Dislocation tilt boundary

Dislocations interact and tend to order if they can move. Consider the arrangement shown in Figure 3-6a. This is called an edge dislocation tilt boundary. It is seen that the number of lattice planes terminating at the boundary is n - (2/6)-sin 0/2, from which the (mean) spacing between the dislocations is found to be... 

Figure 3.21 Low-angle grain boundary (a) two misaligned parts of the crystal represented as a series of steps and (b) a tilt boundary consisting of an array of edge dislocations. The angular orientation difference between the two parts is 0, and the Burgers vector of the dislocations is b.

Low-angle tilt boundaries are the most easily visualized. Two regions of crystal separated by a slight misorientation can be drawn as a set of interlocking steps (Fig. 3.21a)- The edge dislocations coincide with the steps. The separate parts can be linked to make the edge dislocation array clearer (Fig. 3.21b). In the situation in which the misorientation between the two parts of the crystal is 0, the distance between the steps A and C is given by twice the dislocation separation, 2d, where... 

Figure 5.8 Dislocation array in a low-angle tilt boundary.

Tilt boundaries occur if the axis of rotation between the two grains is located in the boundary (interface). In contrast, if the axis of rotation is perpendicular to the boundary, the boundary is called a twist boundary and consists of a collection of screw dislocations (Fig. 3-6b). An equation similar to Eqn. (3.14) holds for twist (and mixed) boundaries. Since dislocation theory is well understood, it is possible to quantitatively treat small-angle grain boundaries [J.P. Hirth, J. Lothe (1982)]. 

The asymmetric small-angle tilt boundary in Fig. B.5a consists of an array of parallel edge dislocations running parallel to the tilt axis. During diffusion they will act as fast diffusion pipes. Show that fast self-diffusion along this boundary parallel to the tilt axis can be described by an overall boundary diffusivity,... 

Solution. Using Eq. 11.2, the force per unit length on each dislocation is /CT = symmetric tilt boundary is d = b/0 [7]. The pressure on the boundary due to all dislocations is then... 

Calculate the average spacing between dislocations in a 1 /2° tilt boundary in aluminum. Look up any required data. 

A low-angle tilt boundary is composed of edge dislocations. 

Knowing that low-angle tilt boundaries are composed of edge dislocations, predict the most common planes for tilt boundaries in fee and in bcc metals. 

M.P. Dewald, W.A. Curtin Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al. Phil. Mag. 87, 4615 1641 (2007)... 

Figure 2.4. (a) A low-angle tilt boundary, (b) Representation as an array of parallel edge dislocations. 

Figure 8.33. Arrays of dislocations forming low-angle tilt boundaries in olivine, (a) Dislocations in the two boundaries shown have the same Burgers vector and sign. (Courtesy J. D. Fitz Gerald.)...

The diffraaion effects directly attributable to periodic arrays of dislocations that form low-angle boundaries in olivine have been studied by Ricoult and Kohlstedt (1983). Figure 8.35 shows an edge-on tilt boundary approximately parallel to (100) and its associated SAD pattern. The extra... 

Figure 8-35. BF image of the dislocations fonning a (100) tilt boundary in olivine viewed edge-on, and the electron diffraction pattern from the boundary re on. Note the fine structure of the 605 and 705 reflections shown in the inserts. (From Ricoult and Kohlstedt 1983.)... 

We begin our geometric discussion with the case of pure tilt boundaries on the grounds that the connection between dislocations and the boundary is most evident visually in this case. As was discussed in some detail in chap. 9, a tilt grain boundary is characterized by a simple misorientation between the two grains as was discussed in chap. 9. The intent of this section is to illustrate that a simple superposition of the elastic displacements implied by the Volterra solution for straight dislocations discussed in chap. 8 can lead to exactly the same type of misorientation. 

The definition of low-angle grain boundaries generally covers the range of misorientations from 0° to 10°. In this regime, the grain boundary plane can be considered to be a linear array of separated dislocation cores. For [001] tilt boundaries in YBCO, the boundary plane will be composed of [100] or [010] dislocations, as shown in Fig. 11.6 (for YBCO the small distortion between the a- and fi-axes needs to be incorporated for quantitative models, but structurally results in no observable differences in the dislocation cores). 

The structural unit model has been used successfully to predict the structures of grain boundaries in perovskite structured SrTiOs bicrystals [11.31-11.34]. The structural units observed for symmetric SrTiOs [001] tilt boundaries are shown in Fig. 11.8. In a similar manner to the isolated dislocation cores in YBCO, the structural units also appear to contain atomic positions where the cations are too close together. Again, depending on the structural unit, the close separation of the atomic columns can occur for either of the sub-lattice sites,... 

Fig. 9. Symmetrical tilt boundary, which has but one type of edge dislocation.

Fig. 10. Asymmetrical tilt boundary, where there must bo at least two kinds of edge dislocation.

Asymmetric (or nonsymmetric) twist boundaries are the analogs of asymmetric tilt boundaries. They do not lie along a crystallographic plane. At least three sets of screw dislocations with different Burgers vectors are required to produce such boundaries. 

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