Accurate low-order structure factors for copper metal have been measured by quantitative convergent beam electron diffraction (QCBED). The standard deviation of the measured structure factors is equal to or smaller than the most accurate measurement by any other method, including X-ray single crystal Pendellösung, Bragg γ-ray diffraction, and high-energy electron diffraction. The electron structure factor for the (440) reflection was used to determine the Debye-Waller (DW) factor. The local heating of the specimen by the electron beam is determined to be 5 K under the current illumination conditions. The low-order structure factors for copper measured by different methods are compared and discussed. The new data set is used to test band theory and to obtain a charge density map. The charge deformation map shows a charge surplus between the atoms and agrees fairly well with the simple model of copper 2+ ions at the atomic sites in a sea of free uniformly distributed electrons.

Quantitative zone-axis convergent beam electron diffraction (CBED) is now an established technique. Over the past decade it has been developed into a tested method for the accurate refinement of structure factors, allowing the details of the charge density and bonding effects to be studied in crystalline materials. Strategies for obtaining the most accurate results have evolved, and the most important influences on the accuracy have been determined. Initial applications of the technique to bond charge density determination have led to the extension of the method to the refinement of other important parameters influencing the experimental data, such as Debye–Waller factors and the absorption potential. The development and current status of quantitative zone-axis CBED are discussed. Prospects for the future development and application of the technique are also considered.

The same Bragg reflection in TiO2 from 12 different (CBED) patterns (from different crystals, orientations, and thicknesses) are analyzed quantitatively to evaluate the consistency of the quantitative CBED method for bond-charge mapping. The standard deviation in the resulting distribution of derived X-ray structure factors is found to be an order of magnitude smaller than that in conventional X-ray work, and the standard error (0.026% for FX(110)) is slightly better than obtained by the X-ray Pendellösung method applied to silicon. This is sufficiently accurate to distinguish between atomic, covalent, and ionic models of bonding. We describe the importance of extracting experimental parameters from CCD camera characterization, and of surface oxidation and crystal shape. The current experiments show that the QCBED method is now a robust and powerful tool for low-order structure factor measurement, which does not suffer from the large extinction (multiple scattering) errors that occur in inorganic X-ray crystallography, and may be applied to nanocrystals. Our results will be used to understand the role of d-electrons in the chemical bonding of TiO2.