Dislocation sources

Frank-Read Sources. It is well known that with increasing deformation, the density of dislocations increases. This effect is illustrated in fig. 8.40 in which the number of dislocations as a function of the strain is indicated schematically. The immediate conclusion from this observation is the fact that there are sources 

The specific analytic ideas associated with the bowing-out of a piimed segment were already described earlier in this section. As a result of these arguments, we find that the applied stress and the radius of curvature of the bowed-out segment are related by 

If we now invoke an approximate expression for the line energy, namely, T = then the critical stress may be rewritten as 

Thus we note that we have argued for a dislocation source which operates at a stress that is smaller than the shear modulus by a factor ofb/L. 

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Figure 3.14. Optical micrograph of a dislocation source in silicon, decorated with copper...

Figure 3-3. Representation of dislocation movement in a Frank-Read dislocation source under stress a. Multiplication of dislocation pinned at a distance l.

A dislocation source that climbs rapidly enough so that ideal diffusion-limited conditions are achieved therefore operates with an efficiency of unity. On the other hand, slowly acting sources can have efficiencies approaching zero. Applications of these concepts to the source action of interfaces are discussed in Section 13.4.2. 

These analyses describe the situation where flow occurs by the motion of single dislocations passing across the interfaces between the two materials. However, if the layers are very thick, dislocation sources within the individual layers will be able to operate. The shear stress required to operate a source in the more compliant layer, B, is given by... 

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... 

Dislocations climb over obstacles in the slip plane. This process lessens hardening by reducing the drag on moving dislocations and by relieving the back stress associated with a pileup of dislocations, thereby allowing the dislocation source to continue to emit dislocations. 

The observed mircrostructures and rheological behavior are consistent with the suggestion by Durham, Goetze, and Blake (1977) that the dislocations glide essentially unhindered by other dislocations and that deformation is limited by the number of active dislocation sources. 

To have any hope of honestly addressing the dislocation-level processes that take place in plastic deformation, we must consider fully three-dimensional geometries. Though we earlier made disparaging remarks about the replacement of understanding by simulation, the evaluation of problems with full three-dimensional complexity almost always demands a recourse to numerics. Just as the use of analytic techniques culminated in a compendium of solutions to a variety of two-dimensional problems, numerical analysis now makes possible the development of catalogs of three-dimensional problems. In this section, we consider several very important examples of three-dimensional problems involving dislocations, namely, the operation of dislocation sources and dislocation junctions. 

Li J. C. M., Dislocation Sources in Dislocation Modeling of Physical Systems, Proceedings of the International Conference, Gainesville, Florida, USA June 22-27, 1980, edited by M. Ashby,... 

The main focus of this of this work is to investigate the interaction between the transmitted wave and dislocation sources. However, when the stress wave hits the rigid base, it reflects back to the material block and interacts with the dislocations again. In order to minimize the effects of the reflected waves, the length of the cell (25 pm) is chosen such that once the wave front reaches the bottom surface, the value of the stresses in the position where the dislocations are located is small so that dislocation relaxation process can take place well before the wave hits the bottom of the RVE. A better solution to isolate the effect of the reflected wave would be by implementing a suitable non-reflective FE boundary condition. 

Here, b is the Burgers length appropriate to the crystal, Pc(i) is the probability of creating a dislocation with the available shear stress energy and the quantity / o is the average thickness of the dislocation source. Ns is the number of active dislocation sources whose dislocations appear on the crystal surface and has dimensions of (length) l... 

It is often convenient to let Ns = sAw-/) where s is the number of dislocation sources whose dislocations intercept the shear region of width w and length /. Equation (4) reduces to... 

When a crystal is subjected to large plastic deformation due to shock or impact the local dislocation sources produce extremely large numbers of dislocations. These so distort and reduce the amplitude of the lattice potential in the bands of slip... 

Whereas film-edge stresses are very localized and tend to create high densities of dislocations in rather small volumes, other sources of stress may afflict the whole volume of the wafer, such as stresses introduced by temperature gradients.Then defects in any location within the wafer may act as dislocation sources, in particular SiOx-precipitates and stacking faults. This may result in warpage or slippage 713/ which renders the whole wafer useless. 

FIGURE 12.21 Schematic and IR image of a Frank-Read dislocation source in Si. 

Figure 4.26 Sketches of various wedge dislocations. Source. Reprinted with permission from Zimmer JE, White JL, Disclination structures in the carbonaceous mesophase, Advin Liq Crysts, 5, Academic Press, New York, 157, 1982. Copyright 1982, Elsevier.

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