Coincidence-site lattice and interface-plane analyses were made of a large set of data on grain-boundary geometry. The analysis showed that, whereas two-thirds of S3 and S19 coincidence-site lattices were classified as having a so-called special geometry (related to a low energy), very few other coincidence-site lattices had such special geometries. It was found that, for S3-types, there was an empirical relationship which related the frequency of occurrence of specific planes (mainly asymmetrical tilt types of the 011 zone), the average interplanar spacing at the boundary and the boundary energy. The S3 boundary, which had a planar coincidence-site density of unity, was much more poorly represented in the data set than were S3-types which had a planar coincidence-site density of 3; thus indicating the far greater importance of boundary planes than the planar coincidence-site density. The occurrence of special planes at S19 boundaries was considered to be partly a geometrical consequence of their contiguity with S3-types.

Relationship between Coincidence Site Lattice, Boundary Plane Indices, and Boundary Energy in Nickel. V.Randle: Materials Science and Technology, 1999, 15[3], 246-52