A New Approach Towards Measuring Structure Factors and Valence-Electron Distribution in Crystals with Large Unit Cells

By focusing a probe of fast electrons above or below the specimen level in convergent-beam electron diffraction, shadow images of many reflections are recorded in one exposure. For wedge-shaped crystals, this procedure provides a means of recording thickness or Pendellösung fringes of many reflections simultaneously, which ensures that the experimental conditions with respect to thickness variations and crystallographic direction of the incident beam are the same for all reflections. Disturbing defects within the illuminated area of the specimen are immediately revealed in the shadow images of the different reflections. The approach is introduced by using strontium titanate and silicon as examples. As a case study, the technique is applied to the dense (00l) reciprocal-lattice row of the superconductor YBa₂Cu₃O₇ to address charge transfer and electron-hole distribution by determining the amplitudes and phases of the 001 and 002 reflections. By this approach, the absolute values of the structure factors are obtained from the very thin regions where the kinematical theory applies. Based on these approximate absolute values, the signs of the structure factors in centrosymmetrical crystals are determined by comparing dynamically calculated and observed intensities in somewhat thicker crystal regions for different combinations of signs. As a third step, the structure factors are refined by comparing the calculated and experimental intensity profiles within the entire observed thickness range.