A unique description of the relative orientation of neighbouring grains

If N denotes the number of symmetry rotations of a crystal lattice, the number, n, of different rotations connecting two orientations of this lattice is a multiple of N and a factor of 2N². Among these n equivalent rotations those with minimum angle are considered. Usually one, but in exceptional cases two or three, of these has its axis in the standard stereographic triangle and is called a disorientation. How equivalent disorientations are connected by symmetry rotations and how the number, n, of equivalent rotations can be found for any disorientation are shown. Additional conditions for selecting a unique reduced rotation among the disorientations are proposed.