Measuring the Burgers Vector of Dislocations with Dark-Field X-ray Microscopy

The behavior of dislocations is essential to understand material properties, but their subsurface dynamics that are representative of bulk phenomena cannot be resolved by conventional transmission electron microscopy (TEM). Dark field X-ray microscope (DFXM) was recently demonstrated to image hierarchical structures of bulk dislocations by imaging lattice distortions along the transmitted X-ray diffracted beam using an objective lens. While today's DFXM can effectively map the line vector of dislocations, it still cannot quantify the Burgers vector required to understand dislocation interactions, structures, and energies. Our study formulates a theoretical model of how DFXM images collected along specific scans can be used to directly measure the Burgers vector of a dislocation. By revisiting the "invisibility criteria" from TEM theory, we re-solve this formalism for DFXM and extend it to the geometric-optics model developed for DFXM to evaluate how the images acquired from different scans about a single hkl diffraction peak encode the Burgers vector within them. We demonstrate this for edge, screw, and mixed dislocations and discuss the observed symmetries. This work advances our understanding of DFXM to establish its capabilities to connect bulk experiments to dislocation theory and mechanics.