Direct retrieval of crystal and surface structures using high energy electrons

Abstract

A direct scheme has been developed for crystal and surface structure determination. This scheme is based on a partition of the crystal potential V( r) into a known part V 0( r) and a perturbation δV( r), i.e. V( r)= V 0( r)+ δV( r). The full dynamical electron diffraction theory is used for treating the dynamical electron diffraction by V 0( r) and perturbation theory is used for dealing with the residual scattering by δV( r). It is shown that this partition is applicable for a wide range of situations of practical importance, including scattering by the re-distributed valence electrons and by a reconstructed surface layer. In some favourable cases, when the crystal thickness is not exceedingly large and atomic displacements from the known structure giving rise to V 0( r) are small (as in the case of structure refinement), crystal structure factors and crystal and surface structure can be directly inverted from dynamical diffraction data. Both the perturbation method and the direct scheme have been extensively tested, and in particular the direct scheme has been used successfully to invert crystal structure factors directly from experimental CBED data obtained from a single crystal of MgO.