North-HollandUltramicr°sc°py 52(1993)436-444 ultramicroscopy Quantitative electron diffraction - new features in the program system ELD Xiaodong Zou, Yuri Sukharev and Sven Hovm611er Structural Chemistry, Stockholm University, S-10691 Stockholm, Sweden Received 5 January 1993 Dedicated to Professor John M. Cowley on the occasion of his seventieth birthday Accurate quantitative intensities from electron diffraction patterns can be obtained by the program system ELD. Such data is needed for solving or refining crystal structures. ELD runs on a personal computer. The quality of normal (i.e. not slow-scan) CCD cameras is sufficient for giving quite accurate structure factor amplitudes from electron diffraction patterns. Several factors which affect the intensity evaluation are discussed and some algorithms in ELD concerned with the problems of extracting high quality quantitative structure factors from electron diffraction patterns are described. 1. Introduction Structure determination of single crystals con- sists of two steps: first solving and then refining the structures. In X-ray crystallography, only the amplitude parts of the structure factors are ex- perimentally available. Various methods have been developed for solving the phase problem, for example, the Patterson method and the so- called direct methods. A structural model can be deduced once the phase information is available, and then subjected to a least-squares refinement against the experimental amplitudes. Crystallographic image processing (CIP) has been developed for solving structures from high resolution electron microscopy (HREM) images [1-3]. In HREM images, both amplitude and phase information from the structure factors are already present, although distorted. After digiti- zation of the image, the Fourier transform is calculated. By correcting for the optical distor- tions and imposing the crystallographic symmetry on the amplitudes and phases, a nearly distor- tion-free map of projected potential can be re- constructed by an inverse Fourier transformation. Atomic coordinates, at least for heavier atoms, can be obtained with an accuracy of 0.1 A and these are good enough to serve as a starting model for the next step, the structure refinement. The resolution of electron diffraction (ED) from inorganic crystals usually extends up to 1 or better. A complete three-dimensional data set can be obtained by merging ED patterns from several zone axes of a crystal (fig. 1). Despite the strong scattering of electrons causing multiple scattering, the data can be utilized for refinement of the structure if the crystal is sufficiently thin. o For a resolution of about 1 A, the number of ED amplitudes is large enough to allow all the vari- ables to be refined. The refinement procedure is similar to that used in X-ray crystallography, combining the Fourier and the least-squares methods. More accurate heavy-atom positions and the coordinates for light atoms are the results of the refinement. If the quality of the ED intensi- ties is good, phases can also be deduced from the intensities, by the same procedures as those used in X-ray crystallography [4]. We are developing a computer program system for structure determination by electron crystallog- 0304-3991/94/$06.00 © 1994 - Elsevier Science Publishers B.V. All rights reserved SSDI 0304-3991 (93)E0109-L