It was recalled that the distribution function of misorientation angles had been determined empirically and had been found to be almost independent of parameters such as the material type, plastic strain, temperature and deformation conditions. In the present work, distribution functions were derived from geometrical considerations, while making general assumptions as to the number of sets of parallel dislocations and their arrangement. The relationship between the resultant distribution functions for the misorientation angles, and general orientation distributions, was clarified. A comparison with experimental results showed that the Rayleigh distribution which was obtained for an equivalent contribution from 2 dislocation sets having perpendicular rotation axes was most suitable for describing the experimental data. For experimental distributions having a larger spread of misorientation angles, and relatively large deviations from a Rayleigh distribution, a superposition of 2 Rayleigh distributions was suggested; thus implying the presence of 2 different types of boundary in a given structure. It was shown that an analysis of the distribution functions of misorientation angles could increase the understanding of deformation-induced structural changes.

Dislocation Boundaries - the Distribution Function of Misorientation Angles. W.Pantleon, N.Hansen: Acta Materialia, 2001, 49[8], 1479–93