COINCIDENCE ORIENTATIONS OF GRAINS IN HEXAGONAL MATERIALS

For arbitrary rotations expressed in hexagonal coordinates, the connection between an axis-angle quadruple and the rotation matrix is given. The relation between hexagonally equivalent quadruples is stated and a unique reduced quadruple is defined. Rotations generating coincidence site lattices (CSLs) correspond to quadruples of coprime integers if a2/c2 is rational. The multiplicity Σ of the CSL is not always equal to the least common denominator of the elements in the rotation matrix. The case a = c is considered in detail