Introduction

The charge carriers in high temperature superconductors are the electron holes confined to the CuO2-plane [9.1, 9.2], and thus, the distribution of charge plays a key role in determining their superconducting properties. Several groups of researchers have calculated the electronic structure of different superconducting oxides [9.3–9.5], and core-level spectroscopic studies are plentiful, both emission spectroscopy, and absorption spectroscopy with incident electrons and incident X-rays. In absorption spectroscopy, attention has focused on the near-edge structure of the K- and L-edge of copper, and, in particular, the Kedge of oxygen which exhibits clear signatures of the electron holes that are responsible for superconductivity [9.6, 9.7]. On the other hand, there have been few experimental studies of the spatial distribution of the electron charge in these superconductors.

In high-temperature superconductors, the density of electron holes is typically considerably less than 1% of the total density of electrons. However, the electron diffraction patterns and images of these superconductors, with their high local concentration of charge, is expected to be strongly influenced by the charge distribution. One reason for this expectation is the large crystal unit cell, resulting in reflections at small angles which are very sensitive to the charge. We realize this from the classical picture of the scattering of fast electrons by an atom. Charged particles interact with the electrostatic potential, and thus, for small scattering angles, which correspond to large impact parameters, the incident particle sees a nucleus that is screened by the electron cloud. Thus, the scattering amplitude is mainly determined by the net charge of the ion at small scattering angles, q.