Bicrystallography in two dimensions: A graphical procedure and comparison of its results to experiments Andrew Maas1, Peter Moeck1, Bryant York2, Nigel Browning3, and Taylor Bilyeu1, 1Nano-Crystallography Group, Department of Physics, Portland State University, Portland, OR 97201, 2Department of Computer Science, Portland State University, Portland, OR 97201 Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352 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 [3]) 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 [2] 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 [001] tilt axis in all cubic holohedral materials and present this procedure in this contribution in a didactic manner We also reproduce from ref [4] (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 2 nm c d Figure 1: [001] projections of migration related segments of a Σ 13a (510) tilt boundary in SrTiO (modified after ref [4].) a and c, as predicted by bicrystallography in 2D, b and d as experimentally observed by aberration-corrected Z-contrast scanning TEM imaging and translation averaging The circles and ellipses in c mark projected Sr and mixed Ti/O columns in energetically unfavorable positions (as those are not occupied in d) Note that (at least on average), the black-white symmetries in the predictions (a,c) are not broken by free energy minimization effects that shows up in the experiments (b,d) We can therefore conclude on the basis of the Shubnikov-Curie and Curie-Minnigerode-Neumann principles [3] that polar phenomena cannot exist in the grain boundary shown in (b) while they are allowed in its migration related counterpart in (d) [1] R C Pond and D S Vlachavas, Proc Royal Soc London 386 (1983) 95 [2] L Priester, Grain Boundaries: From Theory to Engineering, Springer Series in Materials Science 172, Dordrecht, Heidelberg, New York, London, 2013 [3] V A Koptsik, Comput Math Applic 16 (1988) 407 [4] P Moeck et al., Cryst Res Technol 49 (2014) 708 ... Z-contrast scanning TEM imaging and translation averaging The circles and ellipses in c mark projected Sr and mixed Ti/O columns in energetically unfavorable positions (as those are not occupied in. .. projections of migration related segments of a Σ 1 3a (510) tilt boundary in SrTiO (modified after ref [4].) a and c, as predicted by bicrystallography in 2D, b and d as experimentally observed by aberration-corrected... the basis of the Shubnikov-Curie and Curie-Minnigerode-Neumann principles [3] that polar phenomena cannot exist in the grain boundary shown in (b) while they are allowed in its migration related