A general criterion was proposed for the selection of the nearest-neighbour relationship between 2 adjoining crystals. It was applied to the study of the dislocation balance at a Σ = 3-Σ = 3-Σ = 9 triple junction. The orientational relationships in this tricrystalline system could be represented by rotations about a common [101] axis, with the Σ = 3 (boundaries a and b) and Σ = 9 (boundary c) components being characterized by anticlockwise rotations of 70.53º and 218.94º, respectively. The reduced basis vectors [½,½,0], [0,½,½] and [½,0,½] were chosen to be the 3 column vectors of the structure matrix (relative units). Three possible nearest-neighbour relationships were thereby determined for a Σ = 3 boundary, and two for a Σ = 9 boundary.

A Criterion for Determining the Nearest-Neighbour Relation between Two Adjoining Crystals. Z.Liang, J.Muller, C.Esling: Philosophical Magazine Letters, 1996, 73[1], 1-4