Grain boundary planes

Figure 5.34(a) shows the relation between the amount of segregated P and the crystallographic orientation hkl of the grain boundary planes. 

Only x > 0 is considered, since the solution will have mirror symmetry about the grain boundary plane x = 0. 

The nucleus has cylindrical symmetry around an axis normal to the boundary and mirror symmetry across the grain-boundary plane. Figure 19.27 shows a cross section of the nucleus centered in a patch of boundary of constant circular area, Ac. The area of the nucleus projected on the boundary is indicated by A. The total interfacial energy of this configuration is then... 

In the case of an enhanced charge carrier concentration in the space charge (cf. Fig. 4b), mainly the current parallel to the grain boundary plane is important. The corresponding parallel excess grain boundary conductance... 

Hence, in simple cases each bulk layer, each grain boundary plane, and both electrodes of the brick layer model sample, can be represented by separate RC elements (Fig. 7b). The RC elements of the n bulk layers can be combined to a single RC element with the -fold resistance and the 1 / -fold capacitance of a single layer. The n — 1 grain boundary impedances can also be summed, as can the two electrode impedances, and hence the model sample corresponds to a series connection of three RC elements (Fig. 7c) with... 

Fig. 14. Hypothetical bi-grain with microelectrodes (a), and square electrodes on the sides (b). (d) Current density distribution in the grain boundary plane of the 24-grain model sample, and sketch of the grain boundaries for which the current density distribution is plotted (c). Parameters used in the finite element calculations dms = 1/5 Lg, wgb = 10 3 Lg, and p b = 105 phvSk for all grain boundaries. The spikes are due to numerical errors. Owing to computational reasons, the considered plane is not the grain boundary plane itself, but a plane in a distance of 0.052., to the grain boundaries.

For example, if we mentally expand the lattices of both A and B in Figure 1.15, it will be seen that the grain boundary plane cuts the B unit cell at (3 40) in the B coordinate system and the A unit cell at (0 1 0) in the A coordinate system. Thus, Eq. 1.20 yields... 

Fig. 9.40. Schematic of degrees of freedom associated with choice of boundary plane (adapted from Wolf et al. (1992)). This figure illustrates the idea that once the relative orientation of the two grains has been chosen there is still a freedom to choose the grain boundary plane.

Randle V, The Role of the Grain Boundary Plane in Cubic Polycrystals, Acta mater. 46, 1459 (1997). 

To obtain a more uniform orientation of the grain boundary plane at the microscopic level it would be desirable to study considerably smaller junction widths in samples that contain extended facets of uniform geometry. 

The role of the grain boundary plane needs to be established, especially in view of anisotropic superconducting order parameters. In thin films, considerably smaller grain boundary junctions than those used in our work would be feasible and it should thus be possible to prepare samples with reasonably well defined facets. Of course, at inclinations such as for the 45°/[001] grain boundaries, where asymmetric facets dominate supposedly because of their much lower energy than other inclinations (see Fig. 10.4), symmetric facets may not form, at least not exclusively. Whenever there is coexistence of... 

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