Picometer Accuracy in Measuring Lattice Displacements Across Planar Faults by Interferometry in Coherent Electron Diffraction

We calculate the shadow image in far field below a thin crystal when a coherent electron source is placed at micrometer distances above the specimen, and note that the presence of a planar fault results in very strong oscillatory contrast. We realize these predictions experimentally using a field-emission electron source in a microscope. With this technique, we determine displacement vectors at planar faults with an accuracy down to 1 pm in studies of the ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ superconductor containing thin intercalated layers.