Curvature dislocations

When a dislocation segment of length L is pinned at the ends under the influence of an applied shear stress t, a balance between the line tension and the applied stress produces a radius of curvature R given by [37]... 

The use of hexafluoroisopropanol (HFIP) as an SEC eluent has become popular for the analysis of polyesters and polyamides. Conventional PS/DVB-based SEC columns have been widely used for HFIP applications, although the relatively high polarity of HFIP has led to some practical difficulties (1) the SEC calibration curve can exhibit excessive curvature, (2) polydisperse samples can exhibit dislocations or shoulders on the peaks, and (3) low molecular weight resolution can be lost, causing additive/system peaks to coelute with the low molecular weight tail of the polymer distribution... 

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... 

Figure 6.9 Curvature of a screw dislocation near a free surface a. screw dislocation that has moved about halfway thru the specimen and is emerging from the surface, b. by becoming curved the screw dislocation reduces its length and hence its energy.

Figure 3.1 A schematic representation of the defects common in epilayer structures, (a) mismatch, (b) misorientation, (c) dislocation content, (d) mosaic spread, (e) curvature, (f) relaxation, (g) inhomogeneity...

Fig. 4.16 HREM image of carbon nanoshells showing that the basal planes roughly follow the curvature of the shell owing to the presence of a high density of dislocations. The image contrast of the basal planes was enhanced by use of fast Fourier transform (FFT) processing. After [60]...

That a hollow core is formed by the creation of a free surface along a dislocation core implies that the curvature of the spiral step is reversed due to the strain field along the dislocation core. The effect of a strain field upon the advancement of a step was theoretically treated by Cabrera and Levine [14], [15],... 

In the case of growth spirals originating from dislocations with large b, hollow cores with diameters of micrometer order are observed at the spiral center however, when a number of dislocations with small b concentrate in a narrow area, a basin-like depression appears at the central area of the composite spirals, since the curvature of advancement of the spiral steps is reversed near the center. A straight step may appear near the spiral center as an intermediate state in the reversal of step curvature. Several examples are shown in Fig. 5.11. 

Figure 5.11. Various step patterns appear because the advancing rate and the curvature of the spiral layers are affected by the strain field at dislocation cores.

Figure 5.13. Positive phase contrast photomicrograph of composite spiral in hematite, (0001). A bright contrast appears on the higher side of a step. By tracing the route from the lowest step to higher steps, the lowest step becomes the highest step after one turn, corresponding to Escher s staircase. Since the curvatures of the steps are reversed at the center of a group of dislocations, a depression appears due to the associated strain field (refer to Section 5.7). See also Fig. 5.11.

Figure 9.1 presents self-diffusivity data for DD(dissoc), DD(undissoc), DB, DS, DXL, and DL, for f.c.c. metals on a single Arrhenius plot. With the exception of the surface diffusion data, the data are represented by ideal straight-line Arrhenius plots, which would be realistic if the various activation energies were constants (independent of temperature). However, the data are not sufficiently accurate or extensive to rule out some possible curvature, at least for the grain boundary and dislocation curves, as discussed in Section 9.2.3. 

Solution. The line-tension forces acting on a curved differential segment of dislocation having a radius of curvature R due to its line tension will be as shown in Fig. 11.14. The net force exerted on the segment toward the concave side is then... 

Solution. The source will be able to become active if the driving osmotic climb force is large enough to overcome the restraining curvature force that reaches a maximum when the dislocation segment has bowed out to the minimum radius of curvature corresponding to R = L/2. Setting /M = fK, we then have the critical condition... 

Fig, 29. Number z of molecular dislocations for coupled exchange processes z as a function of 3 coupled conformations (curvature a) z as a function of 10 coupled conformations (curvature b)... 

The argument can perhaps be put forward In the following way A step of radius r centered on the dislocation maintains in its neighborhood a concentration c(r) determined by the curvature of the step. Under steady state conditions the concentration in the solution decreases in all directions approaching the value c maintained at a macroscopic distance from the crystal surface. It follows then that the concentration at the dislocation c(0) must obey the condition c(r) > c(0) > c. In fact, a brief calculation shows that the relation among these three quantities is... 

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