Bragg's Law diffraction simulations for electron backscatter diffraction analysis

In 2006, Angus Wilkinson introduced a cross-correlation-based electron backscatter diffraction (EBSD) texture analysis system capable of measuring lattice rotations and elastic strains to high resolution. A variation of the cross-correlation method is introduced using Bragg's Law-based simulated EBSD patterns as strain free reference patterns that facilitates the use of the cross-correlation method with polycrystalline materials. The lattice state is found by comparing simulated patterns to collected patterns at a number of regions on the pattern using the cross-correlation function and calculating the deformation from the measured shifts of each region. A new pattern can be simulated at the deformed state, and the process can be iterated a number of times to converge on the absolute lattice state. By analyzing an iteratively rotated single crystal silicon sample and recovering the rotation, this method is shown to have an angular resolution of ∼0.04° and an elastic strain resolution of ∼7e−4. As an example of applications, elastic strain and curvature measurements are used to estimate the dislocation density in a single grain of a compressed polycrystalline Mg-based AZ91 alloy.