Line dislocations

The density of dislocations is usually stated in terms of the number of dislocation lines intersecting unit area in the crystal it ranges from 10 cm for good crystals to 10 cm" in cold-worked metals. Thus, dislocations are separated by 10 -10 A, or every crystal grain larger than about 100 A will have dislocations on its surface one surface atom in a thousand is apt to be near a dislocation. By elastic theory, the increased potential energy of the lattice near... 

The ultimate trapping site for a photoelectron is influenced by the high dielectric constant of silver haUde (ca 12.5, 11.15, and 7.15 for AgBr, AgCl, and P-AgI, respectively), the negative surface charge, and relative trap depths. Interior traps located at point defects on dislocation lines are probably not as... 

A mesoseale variable deseribing a eolleetion of atomie disloeations is the total length of dislocation line per unit volume in metallurgieal publieations... 

Dislocation motion produces plastic strain. Figure 9.4 shows how the atoms rearrange as the dislocation moves through the crystal, and that, when one dislocation moves entirely through a crystal, the lower part is displaced under the upper by the distance b (called the Burgers vector). The same process is drawn, without the atoms, and using the symbol 1 for the position of the dislocation line, in Fig. 9.5. The way in... 

An electron microscope picture of dislocation lines in stainless steel. The picture was taken by firing electrons through a very thin slice of steel about lOOnm thick. The dislocation lines here ore only about 1000 atom diameters long because they have been chopped off where they meet the top and bottom surfaces of the thin slice. But a sugar-cube-sized piece of ony engineering alloy contains about 10 km of dislocation line. (Courtesy of Dr. Peter Southwick.)... 

By their nature, dislocations cannot end suddenly in the interior of a crystal a dislocation line can only end at a free surface or a grain boundary (or form a closed loop). Where a screw dislocation intersects a free surface there is inevitably a step or ledge in the surface, one atomic layer high, as shown in Fig. 20.30c. Furthermore, the step need not necessarily be straight and will, in fact, almost certainly contain kinks. 

In reactions of the type discussed, the more bulky anions are often regarded as an immobile framework within the solid through which the cations diffuse. Some experiments have been directed towards investigation of the significance of anion migration but results are restricted in scope and more work is clearly desirable. It is possible that anion migrations may occur along dislocation lines, at surfaces, or even by desorption-adsorption, and may be sensitive to the presence of specific impurities. 

In the following diagram, given as 3.1.12. on the next page, amother representation is shown, detailing how the dislocation line (line defect) becomes a screw-dislocation. 

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... 

If materials were homogeneous, the sizes of indenters and indentations would not matter. However, they are not homogeneous. They are heterogeneous aggregates of various objects and configurations. These include grains, precipitates, interfaces, and ordered arrays of atoms and molecules as well as dislocation lines, and distributions of dislocations lines. Therefore, the sizes... 

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

A key feature of the motion of dislocation lines is that the motion is rarely concerted. One consequence is that the lines tend not to be straight, or smoothly curved. They contain perturbations ranging from small curvatures to cusps, and kinks. In covalent crystals where there are distinct bonds between the top... 

If a dislocation line lies parallel to the x-axis of an xy-plane, and is kinked, the kink lies parallel to the y-axis. Therefore, if the line is of edge character, the kink is of screw character. If the line is of screw character, the kink is of edge character. In either case, the displacement gradient is indefinite at the center of the kink. This means that whatever symmetry exists in the undislocated crystal, structure is destroyed at a kink. 

Inelastic shearing of atoms relative to one another is the mechanism that determines hardness. The shearing is localized at dislocation lines and at kinks along these lines. The kinks are very sharp in covalent crystals where they encompass only individual chemical bonds. On the other hand, in metal crystals they are often very extended. In metallic glasses they are localized in configurations that have a variety of shapes. In ionic crystals the kinks are localized in order to minimize the electrostatic energy. 

In three dimensions, there may be more than one glide system, and the dislocation line need not be straight, and there may be more than one velocity, so this becomes ... 

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

Figure 5.9 Plan view of the (111) plane of the diamond structure. A—Normal structure with open circles in the plane of the paper, and crossed circles in the plane above. Each pair is connected by a covalent bond. B—Partial shear of the upper plane over the lower one on the right-hand side creating a screw dislocation line with a kink in it (dashed line). C—Upper plane sheared down-ward by the displacement, b.

Figure 5.10 Schematic dislocation core. Arrangement at kink on screw dislocation line.

When a moving dislocation line encounters a precipitate that is harder than the matrix in which it is moving, there two ways (in general) for it to get past the precipitate Passing around it or shearing it (i.e., passing through it). 

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