Crystal structure determination by convergent-beam electron diffraction

In recent years, significant progress has been made towards a solution for the general problem of crystal structure determination by convergent beam electron diffraction (CBED). Even if we consider only perfectly ordered, periodic crystals defined by one of the conventional space groups, diffraction methods based on a focussed sub-micron beam of electrons are applicable to several related sets of structural problems that are not accessible to conventional X-ray or neutron diffraction techniques. We assume here that the space group either is known or has been determined from CBED patterns and that phases and amplitudes for some subset of the structure factors are required. Two limiting cases have been explored in some detail. For crystals where the atomic parameters and Debye-Waller factors are known accurately from high quality X-ray data, information on the charge redistribution for bonding electrons is available from precise measurements of the low order structure factors. Following the original research of Kambe, some recent work has demonstrated that accurate structure amplitudes and three-beam phase invariants can be extracted from the dynamical intensity distribution in CBED reflections. In principle, this approach is completely general but considerable labour would be required to extract sufficient data to solve the structure of an unknown crystal, whereas a large set of kinematic intensities is acquired from a single X-ray pattern.