Determination of a mean orientation in electron backscatter diffraction measurements

The average orientation of an electron backscatter diffraction (EBSD) map is calculated by the quaternion method and is compared with nonlinear solving by the Hill Climbing and Barton-Davison methods. An automated EBSD system acquires orientations on a regular grid of pixels based on indexation of Kikuchi patterns and the orientation is described by one of the crystal symmetry-related equivalents; In order to calculate the quaternion average, it is necessary to make a cloud for a set of pixels in a grain. A cloud consists of the representative orientations with small misorientation between each and every pair of points. The position criterion says that two adjacent pixels have a smaller misorientation than with all others. With this, the proper equivalent orientation, or representative orientation, for the cloud, can be selected from among all the crystal symmetry-related equivalents. The orientation average is the quaternion summation divided by its norm. The instant average or cumulative average is useful for dealing with polycrystalline grains or orientation discontinuity and is also useful for selection of the proper orientation of EBSD map with large scattering. The quaternion, Hill Climbing, and Barton-Dawson nonlinear methods are tested with a Gaussian distribution around the ideal texture component, Brass {110} < 112 >. The accuracy of the three results is similar but the nonlinear methods are associated with longer computation times than the quaternion method. The quaternion method is adapted for characterization of a partially-recrystallized interstitial-free (IF) steel and randomly distributed Brass, S, and cube texture components according to several different orientation spreads.