, where a line is missing, the lattice is under tension while the other side of the lattice is under compression. 

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