Accurate Measurements of Valence Electron Distribution and Interfacial Lattice Displacement Using Quantitative Electron Diffraction

We developed a novel electron-diffraction technique by focusing a small probe above (or below) the sample in an electron microscope to measure charge density and lattice displacement in technologically important materials. The method features the simultaneous acquisition of shadow images within many Bragg reflections, resulting in parallel recording of dark-field images (PARODI). Because it couples diffraction with images, it is thus suitable for studying crystals as well as their defects. We used this technique to accurately locate the charge-carrying holes in superconducting crystals, and to determine displacement vectors across planar faults by comparing the experiments with calculations, and by using fitting and error analyses. Examples are given for complex YBa₂Cu₃O₇ and Bi₂Sr₂CaCu₂O_8+δ oxides and the newly discovered MgB₂ superconductor.