Three dimensional (3D) bicrystallography describes ideal structures of grain boundaries comprehensively at the atomic level as a function of the five macroscopic and two of the four microscopic parameters [1,2]. Free energy minimization of these structures leads to the real structure of these topologically distinct regions within crystals. These minimizations may either reduce the symmetries of ideal bicrystals or leave them intact. Since the symmetries of physical properties need to be compatible (by the Shubnikov-Curie and Curie-Minnigerode-Neumann principles ) with the symmetries of the atomic arrangements from which they arise, bicrystallography allows for predictions about which phenomena can occur in the 3D regions around grain boundaries. Because it provides atomically resolved (real space) images, the most popular structure analysis technique for grain boundaries  is Transmission Electron Microscopy (TEM). Since this is a projection technique, there is a need for the development of bicrystallography in two dimensions in order to make sense of TEM images in a straightforward way. We utilized a graphical procedure for 2D bicrystallography recently in the analysis of coincidence site lattice boundaries with  tilt axis in all cubic holohedral materials and present this procedure in this contribution in a didactic manner. We also reproduce from ref.  (with permission by the publisher) pairs of predicted and experimentally observed Σ13a (510) boundaries in SrTiO3 that are related by grain boundary migration, Fig. 1, in order to illustrate both the predictive power and the limitations of the bicrystallography approach.
Available at: http://works.bepress.com/peter_moeck/61/