Statistical treatment of measured orientation relationships in orientation space

Measured orientation relationships between neighbouring grains in single-phase α- and β- and dual-phase α + β-brasses are analysed by means of the χ²-test. The orientation relationships are characterized by the three Euler angles and hence can be represented as points in orientation space. A description of the symmetry relations of equivalent points in this space is given and then the distribution function for random orientation relationships is derived. This distribution is compared with the distribution of the measured orientation relationships using only a single χ²-test for each boundary type. The results of the tests are the same as obtained from the analysis of axis-angle pairs, in which case twoχ²-tests are necessary. None of the measured distributions is random.