Measurement of individual structure-factor phases with tenth-degree accuracy: the 00.2 reflection in BeO studied by electron and X-ray diffraction

Abstract

Measurements of the phase (and amplitude) of the 00.2 structure factor of BeO are reported. These were obtained by applying an automated least-squares refinement method to experimental convergent-beam transmission electron diffraction data, collected from sub-micrometer single-crystal regions of two different thicknesses. Multiple-scattering effects were included, using the Bloch-wave method. Perturbation methods were used to include weak beams and to estimate errors. After conversion to X-ray structure factors, it was found that ϕx (00.2) = −1.190 (9) rad. The same value was found, within experimental error, using data collected from a region of different thickness. New single-crystal X-ray results are also reported, which are in good agreement with the electron diffraction results. Phases derived from multipole refinement using X-ray data are about fifty times less accurate than the electron results. This electron diffraction technique may be the most accurate method for the measurement of low-order structure-factor phases from acentric crystals with small unit cells. The method may therefore allow the extension of previous highly accurate studies of charge density in silicon to acentric materials from which large single crystals cannot be grown.