Grain boundary curvatures in polycrystalline SrTiO3: Dependence on grain size, topology, and crystallography

By mapping grain orientations on parallel serial sections of a SrTiO3 ceramic, it was possible to reconstruct three-dimensional orientation maps containing more than 3000 grains. The grain boundaries were approximated by a continuous mesh of triangles and mean curvatures were determined for each triangle. The integral mean curvatures of grain faces were determined for all grains. Small grains with fewer than 16 neighbors mostly have positive mean curvatures while larger grains with more than 16 neighbors mostly have negative mean curvatures. It is also possible to correlate the mean curvature of individual triangles with the crystallographic characteristics of the grain boundary. The mean curvature is lowest for grain boundaries with (100) orientations and highest for grain boundaries with (111) orientations. This trend is inversely correlated to the relative areas of grain boundaries and directly correlated to the relative grain boundary energy. The direct correlation between the energy and curvature is consistent with the expected behavior of grain boundaries made up of singular orientations. Furthermore, because both the relative energy and curvature of grain boundaries with (100) orientations are minima in the distributions, these boundaries also have the lowest driving force for migration.