Dislocation boundaries—the distribution function of disorientation angles

In dislocation structures orientation differences arise across dislocation boundaries during plastic deformation. The distribution function of the disorientation angles related to dislocation boundaries has been determined empirically and is almost independent of experimental parameters such as material type, plastic strain, temperature and deformation conditions (Hughes et al., Phys. Rev. 81 (1998) 4664). In the present paper distribution functions are derived from geometrical considerations for quite general assumptions on the number of sets of parallel dislocations and their arrangement. The relation between the obtained distribution functions for the disorientation angles and general orientation distributions is elucidated. A comparison with the experimental results shows that the Rayleigh distribution obtained for an equivalent contribution from two dislocation sets with perpendicular rotation axes is most appropriate for describing the experimental data. For experimental distributions with a larger spread in the disorientation angles and relatively large deviations from a Rayleigh distribution a superposition of two Rayleigh distributions is suggested implying the presence of two different types of boundaries in a given structure. Finally, it is shown that an analysis of distribution functions of disorientation angles can further the understanding of deformation induced structural changes.