On the validity of the direct phasing and Fourier method in electron crystallography

The validity of the direct phasing and Fourier method for direct crystal structure determination is examined. It is shown that, while the kinematic approximation for electron diffraction is not strictly valid for all materials containing heavy atoms in real space, many of the low-order diffracted beams behave kinematically for a small crystal thickness. For thin crystals, structure maps constructed from compound crystals containing heavy atoms using low-order reflections are found to be faithful representations of the crystal structures. The inclusion of high-order diffracted beams is shown, however, to introduce intensity maxima that do not coincide with atom positions. It is shown that, if dynamical phases of the diffracted beams are available, as in the case of electron holography, an electron-density map using dynamical phases is a better map of the crystal structure than the structure map constructed using kinematic phases.