Structure determination and correction for distortions in HREM by crystallographic image processing

Electron Crystallographic Investigation of Crystals on the Mesostructural Scale

The precise structural solution of crystals on a mesostructural scale is challenging due to the difficulties in obtaining electron diffraction and the complicated relationship between the crystal structure factors (CSFs) and the conventional underfocus phase-contrast transmission electron microscopy (TEM) images due to the large unit cell and the complex structures. Here, we present the structural investigation of mesostructured crystals via the combination of electron crystallographic Fourier synthesis and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) that only relies on the mass-thickness contrast. The three-dimensional electrostatic potential is reconstructed from the amplitudes and phases extracted from the Fourier transforms of the corresponding HAADF-STEM images and merged into a set of CSFs. This method is verified on silica scaffolds following a shifted double-diamond surface network with space group I41/amd. The results indicate that electron crystallography reconstruction by HAADF-STEM images is more suitable and accurate in determining the structure in comparison with conventional TEM electron crystallography reconstruction. This approach transfers the contrast of mesostructured crystals to images more accurately and the relationship between the Fourier transforms of HAADF-STEM images and the CSFs is more intuitive. It shows great advantages for the structural solution of crystals on the mesostructural scale.

Electron Crystallography of Phthalocyanines

It is shown that it is possible to obtain structural information from small (<100 nm) phthalocyanine crystals by using crystallographic direct phasing methods applied to electron diffraction data. This technique is both quantitative and does not suffer from the difficulties associated with high-resolution electron microscopy. Structural information has been obtained from both tetra- and octa chloro-copper phthalocyanines, and the results compared with the hydrogenated and perchloro members of the series.

Limiting factors in atomic resolution cryo electron microscopy: no simple tricks

To bring cryo electron microscopy (cryoEM) of large biological complexes to atomic resolution, several factors--in both cryoEM image acquisition and 3D reconstruction--that may be neglected at low resolution become significantly limiting. Here we present thorough analyses of four limiting factors: (a) electron-beam tilt, (b) inaccurate determination of defocus values, (c) focus gradient through particles, and (d) particularly for large particles, dynamic (multiple) scattering of electrons. We also propose strategies to cope with these factors: (a) the divergence and direction tilt components of electron-beam tilt could be reduced by maintaining parallel illumination and by using a coma-free alignment procedure, respectively. Moreover, the effect of all beam tilt components, including spiral tilt, could be eliminated by use of a spherical aberration corrector. (b) More accurate measurement of defocus value could be obtained by imaging areas adjacent to the target area at high electron dose and by measuring the image shift induced by tilting the electron beam. (c) Each known Fourier coefficient in the Fourier transform of a cryoEM image is the sum of two Fourier coefficients of the 3D structure, one on each of two curved 'characteristic surfaces' in 3D Fourier space. We describe a simple model-based iterative method that could recover these two Fourier coefficients on the two characteristic surfaces. (d) The effect of dynamic scattering could be corrected by deconvolution of a transfer function. These analyses and our proposed strategies offer useful guidance for future experimental designs targeting atomic resolution cryoEM reconstruction.

Structure determination of the zeolite IM-5 using electron crystallography

The structure of the complex zeolite IM-5 (Cmcm, a = 14.33(4) Å, b = 56.9(2) Å, c = 20.32(7) Å) was determined by combining selected area electron diffraction (SAED), 3D reconstruction of high resolution transmission electron microscopy (HRTEM) images from different zone axes and distance least squares (DLS) refinement. The unit cell parameters were determined from SAED. The space group was determined from extinctions in the SAED patterns and projection symmetries of HRTEM images. Using the structure factor amplitudes and phases of 144 independent reflections obtained from HRTEM images along the [100], [010] and [001] directions, a 3D electrostatic potential map was calculated by inverse Fourier transformation. From this 3D potential map, all 24 unique Si positions could be determined. Oxygen atoms were added between each Si–Si pair and further refined together with the Si positions by distance-least-squares. The final structure model deviates on average 0.16 Å for Si and 0.31 Å for O from the structure refined using X-ray powder diffraction data. This method is general and offers a new possibility for determining the structures of zeolites and other materials with complex structures.

Electron crystallography: imaging and single-crystal diffraction from powders

The study of crystals at atomic level by electrons – electron crystallography – is an important complement to X-ray crystallography. There are two main advantages of structure determinations by electron crystallography compared to X-ray diffraction: (i) crystals millions of times smaller than those needed for X-ray diffraction can be studied and (ii) the phases of the crystallographic structure factors, which are lost in X-ray diffraction, are present in transmission-electron-microscopy (TEM) images. In this paper, some recent developments of electron crystallography and its applications, mainly on inorganic crystals, are shown. Crystal structures can be solved to atomic resolution in two dimensions as well as in three dimensions from both TEM images and electron diffraction. Different techniques developed for electron crystallography, including three-dimensional reconstruction, the electron precession technique and ultrafast electron crystallography, are reviewed. Examples of electron-crystallography applications are given. There is in principle no limitation to the complexity of the structures that can be solved by electron crystallography.

On the phase problem in electron microscopy: the relationship between structure factors, exit waves, and HREM images

In electron microscopy, the word phase is used for different physical phenomena, including crystallographic structure-factor phases and the electron wave phases. This has resulted in great confusion, as to whether the phase information is present or lost when an image is recorded. The aim of this paper is to solve this phase confusion problem by studying the relationships between structure factors, exit waves, and high-resolution electron microscopy (HREM) images. Three approaches are taken. First phases at different stages of the imaging processes are compared analytically for a crystal that can be considered a weak phase object (WPO). Then these different phases are calculated by the multi-slice method based on dynamical diffraction theory, and their numerical values are compared. Finally, the validity of the theoretical description is checked by comparison with experimental data on a real crystal, Ti(2)S. It is demonstrated that it is possible to obtain accurate structure factor-phases directly from HREM images by crystallographic image processing. The two major methods for structure determination from HREM images-exit wave reconstruction and crystallographic image processing-are compared. It is shown that the information utilised by the two methods as well as the results are essentially the same.

Measurement of crystal thickness and crystal tilt from HRTEM images and a way to correct for their effects

The effects of thickness and tilt angle are studied numerically on experimental high-resolution transmission electron microscope (HRTEM) images of a wedge-shaped metal oxide crystal. For sufficiently thin and well-aligned crystals, the amplitudes and phases of the Fourier transforms of the HRTEM images are essentially the same as the crystallographic structure factors. For tilted crystals, the changes of amplitudes and phases as a function of increased thickness and tilt angle can be described by a simple model. A method is presented by which the local thickness can be determined from one HRTEM image and one convergent-beam electron diffraction pattern from the same crystal. It is also shown how the projected potential can be reconstructed from HRTEM images of tilted crystals, disclosing the crystal structure, even from quite thick (>20 nm) samples.