Dislocations core size

The Peierls-Nabarro model has been used to determine properties of dislocation cores, the misfit energy and particularly changes with pressure. This is based on the assumption of a planar core which is the most able to ghde. It has direct implications for slip systems. In order to move, a dislocation must overcome an energy barrier under an applied stress. The Peierls-Nabarro model has been used to constrain dislocation core sizes and Peierls stresses in several oxides and sihcates relevant to the Earth s mantle, particularly periclase [439], ohvine [440,441], ringwoodite [80],... 

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

Only a few crystals exhibit hollow cores at the centers of growth spiral layers. However, on the (0001) faces of SiC, which has a large fx value, hollow cores due to growth have often been observed. According to the summary by Sunagawa and Bennema [16], various degrees of the effect of the strain associated with dislocation cores have been observed depending on the sizes of b and the concentration of dislocations. 

Consequently, as the dislocation cores get more closely spaced with increasing tilt angle, the well-coupled regions get smaller and smaller. Indeed, using the Read-Shockley formula together with the observed size of the cores, one... 

When the two edge dislocations are in the same horizontal plane, i.e., Zo = 0, the interaction is negligible. When z > r IAn X, i.e., the vertical separation between the dislocations is much greater than the core size, can be simplified to... 

One of the achievements of the PN theory is that it provides a reasonable estimate of the dislocation size. The optimal size of the dislocation core, characterized by the value of is a result of the competition between the two energy terms in Eq. (10.20), as shown schematically in Fig. 10.9 If the unstable stacking energy Yus is high or the elastic moduli K are low, the misfit energy dominates and the dislocation becomes narrow ( is small) in order to minimize the misfit energy. 

If the grain size falls below the effective boundary layer thickness (here 2A ) extreme effects, such as discussed for ionic conductors, naturally also occur for electronic conductors. An interesting recent example, refers to the overlap of depletion zones around dislocation cores constituting low angle grain-boundaries in SrTiOa (cf. Section 5.4 and Fig. 5.20) [316]. 

Because there are a large number of sites along the dislocation line, a large number of impurity atoms can be accommodated in the dislocation core. The interaction energy of an impurity located at position r and angle 0 with respect to a pure edge dislocation, where the impurity has a size AR different from the matrix atom radius R can be shown to be ... 

Figure 19.15 Possible free energy vs. size behavior for the formation of an incoherent cylindrical precipitate along the core of a dislocation. From Cahn [19],...

In the end, the mechanism that causes strong adhesion of the coating particles to the cores is due to mechanical forces acting in the system. It works best, if the coating particles are somewhat harder than the core material. Because the coating particles are often so small, that no dislocations are present in their structure, they behave as very hard entities (see Section 5.4). Therefore, it is for example possible to partially embed submicron-sized Ti particles in the surface of glass. 

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