Structure solution with three-dimensional sets of precessed electron diffraction intensities

The use of the precession technique for obtaining three-dimensional (3D) sets of electron diffraction intensities suitable for structure solution is discussed. The minerals uvarovite and ?kermanite have been used as testing structures. The electron diffraction data sets obtained on these samples retain an acceptable linear relation with calculated structure factor amplitudes. The quality of these data is suitable to solve both structures using direct methods opening the possibility to use 3D precession ED data for solving unknown mineral structures.     

A practical guide to the measurement of structure phases and magnitudes by three-beam convergent beam electron diffraction

The practical details for the direct measurement of structural phases and magnitudes from centrosymmetric crystals using three-beam convergent beam electron diffraction patterns are given. These details are presented as a step-by-step guide for easy implementation. Each step is illustrated with worked examples from alpha-Al(2)O(3). Twenty-nine measurements of 6 independent three-phase invariants and 87 measurements of 10 independent structure magnitudes have been made.     

Towards automated diffraction tomography: part I--data acquisition

The ultimate aim of electron diffraction data collection for structure analysis is to sample the reciprocal space as accurately as possible to obtain a high-quality data set for crystal structure determination. Besides a more precise lattice parameter determination, fine sampling is expected to deliver superior data on reflection intensities, which is crucial for subsequent structure analysis. Traditionally, three-dimensional (3D) diffraction data are collected by manually tilting a crystal around a selected crystallographic axis and recording a set of diffraction patterns (a tilt series) at various crystallographic zones. In a second step, diffraction data from these zones are combined into a 3D data set and analyzed to yield the desired structure information. Data collection can also be performed automatically, with the recent advances in tomography acquisition providing a suitable basis. An experimental software module has been developed for the Tecnai microscope for such an automated diffraction pattern collection while tilting around the goniometer axis. The module combines STEM imaging with diffraction pattern acquisition in nanodiffraction mode. It allows automated recording of diffraction tilt series from nanoparticles with a size down to 5nm.     

QtUCP-a program for determining unit-cell parameters in electron diffraction experiments using double-tilt and rotation-tilt holders

A computer program, QtUCP, has been developed based on several well-established algorithms using GCC 4.0 and Qt 4.0 (Open Source Edition) under Debian GNU/Linux 4.0r0. It can determine the unit-cell parameters from an electron diffraction tilt series obtained from both double-tilt and rotation-tilt holders. In this approach, two or more primitive cells of the reciprocal lattice are determined from experimental data, in the meantime, the measurement errors of the tilt angles are checked and minimized. Subsequently, the derived primitive cells are converted into the reduced form and then transformed into the reduced direct primitive cell. Finally all the patterns are indexed and the least-squares refinement is employed to obtain the optimized results of the lattice parameters. Finally, two examples are given to show the application of the program, one is based on the experiment, the other is from the simulation.     

Application of a 2-beam model for improving the structure factors from precession electron diffraction intensities

A 2-beam model is used to simulate precession electron diffraction (PED) intensities. It is shown that this model can be inverted with minimal knowledge of the underlying crystal structure, permitting structure factor amplitudes to be deduced directly from measured intensities within the 2-beam approximation. This approach may be used in conjunction with direct methods to obtain correct, kinematically interpretable structure indications for data sets from relatively thin crystals (less than approximately 400A), and an experimental example based on (Ga,In)(2)SnO(5) is presented. The failure of this approach at large thickness is illustrated by an additional data set for MFI zeolite. The 2-beam approximation provides a simple model for PED intensities, and inversion using this model shows advantages over a kinematical approximation. It is however too rough approximation to be of general use and ultimately it is to be hoped that more accurate models with similar ease of use can be derived to treat PED data.     

Towards automated diffraction tomography. Part II--Cell parameter determination

Automated diffraction tomography (ADT) allows the collection of three-dimensional (3d) diffraction data sets from crystals down to a size of only few nanometres. Imaging is done in STEM mode, and diffraction data are collected with quasi-parallel beam nanoelectron diffraction (NED). Here, we present a set of developed processing steps necessary for automatic unit-cell parameter determination from the collected 3d diffraction data. Cell parameter determination is done via extraction of peak positions from a recorded data set (called the data reduction path) followed by subsequent cluster analysis of difference vectors. The procedure of lattice parameter determination is presented in detail for a beam-sensitive organic material. Independently, we demonstrate a potential (called the full integration path) based on 3d reconstruction of the reciprocal space visualising special structural features of materials such as partial disorder. Furthermore, we describe new features implemented into the acquisition part.     

