Visual computing in electron crystallography

Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancement

Information-theoretic crystallographic symmetry classifications distinguish between genuine symmetries and strong Fedorov-type pseudo­symmetries in noisy crystal patterns in two dimensions. Because these classifications require neither visual comparisons of image pairs nor subjective interpretations of ‘symmetry deviation quantifiers’ by human beings, they enable the optimal crystallographic processing of an experimental image that results in a significantly enhanced signal-to-noise ratio of a microscopic study of a crystal.

Statistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudo­symmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), also known as crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists of the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal-to-noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.

Effect of diffraction crystallography on HREM

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.

Unmasking Melon by a Complementary Approach Employing Electron Diffraction, Solid-State NMR Spectroscopy, and Theoretical Calculations—Structural Characterization of a Carbon Nitride Polymer

Poly(aminoimino)heptazine, otherwise known as Liebig's melon, whose composition and structure has been subject to multitudinous speculations, was synthesized from melamine at 630 degrees C under the pressure of ammonia. Electron diffraction, solid-state NMR spectroscopy, and theoretical calculations revealed that the nanocrystalline material exhibits domains well-ordered in two dimensions, thereby allowing the structure solution in projection by electron diffraction. Melon ([C(6)N(7)(NH(2))(NH)](n), plane group p2 gg, a=16.7, b=12.4 A, gamma=90 degrees, Z=4), is composed of layers made up from infinite 1D chains of NH-bridged melem (C(6)N(7)(NH(2))(3)) monomers. The strands adopt a zigzag-type geometry and are tightly linked by hydrogen bonds to give a 2D planar array. The inter-layer distance was determined to be 3.2 A from X-ray powder diffraction. The presence of heptazine building blocks, as well as NH and NH(2) groups was confirmed by (13)C and (15)N solid-state NMR spectroscopy using (15)N-labeled melon. The degree of condensation of the heptazine core was further substantiated by a (15)N direct excitation measurement. Magnetization exchange observed between all (15)N nuclei using a fp-RFDR experiment, together with the CP-MAS data and elemental analysis, suggests that the sample is mainly homogeneous in terms of its basic composition and molecular building blocks. Semiempirical, force field, and DFT/plane wave calculations under periodic boundary conditions corroborate the structure model obtained by electron diffraction. The overall planarity of the layers is confirmed and a good agreement is obtained between the experimental and calculated NMR chemical shift parameters. The polymeric character and thermal stability of melon might render this polymer a pre-stage of g-C(3)N(4) and portend its use as a promising inert material for a variety of applications in materials and surface science.

Maximum entropy image deconvolution applied to structure determination for crystal Nd1.85Ce0.15CuO4−δ

Eight [100] images from a through-focus series of tetragonal crystal Nd1.85Ce0.15CuO4-delta were transformed separately into the structure images by means of maximum entropy image deconvolution. The constructed projected structure model based on the deconvoluted image is confirmed by image simulation. It is demonstrated that the image deconvolution is still successful even when some reflections fall in the vicinity of zero cross of contrast transfer function. The effectiveness and advantages of the technique are discussed.

EDM 1.0: Electron direct methods

A computer program designed to provide a number of quantitative analysis tools for high-resolution imaging and electron diffraction data is described. The program includes basic image manipulation, both real space and reciprocal space image processing, Wiener-filtering, symmetry averaging, methods for quantification of electron diffraction patterns and two-dimensional direct methods. The program consists of a number of sub-programs written in a combination of C++, C and Fortran. It can be downloaded either as GNU source code or as binaries and has been compiled and verified on a wide range of platforms, both Unix based and PC's. Elements of the design philosophy as well as future possible extensions are described.