Bicrystal Geometry

In addition, as was mentioned above, it is possible that there is a shift of origin associated with some translation vector t. The matrix Q imposes a linear transformation which, since it describes a rotation, may be characterized by three parameters. We now have two interpenetrating lattices as indicated in the simplified two-dimensional setting in fig. 9.39. As yet, there is no grain boundary. The remainder of our work in identifying the macroscopic degrees of freedom is to select the boundary plane itself. This plane is characterized by a unit vector n 

---

As is evidenced by fig. 9.38, there are a number of points of entry into a discussion of polycrystalline microstructures. In particular, fig. 9.38 shows that at the simplest level (frame (a)) we can consider bicrystal geometries. In keeping with... 

Fig. 9.38. Schematic of increasingly complex grain boundary distributions within materials (adapted from Randle (1994)) (a) bicrystal geometry with a single grain boundary, (b) bamboo-like distribution of grain boundaries in a one-dimensional array, (c) polycrystalline film, and (d) three-dimensional polycrystal.

Fig. I Geometry of used bicrystals and measuring principle of the XICTD ...

---