Quantitative measurements of Kikuchi bands in diffraction patterns of backscattered electrons using an electrostatic analyzer

Diffraction patterns of backscattered electrons can provide important crystallographic information with high spatial resolution. Recently, the dynamical theory of electron diffraction was applied to reproduce in great detail backscattering patterns observed in the scanning electron microscope (SEM). However, a fully quantitative comparison of theory and experiment requires angle-resolved measurements of the intensity and the energy of the backscattered electrons, which is difficult to realize in an SEM. This paper determines diffraction patterns of backscattered electrons using an electrostatic analyzer, operating at energies up to 40 keV with sub-eV energy resolution. Measurements are done for different measurement geometries and incoming energies. Generally a good agreement is found between theory and experiment. This spectrometer also allows us to test the influence of the energy loss of the detected electron on the backscattered electron diffraction pattern. It is found that the amplitude of the intensity variation decreases only slowly with increasing energy loss from 0 to 60 eV.     

Low-dose performance of parallel-beam nanodiffraction

We evaluate the low-dose performance of parallel nano-beam diffraction (NBD) in the transmission electron microscope as a method for characterizing radiation sensitive materials at low electron irradiation dose. A criterion, analogous to Rose's, is established for detecting a diffraction spot with desired signal-to-noise ratio. Our experimental data show that a dose substantially lower than in high-resolution bright-field imaging is sufficient to determine structure and orientation of individual nanoscale objects embedded in amorphous matrix. In an instrument equipped with a cold field-emission gun it is possible to form a probe with sub-3 nm diameter and sub-0.3 mrad convergence angle with sufficient beam current to record a diffraction pattern with less than 0.2 s acquisition time. The interpretation of NBD patterns is identical to that of selected area diffraction patterns. We illustrate the physical principles underlying good low-dose performance of NBD by means of a phase grating. The electron irradiation dose needed to detect a diffraction peak in NBD is found proportional to 1/N2, where N is the number of lattice planes contributing to the peak.     

Comparison of electron diffraction data from non-linear optically active organic DMABC crystals obtained at 100 and 300 kV

During the recent past, we have synthesized a new class of molecules with intramolecular two-dimensional charge transfer upon excitation. The present report presents such a molecule, 2,6-bis(4-dimethylamino-benzylidene)-cyclohexanone (DMABC), with an unusually high value of the second-order non-linear optical (NLO) coefficients. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refinement by X-ray methods, is a time consuming and sometimes impossible task. We have performed a complete structural analysis by electron diffraction combined with simulation methods and with maximum entropy and log likelihood statistics. In order to improve the quantitative analysis, a 300 kV data set using an on-line CCD camera was added and the best attainable R-values were compared with those from 100 kV data using film emulsions. Details regarding the maximum attainable resolution for both data sets are discussed as well as the problems which arise from the limited dynamic range in photographic emulsions as compared to a 14 bit CCD camera. Once the crystal structure was known, quantum-chemical methods were used to calculate non-linear optical susceptibility tensor components and these were related to the macroscopic coefficients of the crystalline quadratic non-linearity tensor. In the present work, both ab initio and semi-empirical quantum-chemical calculations were employed.     

Direct space structure solution from precession electron diffraction data: Resolving heavy and light scatterers in Pb13Mn9O25

The crystal structure of a novel compound Pb₁₃Mn₉O₂₅ has been determined through a direct space structure solution with a Monte-Carlo-based global optimization using precession electron diffraction data (a=14.177(3) Å, c=3.9320(7) Å, SG P4/m, R_F=0.239) and compositional information obtained from energy dispersive X-ray analysis and electron energy loss spectroscopy. This allowed to obtain a reliable structural model even despite the simultaneous presence of both heavy (Pb) and light (O) scattering elements and to validate the accuracy of the electron diffraction-based structure refinement. This provides an important benchmark for further studies of complex structural problems with electron diffraction techniques. Pb₁₃Mn₉O₂₅ has an anion- and cation-deficient perovskite-based structure with the A-positions filled by the Pb atoms and 9/13 of the B positions filled by the Mn atoms in an ordered manner. MnO₆ octahedra and MnO₅ tetragonal pyramids form a network by sharing common corners. Tunnels are formed in the network due to an ordered arrangement of vacancies at the B-sublattice. These tunnels provide sufficient space for localization of the lone 6s² electron pairs of the Pb²⁺ cations, suggested as the driving force for the structural difference between Pb₁₃Mn₉O₂₅ and the manganites of alkali-earth elements with similar compositions.     

