QED v 1.0: a software package for quantitative electron diffraction data treatment

A simple program for fast tilting electron-beam sensitive crystals to zone axes

Tilting crystals to proper zone axes is a necessary but tedious work in taking selected area electron diffraction patterns (SAED) and high-resolution images using transmission electron microscope (TEM). This process not only costs a lot of time but also limits the application of TEM in electron-beam sensitive materials. Therefore, it is desirable to develop a simple method for tilting crystals from random orientations to a specific zone axis quickly. Herein, we describe a novel program, Zones, which can index the electron diffraction pattern and calculate the tilting angles of a double-tilt sample holder from the current orientation to a desired zone axis. It can also bring crystals that are slightly deviated from a zone axis to the exact zone with the help of Laue ring in the diffraction pattern. This program has been successfully applied to studies of zeolites and metal-organic frameworks (MOFs), known as being electron-beam sensitive. The program shows its power not only in saving the operator's time but also in preventing the crystals from quick beam damages.

Pattern Center and Distortion Determined from Faint, Diffuse Electron Diffraction Rings from Amorphous Materials

Diffuse rings from amorphous materials sit on a steep background resulting in a monotonically decreasing intensity over scattering vector length, frequently with no clear local maximum that could be used to determine the center of the ring. The novelty of the method reported here is that it successful processes such weak patterns. It is based on separating the angular dependence of the positions of the maxima on the azimuthal angle in the measured two-dimensional pattern for a manually preselected peak. Both pattern center and elliptical distortion are simultaneously refined from this angular dependence. Both steps are based on nonlinear least square fitting, using the Levenberg-Marquardt method. It can be successfully applied to any amorphous patterns provided they were recorded with experimental conditions that facilitate dividing them into sectors with acceptable statistics. Patterns with the center shifted to the camera corner (recording a quadrant of a ring) can also be reliably evaluated, keeping precalibrated values of the elliptical distortion fixed during the fit. Finally, the limited number of counts in any pattern is overcome by cumulating many patterns (from equivalent areas) into a single pattern. Eliminating false effects is facilitated by masking out unwanted parts of any recorded pattern from processing.

Crystallographic Tool Box (CrysTBox): automated tools for transmission electron microscopists and crystallographers

Three tools for an automated analysis of electron diffraction pattern and crystallographic visualization are presented. Firstly, diffractGUI determines the zone axis from selected area diffraction, convergent beam diffraction or nanodiffraction patterns and allows for indexing of individual reflections. Secondly, ringGUI identifies crystallographic planes corresponding to the depicted rings in the ring diffraction pattern and can select the sample material from a list of candidates. Both diffractGUI and ringGUI employ methods of computer vision for a fast, robust and accurate analysis. Thirdly, cellViewer is an intuitive visualization tool which is also helpful for crystallographic calculations or educational purposes. diffractGUI and cellViewer can be used together during a transmission electron microscopy session to determine the sample holder tilts required to reach a desired zone axis. All the tools offer a graphical user interface. The toolbox is distributed as a standalone application, so it can be installed on the microscope computer and launched directly from DigitalMicrograph (Gatan Inc.).

High-resolution electron diffraction: accounting for radially and angularly invariant distortions

The distortions present in an electron diffraction pattern can be classified into two categories: one is radially invariant and the other is angularly invariant. We report a method to compensate these displacements undergone by diffraction features promoted by any kind of artifacts generated in parallel beam electron diffraction conditions. This approach is not aimed at quantifying these distortions but only intends to aid in the measurement of lattice parameters of crystals with a significant increase of accuracy and precision as compared to previous approaches. It is based on statistical estimations of the relative positions between diffraction rings and/or spots after performing a transformation of the digitalized patterns to polar coordinates. The analytical method is based on fitting a Gaussian type profile to intensity distributions. This makes it possible to determine the lattice parameters of a polycrystal or single crystal with relative errors smaller than 0.1% for diffractograms acquired in photographic films and below 0.01% for those collected in imaging plates.

Structure of the new mineral sarrabusite, Pb5CuCl4(SeO3)4, solved by manual electron-diffraction tomography

The new mineral sarrabusite Pb5CuCl4(SeO3)4 has been discovered in the Sardinian mine of Baccu Locci, near Villaputzu. It occurs as small lemon–yellow spherical aggregates of tabular crystals (< 10 µm) of less than 100 µm in diameter. The crystal structure has been solved from and refined against electron diffraction of a microcrystal. Data sets have been measured by both a manual and an automated version of the new electron-diffraction tomography technique combined with the precession of the electron beam. The sarrabusite structure is monoclinic and consists of (010) layers of straight chains formed by alternating edge-sharing CuO4Cl2 and PbO8 polyhedra parallel to the c axis, which share corners laterally with two zigzag corner-sharing chains of PbO6Cl2 and PbO4Cl4 bicapped trigonal prisms. These blocks are linked together by SeO_3^{2-} flat-pyramidal groups.

