Misorientation Angle and Axis Distributions

Abstract

The misorientation angle ω between two objects is defined as the smallest of rotation angles among equivalent rotations relating two given orientations of the objects¹ It is the simplest characteristic of the difference between orientations of two crystallites in a polycrystalline material Measured distributions of misorientation angles are compared with a special function: the distribution of the misorientation angles obtained in the case when orientations of crystallites are random This particular distribution is a reference for distributions of misorientation angles of grains in real materials with non-random textures and orientation correlations (Mackenzie, 1958, Grimmer, 1979a, b) In relation to misorientation angles, there is also a question about the distributions of corresponding axes for randomly oriented crystallites Such a function for octahedral symmetry was calculated by Mackenzie (1964) For other cases see, e.g., Morawiec (1996a, 1997) Again, the distributions of rotation axes corresponding to randomly oriented crystallites constitute a reference for distributions occurring in real materials The misorientation angle and the corresponding axis depend on symmetries of the crystallites (or objects in general) Therefore, also the distributions are influenced by the symmetries.