Symmetries of grain boundary distributions

A function representing the distribution of grain boundaries is needed for a statistical description of the boundaries in polycrystalline aggregates. It is assumed to be determined in the space of macroscopic boundary parameters. Equivalences between points of the space caused by crystal symmetries lead to symmetries of the grain boundary distribution. These symmetries are investigated for both homophase and heterophase grain boundaries. Using known asymmetric domains for misorientation distributions, a method of determining the domains of grain boundary distributions is given for all possible combinations of crystallographic symmetries.