The determination of atomic structure using the difference potential

Full text: Many oxides, especially those existing as nanocrystals, are not amenable to x-ray and neutron diffraction methods, and their structures can only be determined using high resolution electron microscopy (HREM). Although visually impressive HREM images give only approximate cation positions, and the oxygen atom locations must be inferred. This contrasts with diffraction studies of bulk materials, where resolution is set by the diffraction limit, typically 0.035 nm, and oxygen positions are determined directly. Unfortunately the solid-state chemist is mainly interested in the oxygen atom positions. This problem can be approached in various ways. For microcrystalline oxides, a trial structure from HREM images may, if the unit cell is not too large, be refined using Reitveld powder diffraction methods but disorder or line broadening effects resulting from nanocrystalline particles with unknown sizes can make this impossible. An alternative approach is to use single crystal electron diffraction, where the resolution limit is far beyond that of HREM, but the crystallographic phase problem must then be solved and the drawback of multiple scattering remains. Another alternative is to extend the resolution limit in the imaging mode, either by reconstruction from a series of images, or by improvements in both lens design and the nature of the illumination system. However, the difficulties involved in this course of action are well-known. The approach presented here is an amalgamation of HREM and electron diffraction. Approximate cation positions in a lead-tungsten oxide are obtained from the HREM image and these may be used to calculate diffracted beam amplitudes and phases, including the effects of multiple scattering. This data, together with experimentally measured diffracted intensities, may be used to calculate a difference potential, analogous to the difference density of x-ray diffraction, in which the anion positions and inaccuracies in the cation positions are revealed. The final refinement shows excellent agreement with the structure derived from single crystal χ ray diffraction studies, and reveals the structure at much higher resolution than is possible in the HREM image alone. Future applications of the technique will be discussed. Copyright (2002) Australian Society for Electron Microscopy Inc