The concept of coincidence was here generalized beyond that used in the coincidence site lattice, DSC or O-lattice theories. Instead of requiring that 2 lattices points (one from each lattice) should coincide exactly, it was merely required that they be sufficiently close. This permitted the formulation of a general geometrical theory of crystalline interfaces. This theory was able to explain how some boundaries, with low values of S (such as 17), could nevertheless offer poor registration between lattices while S = 41 boundaries could lead to relatively high agreement. The associated problem of finding points of good fit between a pair of arbitrarily chosen 3-dimensional lattices was also solved.

A Generalized Coincidence-Site Network Model for Grain Boundaries. A.Gomez, L.Beltran, J.L.Aragon, D.Romeu: Scripta Materialia, 1998, 38[5], 795-801