On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Abstract

A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1 °. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting K_ikuchi-and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.

Increase of the mean inner Coulomb potential in Au clusters induced by surface tension and its implication for electron scattering

“…The MIP can be determined by off-axis EH under kinematical diffraction conditions according to the relation ∆ϕ = C E V 0 t (C E : interaction constant) by measuring the phase shift ∆ϕ between the electron wave passing through the sample with a known thickness t and a vacuum reference wave [6]. On the other hand, local TEM sample thicknesses can be determined by EH, if precise values of the MIP are known, but thus far only MIP values for few materials with limited accuracy are available [7,8,9,10,11]. For instance, experimental values for the MIP of Au between 16.8 and 30.2 V were reported [8], whereas calculations yield values of 25.0 to 35.9 V [7,8,11].…”

Electron Diffraction Tomography and Dynamical Refinement for Crystal-Structure Characterization of Nanocrystalline Materials

“…The diracted intensities are integrated over all orientations of the beam during the precession. As a consequence, the intensities are less sensitive to imperfections of the crystal and more sensitive to the structural parameters like atomic positions [4,5]. The use of PED in combination with EDT results in reliable structure parameters.…”

Introduction to electron crystallography

“…However, it is more favourable for thick crystals (> 500 Å) with small unit cells (< 10 Å). Structure analysis by CBED has been summarised in two review articles [40,41]. Structure determination of inorganic crystals by HRTEM and selected area electron diffraction has been reviewed recently [42].…”