Volume 218, Issue 4 - Electron Crystallography

Although often an object of controversy, electron crystallography has emerged as a useful technique for characterization of the microcrystalline state, capable of elucidating crystal structures of unknown substances. Despite the complicated multiple scattering perturbations to diffracted intensities, experimental conditions can be adjusted to favor data collection where the experimental Patterson function still resembles the autocorrelation function of the actual crystal structure. Satisfying this condition is often sufficient to permit structure solution from such data by direct methods. While the application to organic structures may seem obvious, there are surprising successes with data sets from inorganic materials. The account given in this paper, in part, portrays work leading to the A. L. Patterson Award to the author from the American Crystallographic Association.

The development of the electron diffractometry methods jointly the analytical methods of electrostatic potential (ESP) reconstruction and its topological analysis allowd one to proceed to the quality new level of electron diffraction structure analysis (EDSA): investigation inner crystalline electrostatic field, which knowledge permitts to study the relation of the atomic structure with physical properties of crystals. The review of the last achivements in this direction, obtained in the Institute of Crystallography of Russian Academy of Sciences, in which EDSA method was discovered, is done. The possibility of the EDSA method to solve precise problems of quantitative analysis of the electrostatic potential is shown on the examples of investigations of the ESP distributions and chemical bonding in crystals with NaCl-type structure and covalent crystal Ge. It is also shown that quantitative data on the potential distribution considerably enlarge conceptions on the nature of interatomic and inetrmolecular interactions in crystals.

Organic materials, such as non-linear optical active compounds (1-(2-furyl)-3-(4-aminophenyl)-2-propene-1-one (FBAPPO) and 1-(2-furyl)-3-(4-benzamidophenyl)-2-propene-1-one (FAPPO)), polymeric materials like the metal coordinated polyelectrolyte (Fe(II) [ditopic bis-terpyridin] (MEPE)) or polymorphic materials (e.g. Cu-phthalocyanine), which do not crystallize big enough for single crystal x-ray structure analysis have been investigated by electron diffraction (ED) at 100 and 300 kV acceleration voltage. Sample preparation (direct crystallization, ultra sonication, ultra microtomy), diffraction strategies (selected area diffraction, nano diffraction, use of double-tilt rotation holder), data collection and data processing as well as structure solution strategies have been chosen dependent on the different requirements of the compounds under investigation. Structure analysis was carried out by simulation using ab initio quantum-mechanical methods like density functional theory (DFT), semi-empirical approach (MNDO/AM1/PM3) and force field packing energy calculations (DREIDING). The structure models resulting from simulation were refined kinematically as rigid bodies. Subsequently, refinements by multi-slice least squares (MSLS) procedures taking dynamical scattering into account were performed. The described combination of different methods which was used successfully on crystallizable materials is also adaptable to insoluble organic materials (e.g. pigments) and polymorphic systems.

Electron Diffraction Structure Analysis (EDSA) with data from standard selected-area electron diffraction (SAED) is still the method of choice for structure determination of nano-sized single crystals. The recently determined heavy atom structure α -Ti 2 Se (Albe & Weirich, 2003) is used as an example to illustrate the developed procedure for structure determination from two-dimensionally SAED data via direct methods and kinematical least-squares refinement. Despite the investigated crystallite had a relatively large effective thickness of about 230 Å as determined from dynamical calculations, the obtained structural model from SAED data was found in good agreement with the result from an earlier single crystal X-ray study (Weirich, Pöttgen & Simon, 1996). Arguments, which support the validity of the used quasi-kinematical approach, are given in the text. The influences of dynamical and secondary scattering on the quality of the data and the structure solution are discussed. Moreover, the usefulness of first-principles calculations for verifying the results from EDSA is demonstrated by two examples, whereas one of the structures was unattainable by conventional X-ray diffraction.

A simple image contrast theory in high-resolution electron microscopy (HREM) is introduced to demonstrate that below a certain critical crystal thickness the intensity of the Scherzer focus image is linear to the projected potential of an artificial crystal that is isomorphic to the examined one. It has become the theoretical base of electron crystallographic image processing techniques relying on the weak-phase-object approximation and kinematical diffraction. Two techniques of image processing are introduced. One of them aims at determining crystal structures by combining electron diffraction data and applying diffraction analysis methods. To reduce various kinds of electron diffraction intensity distortion the diffraction data are corrected by means of an empirical method set up by referring to the heavy atom method and Wilson statistic. The other one aims at revealing crystal defects at atomic resolution from the image taken with a medium-voltage field-emission high-resolution electron microscope. The dynamical effect is corrected by forcing the integral amplitudes of reflections in the diffractogram of image equal to the amplitudes of corresponding structure factors for the perfect crystal. The principle of the two techniques is briefly introduced, and examples of applications to crystal structure and defect determination are given.

A series of structure analyses during 1994-2001 by electron crystallographic techniques applied to phases in aluminum alloys are reviewed. Methods for structure solution employ electron diffraction intensity data collected by the precession technique, by selected area micro-diffraction and by the convergent-beam technique. High-resolution electron microscope images (HRTEM) are treated by different kind of processing, including exit wave reconstruction. Crystallographic calculations are performed either by direct method or Patterson and Fourier procedures, assuming kinematical scattering, or by refinement from models derived from HRTEM images. Dynamical scattering calculations can be introduced in the refinement stage or as a correction procedure applied to part of the intensity data. The phases studied include primary Al-Fe-(Si) particles, Al-Mn-Si dispersoids, Al-Co quasicrystals and two types of precipitate phases in age-hardening Al-Mg-Si and Al-Zn-Mg alloys.

VEC is a program package for V isual computing in E lectron C rystallography. The program is written mainly in C++ and Fortran and is for running under MS Windows 95, 98, NT and 2000. Apart from its user-friendly interface, sophisticated text-sensitive online helps and tutorials, VEC includes same unique crystallographic methods. They are direct-method image-processing techniques, ab-initio solution of incommensurate crystal structures and algorithms for searching one-dimensionally modulated atoms in 4-dimensional Fourier maps. Examples are given in details.

The role of electron diffraction structure analysis in mineralogy is discussed with special reference to developments in the former Soviet Union and the current Russian Federation.