Tilt boundaries asymmetrical

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,... 

Figure B.5 (a) Small-angle asymmetric tilt boundary in a primitive cubic lattice viewed...

For asymmetric tilt boundaries between cubic crystals, E is calculated from (Randle, 1993)... 

Fig. 9.43. Distribution of grain boundaries in polycrystals (adapted from Randle (1997)). The numbers on the vertical axis refer to the coordinates of the boundary plane, while ATGB and TWGB refer to the asymmetric tilt boundaries and twist boundaries, respectively.

Fig. 11.2. Z-contrast image of an asymmetric section of a YBCO 30° [001] tilt boundary. For this boundary, grown on a similarly oriented SrXi03 substrate, an asymmetric boundary plane was the predominant feature.

Fig. 11.3. The Z-contrast image of the YBCO asymmetric 30° [001] tilt boundary shown in Fig. 11.2 after maximum entropy processing.

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. 

Figure 11.16. Examples of grain boundaries between cubic crystals for which the projection along one of the crystal axes, z, produces a 2D square lattice. Left asymmetric tilt boundary at 0 =45° between two grains of a square lattice. Right symmetric tilt boundary at 0 = 28° between two grains of a square lattice. Four different sites are identified along the boundary, labeled A, B, C, D, which are repeated along the grain boundary periodically the atoms at each of those sites have different coordination. This grain boundary is equivalent to a periodic array of edge dislocations, indicated by the T symbols.

Fig. 10.8. HREM images of various 90° grain boundaries in YBCO (a) [100] tilt, a and b interchanged across boundary (b) [100] tilt grain boundary showing two distinct facets, the (013) symmetric boundary with the CuOi planes joining at the interface and the (010)(001) asymmetric grain boundary (c) same as the asymmetric boundary in (b), but viewed at 90°, with one grain in the [001] projection (d) tilt and twist facets combined (continues overleaf).

Fig. 11.8. The structural units for symmetric SrTi03 [001] tilt grain boundaries. Each of the units contains a reconstructed atomic column projecting as two closely spaced sites, either a Ti—O column or a Sr column. Asymmetric [001] tilt grain boundaries use only the units with the Ti—O reconstruction.

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