Algorithms and programs were developed for the analysis of multiple twinning in these grain boundaries. The programs were used to determine the crystallographic parameters of such boundaries on the basis of quaternion theory. Also determined were the class of equivalent rotations for an arbitrary value of , and the elementary vectors and space symmetry of coincidence lattices and interfaces. Atomic models of multiple junctions of  = 3n grain boundaries were used to simulate processes in face-centered cubic materials which had a low stacking fault energy. The symmetry properties of multiple junctions and nodes with  = 3n boundaries were established.

A.V.Andreeva, A.A.Firsova: Materials Science Forum, 1996, 207-209, 189-92