Determination of a Mean Orientation from a Cloud of Orientations. Application to Electron Back-Scattering Pattern Measurements

The purpose of this work was to determine the orientations of grains in polycrystals using electron back-scattering patterns (EBSP). In order to lower the degree of statistical uncertainty, the orientation of the same grain was measured several times. The orientation of the corresponding grain was assumed to be the mean of the orientations measured. From a theoretical point of view, the way to calculate a mean orientation from several orientations was solved on the basis of the properties of quaternions. The accuracy of the measurements, including the mean and maximum deviation of the orientations established, could be evaluated. The orientation of α plates of Ti-64 products was determined and it was possible to show that the metallurgical state of the parent β phase prior to the β–α phase transformation is likely to influence the orientation spread of the variants inherited from the same β grain, belonging to the same orientation family.