Abstract
The determination of the full space symmetry of two interpenetrating lattices in a coincidence-site lattice orientation is discussed. The considered coincidence-site lattices are formed by two primitive cubic, face-centred cubic or body-centred cubic lattices. The two interpenetrating lattices form a dichromatic pattern and its symmetry is investigated by combining the three-dimensional periodicity of the coincidence-site lattice with the point-symmetry operations of the motif characterizing the particular dichromatic pattern. This provides a very concise formulation for treating this subject, especially if antisymmetry (two- coloured symmetry) is used. The translational symmetry of coincidence-site lattices with Σ < 50 is specified by determining the finest common sublattice of the two interpenetrating lattices. The point symmetry is determined by using the principle of the symmetry of composites and it is shown that the permissible point groups of dichromatic patterns in the cubic system are 4/mm'm', 6'/m'mm', \bar 3m', mm'm', 2'/m', \bar 1.
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