Definition of an asymmetric domain for intercrystalline misorientation in cubic materials in the space of Euler angles

A new asymmetric domain for intercrystalline misorientation is defined in the space of Euler angles for materials exhibiting cubic (O_h point-group) lattice symmetry. The invariant measure for this new domain is nearly constant; this is in significant contrast to the previous domain defined by MacKenzie [Biometrika (1958), 45, 229-240]. Distribution functions in the misorientation can now be represented with greater clarity and convenience in the new domain. A detailed theoretical analysis of special misorientations exhibiting multiplicities m > 1 is described. It is demonstrated that all such special misorientations fall upon the surfaces separating distinct asymmetric domains. This result convincingly proves that the derived asymmetric domain is correct. The location of all possible coincidence site lattice boundaries for Σ ≤ 49 are identified in the asymmetric domain, and their characteristic multiplicities are given.