A software tool for automatic analysis of selected area diffraction patterns within Digital Micrograph™

A software package "SADP Tools" is developed as a complementary diffraction pattern analysis tool. The core program, called AutoSADP, is designed to facilitate automated measurements of d-spacing and interplaner angles from TEM selected area diffraction patterns (SADPs) of single crystals. The software uses iterative cross correlations to locate the forward scattered beam position and to find the coordinates of the diffraction spots. The newly developed algorithm is suitable for fully automated analysis and it works well with asymmetric diffraction patterns, off-zone axis patterns, patterns with streaks, and noisy patterns such as Fast Fourier transforms of high-resolution images. The AutoSADP tool runs as a macro for the Digital Micrograph program and can determine d-spacing values and interplanar angles based on the pixel ratio with an accuracy of better than about 2%.

Automated Electron Nanocrystallography

We review methods to solve nanocrystals and obtain a 3D charge-density map at the electron microscope. Experimental tests are demonstrated for kinematic CBED and precession techniques.

Structure solution of the new titanate Li4Ti8Ni3O21 using precession electron diffraction

A sample having stoichiometry Li[Ti(1.5)Ni(0.5)]O(4) has been synthesized to obtain a spinel structure. The resulting crystalline powder revealed a multiphase nature with spinel as the minor phase. The main phase is a new trigonal phase having a = 5.05910 (1), c = 32.5371 (1) A. The structure has been solved by direct methods working on a three-dimensional set of intensities obtained from a precession electron-diffraction experiment, and refined on synchrotron powder diffraction data in the space group P3c1. The model consists of hexagonal layers of edge-sharing octahedra occupied either by the heavy cations Ti and Ni, or preferentially by Li. On the basis of cation-site occupancies the stoichiometry becomes Li(4)Ti(8)Ni(3)O(21), which is compatible with the microanalysis results.

Consistent indexing of a (set of) single crystal SAED pattern(s) with the ProcessDiffraction program

A computer program called "ProcessDiffraction" helps indexing a set of single crystal selected area electron diffraction (SAED) patterns by determining which of the presumed structures can fit all the measured patterns simultaneously. Distances and angles are measured in the digitalized patterns with a graphical tool by clicking on the two shortest non-collinear vectors (spots), using user-supplied calibration data. Centers of the spots and center of the pattern are optionally refined by the program. Suggested individual indexing solutions (consistent with an assumed unit cell) are listed by the program for each pattern. Simulated patterns are also consulted to check if the shortest calculated distances coincide with measured ones. Common solutions for the set are selected by checking the angles between the suggested zone axes against the angles between the experimental goniometer settings. The indexing process is manually controlled by selecting the candidate structures (one-by-one) for indexing and by specifying the tolerances for d-values, plane angles and zone angles. Patterns of any crystal system can be indexed successfully. Although error bars are larger in electron diffraction than in X-ray diffraction (XRD), frequently, many unrelated indexings are possible for any one electron diffraction pattern (irrespective of the indexing method), a set of SAED patterns can generally be indexed unambiguously, i.e. the three-dimensional reciprocal space can be identified correctly. Two other tools also help planning tilting experiments: zones along a plane can be listed (with their angles extended from a pre-selected zone in that plane) and zones lying at a given angle (specified with a tolerance) from a zone can also be identified (as they are situated between two cones). Another tool searches the XRD database directly either for advice on possible structures for a composition or to help calibration.

Structure determination of oxide compounds by electron crystallography

Among different techniques, electron crystallography presents the advantage to determine structures on a local scale or from very small samples. Different methods such as image processing, exit wave reconstruction, Patterson analysis, or direct methods can be applied for getting a starting structural model. Results obtained on various oxides have shown that the dynamical nature of electron scattering, far from being detrimental, can even help in the localization of oxygen atoms close to heavier scatters. Concerning the structure refinement step, it is now possible to introduce dynamical effect correction through multislice calculations combined with least-squares refinement. However, depending on the problem to solve and the accuracy needed, the alternative solution consisting in getting as close as possible to kinematical conditions is still worth considering. Different examples of structures refined from electron diffraction data are given.

Structure determination of phi-Bi8Pb5O17 by electron and powder X-ray diffraction

The triclinic crystal structure of phi-Bi8Pb5O17, a ionic fast conductor material, has been determined by the synergy of both electron and powder X-ray crystallography. The heavy atom positions were found by direct methods on electron diffraction data and the structure was completed by iterative use of a priori information in direct methods and difference Fourier maps on both types of data. Structure refinement was performed by the Rietveld method on powder X-ray data. The results suggest that phi-Bi8Pb5O17 is an ordered phase, with Bi and Pb atoms occupying different sites of the lattice, at variance with the other structural phases known for similar composition in the Bi-Pb-O phase diagram, which are solid solutions characterised by a wide compositional range.