asymmetric domain, coincidence site lattice boundaries, Cubic lattice symmetry, Euler angles, intercrystalline misorientation


The authors wish to acknowledge the support of the United States Department of Energy, Office of Basic Energy Sciences, under grant No. DE-FG02-85ER45203. Critical review by Professor Dorian Hatch of the Physics Department at Brigham Young University is gratefully acknowledged. A new asymmetric domain for intercrystalline misorientation is defined in the space of Euler angles for materials exhibiting cubic (Oh 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 [Biornetrika (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 E <= 49 are identified in the asymmetric domain, and their characteristic multiplicities are given.

Original Publication Citation

Acta Cryst. (1998). A44, 326-336

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL


International Union of Crystallography




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering