Dislocation width

If one considers dislocations in more detail, it becomes clear that not just the atoms in the dislocation line are displaced but also the neighboring atoms. For example, consider the edge dislocation shown in Fig. 6.7. The plane of atoms below and above the slip plane are shown. In the initial configuration, several atoms in the upper row (five) are displaced from their normal positions, i.e., there is a dislocation width. It is useful to compare this figure with Fig. 6.2 in which the displacement b is obtained by simultaneous motion of all the atoms. The same displacement b is obtained in both cases but for the dislocation it is produced by a localized motion of atoms rather than the simultaneous shear of a perfect plane. Thus, the displacement associated with the dislocation is spread across... 

The values of obtained from Eq. (6.4) are usually found to be less than the experimental yield strength values in many materials and, thus, one concludes these materials must contain strengthening mechanisms. The frictional stress is clearly very sensitive to the dislocation width and, thus, it is important to identify the material properties that govern this parameter. Dislocation width is governed primarily by the nature of the atomic bonding and crystal structure. In covalent solids, the bonding is strong and directional and, hence, dislocations are very narrow (w b). In ionic solids and bcc metals, the dislocations are moderately narrow whereas in fee metals dislocations are wide (w>106). 

The stress, which is clearly a function of the crystal structure and bonding, depends on b and w. You will recall from Chapter 12 that dislocation widths in covalent solids are quite narrow (w b) compared with those in face-centered cubic (fee) metals (w 10b). 

At low temperatures, the surface mobiUty of the atoms is limited and the stmcture grows as tapered crystaUites from a limited number of nuclei. It is not a full density stmcture but contains longitudinal porosity on the order of a few tens of nm width between the tapered crystaUites. It also contains numerous dislocations with a high level of residual stress. Such a stmcture has also been caUed botryoidal and corresponds to Zone 1 in Figures 6 and . 

The distance that the small segment of a dislocation line moves when a kink moves is called the Burgers displacement, b. Figure 11.2 illustrates it for the case of quartz. It determines the amount of work that is done by the advance of a kink (per unit width of the kink) which is acted upon by the virtual force generated by the applied shear stress, x. This force is xb per unit length of the dislocation line. Letting the kink width be b since the displacement is b, the work done is xb3. This is resisted by the strength, U (eV) of a Si-O bond which... 

Figure 6.1 Double-axis rocking curve of CdTe on GaAs showing the broadening due to the very high dislocation density in the layer. (Courtesy R.l.Port, Durham University.) The rocking curve width in such thick, high mismatched layers falls with increasing layer...

The width of the image can be deduced using this simple idea of contrast being formed when the misorientation around the defect exceeds the perfect crystal reflecting range. We consider the case of a screw dislocation nmning normal to the Bragg planes, where the line direction / coincides with the diffraction vector g. The effective misorientation at distance r from the core is =bH r (8.41)... 

The width of the dislocation image D, which is twice the value of r for which and is thus... 

Miltat and Bowen showed that direct images can be synthesised from the cylinders of misorientation drawn aroimd a dislocation line using continuum elasticity theory. The image full width can be calculated from the projected width circumscribed by the contour where ( ) is equal to times the reflecting range,... 

As seen in the last chapter, the image width is easy to quantify for a screw dislocation, where the diffraction vector is parallel to the dislocation line. Around a screw dislocation, the misorientation at a distance r from the core is given by... 

Figure 10.7 Width of a dislocation image under conditions where harmonics are strong as at the ESRF. (Courtesy F.Zontone)...

Figure 10.15 Simulated image width as a function of deviation parameter in Bragg case weak beam topographs. Here, the specimen is set off the Bragg peak and an image of the defect occurs only when the lattice planes are locally rotated or dilated back into the Bragg condition. As this occurs only close to the dislocation core, the images are narrowed from those under strong beam conditions...

It has also been suggested that flow might occur at lower stresses than those predicted above by movement of material within the individual layers (Chu and Barnett, 1995). This has been observed in pearlitic structures made up of alternating layers of ferrite and cementite, and observations in other multilayer systems suggest that that deformation might occur in this way (Gil-Sevillano, 1979). Two cases have been identified the first where only the movement of a pre-existing dislocation loop is required, the second where the activation of a dislocation source within the layer is needed. Gil-Sevillano (1979) showed that the extra stress, Atm, required to move a dislocation half-loop in a layer of width 1 is... 

As seen from Fig. 2a, the van der Waals gap width is modulated periodically in positions of In atoms it is larger than in positions of Se atoms. This gap can be described as a layer of closely packed parallelepipeds, at the both ends of which pyramids are placed. The volume of this body (cavity) is equal to 50.5 A3, and for an ideal crystal, when defects of the dislocation type are absent the relative gap volume comprises 43% of the crystal bulk. It is obviously larger than the lower estimate 37% obtained using the ratio Q/(Q+Ci). 

---