Tthe data of EBSD maps of pipe AZ31 magnesium alloy was processed. The purpose of the data analysis was to find evidence to secondary slip systems other special type of locally rebuild lattice inside of grains, called twinning. It was also shown by the way, that used in our laboratory formula of calculation orientation from the (hkl) <uvw> form only works for the cubic network, and therefore the application was written which calculates the matrix in the correct manner for any orientation of the (hkl) <uvw > in the hexagonal system.
To describe any disorientation, one inputs for the two orientations, given eg. by Euler angles, rotation matrices to calculate the passive g1, g2. Then you come up with a lattice symmetry operators. In a hexagonal network of 12, which means that for any orientation, there are 11 consecutive orientation which are set in the configuration of elementary cell indistinguishable in terms of physical properties and also for the human eye. We use left side symmetry operators, call it O. Thus each orientation symmetric matrix is expressed as the overall to get all the combinations of two possible orientations in the hexagonal lattice: O.g1.(O.g2^-1) which is equivalent to O.g1.g2^T.O. Of course we have to add the case: O.g2.g1^T.O to get all 12*2*12 possible combinations. But that's not all, you now need to simplify further considerations, bringing combinations to the area of a given base. This is not a trivial task, as long as we do not know the Rodriguez parametrization and shapeof the fundamental zone of the crystal lattice. In the case of a hexagonal network fundamental zone looks like a piece of cake.