Maximum entropy methods in electron crystallography

Revolutionizing the structural design and determination of covalent-organic frameworks: principles, methods, and techniques

Covalent organic frameworks (COFs) represent an important class of crystalline porous materials with designable structures and functions. The interconnected organic monomers, featuring pre-designed symmetries and connectivities, dictate the structures of COFs, endowing them with high thermal and chemical stability, large surface area, and tunable micropores. Furthermore, by utilizing pre-functionalization or post-synthetic functionalization strategies, COFs can acquire multifunctionalities, leading to their versatile applications in gas separation/storage, catalysis, and optoelectronic devices. Our review provides a comprehensive account of the latest advancements in the principles, methods, and techniques for structural design and determination of COFs. These cutting-edge approaches enable the rational design and precise elucidation of COF structures, addressing fundamental physicochemical challenges associated with host-guest interactions, topological transformations, network interpenetration, and defect-mediated catalysis.

Structure analysis of inorganic crystals by energy-filtered precession electron diffraction

We performed structure analysis of Si single crystal and CaMoO(4) inorganic crystal by energy-filtered precession electron diffraction (PED). Structure analysis was performed using conventional selected area electron diffraction, PED and energy-filtered PED (EF-PED). The EF-PED method proved to be advantageous in determining the crystal structures and accurate cell parameters of inorganic crystals due to resolution enhancement by sharpening the peak shapes and reducing inelastic scattering. Among the EF-PED methods, zero-loss PED was most useful for structure analysis by minimizing inelastic scattering intensities, while plasmon-loss PED could be used effectively to determine crystal symmetry by closely observing the conditions of forbidden reflections.

Direct structure analysis in protein electron crystallography via the density histogram: deoxycholate-treated purple membrane

The crystal structure of bacteriorhodopsin in purple membrane treated with sodium deoxycholate (plane group p3, a = 57.3 Å) was solved ab initio in projection from previously published electron diffraction amplitudes to 6.2 Å by direct methods for crystallographic phase determination. The best solution form the Sayre equation was identified by minimizing the skew properties of the cross-correlation of the experimental density histogram with the expected histogram. After Fourier refinement, the overall mean phase error is 43.3° for all 35 unique reflections of 16.9° for the 14 most intense maxima. For six clearly identified helix sites, the mean deviation of positions, when compared to the original model, was 0.7 Å.

Electron diffraction structure analysis: structural research with low-quality diffraction data

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-Ti2Se (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.

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.

An accurate analytical approach to electron crystallography

A much more accurate analytical expression of dynamical electron diffraction than the phase object approximation (POA) formula has been derived in this paper which decreases the restriction of sample thickness up to almost one order of magnitude compared to POA theory. The importance of the new expression is twofold. First, a sample with such a thickness that new expression remains valid can be prepared experimentally. Second, the new expression reveals a clear and straightforward relationship between the wave function and crystal potential. In the expression, the effect of dynamical diffraction on wave function can be simply attributed to two factors TP(D) = (sin(lambda pi zg2))/(4pi2g2) and TA(D) = [1 - cos(lambda pi zg2)]/4pi2g2. Compared to the effect of transfer functions of an electron microscope on wave function, we found that TP(d) and TA(d) play the same role as transfer function but are independent of the instrument. For this reason, we here call the former as "extrinsic transfer functions" and the latter as "intrinsic" ones. In principle, one should correct not only extrinsic transfer functions but also intrinsic ones if one desires to achieve higher resolution.

Electron crystallography in surface structure analysis

Surface structure analysis is an important area of research, and in recent years notable advances have been made in this field, both in improved techniques for studying surfaces and in methods of analyzing them. This review aims to summarize the techniques available, particularly those relating to electron microscopy, and also to outline one of the newest areas of development, the application of direct methods to surface structure analysis.