Retrieval of object information by inverse problems in electron diffraction

The imaging of crystal defects by high-resolution transmission electron microscopy or with the help of the electron diffraction contrast technique is well known and routinely used. However, a direct and phenomenological analysis of electron micrographs is mostly not possible, but requires the application of image simulation and matching techniques. The trial-and-error matching technique is the indirect solution to the direct scattering problem applied to analyse the nature of the object under investigation. Alternatively, inverse problems as direct solutions of electron scattering equations can be deduced using either an invertible linearized eigenvalue system or a discretized form of the diffraction equations. This analysis is based on the knowledge of the complex electron wave at the exit plane of an object reconstructed for the surrounding of single reflections by electron holography or other wave reconstruction techniques. In principle, it enables directly the retrieval of the local thickness and orientation of a sample as well as the refinement of potential coefficients or the determination of the atomic displacements, caused by a crystal lattice defect, relative to the atom positions of the perfect lattice. Considering especially the sample orientation as perturbation the solution is given by a generalized and regularized Moore–Penrose inverse, where the resulting numerical algorithms imply ill-posed inverse problems.     

Structural and electron diffraction data for sapphire (α-al2o3)

Crystallographic and electron diffraction data for sapphire (α-Al₂O₃) are presented which enable ready and unique identification of TEM diffraction patterns and facilitate image analysis. Crystallographic data is presented in the form of stereographic projections and in figures listing angles between planes and angles between zones. Electron diffraction data consist of computer-simulated diffraction patterns and tables of extinction distances calculated using atomic and ionic electron scattering factors.     

A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite

Fluctuation electron microscopy (FEM) is a quantitative electron microscopy technique in which we use the variance V of spatial fluctuations in nanodiffraction as a function of the diffraction vector magnitude k and real-space resolution R to detect medium-range order in amorphous materials. We have developed a model for V(k, R) from a nanocrystal/amorphous composite, which is an idealized form of the medium-range order in various amorphous materials found by previous FEM measurements. The resulting expression for V(k, R) as a function of the nanocrystal size, nanocrystal volume fraction, and the sample thickness connects the FEM signal to well-defined aspects of the material's structure, emphasizes the need for samples of controlled thickness, and explains in some cases the relative height of peaks in V(k). We give an example of interpreting FEM data in terms of this model using recent experiments on amorphous Al88Y7Fe5.     

Structural study of new hydrocarbon nano-crystals by energy-filtered electron diffraction

A new brittle hydrocarbon has been successfully synthesized in polycrystalline form, and its crystal structure solved by quantitative electron diffraction. By 3D tilting of the nano-crystals, the lattice type and unit cell parameters were determined. (Triclinic, [Formula: see text] A, [Formula: see text] A, [Formula: see text] A, [Formula: see text] degrees, [Formula: see text] degrees, and [Formula: see text] degrees.) Spot diffraction patterns were obtained at -165 degrees C using the Koehler selected-area mode on a LEO 912 TEM fitted with an omega in-column elastic energy filter. The direct methods algorithm was then applied to merged intensities and a trial structure obtained assuming single scattering. This was further refined to obtain good agreement with a small residual of about 10% using multiple scattering calculations. A diagram of the proposed structure is given.     

Precession electron diffraction using a digital sampling method

A software-based method for collecting precession electron diffraction (PED) patterns is described. The PED patterns are obtained on a computer controlled transmission electron microscope. A series of electron diffraction (ED) patterns are collected as still ED frames at equal intervals, while the electron beam is precessed by one period (360°) around the optical axis. A PED pattern is obtained by combining the different ED frames, which resembles the sampling of a conventional PED pattern. Since intermediate ED frames are collected, it is possible to perform different post-processing strategies on the ED data. This can be used for geometric corrections to obtain accurate integrated intensities. The alignments and data collection are fully automated and controlled by software. The data quality is comparable to what can be achieved using specialized hardware for precession. The PED data can be used for structure solution and refinement with reasonably good R-values.     

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.     

HANSIS software tool for the automated analysis of HOLZ lines

A software tool, named as HANSIS (HOLZ analysis), has been developed for the automated analysis of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns. With this tool, the angles and distances between the HOLZ intersections can be measured and the data can be presented graphically with a user-friendly interface. It is capable of simultaneous analysis of several HOLZ patterns and thus provides a tool for systematic studies of CBED patterns.     

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

A new software package for quantitative electron diffraction data treatment of unknown structures is described. No "a priori" information is required by the package which is able to perform in successive steps the 2-D indexing of digitised diffraction patterns, the extraction of the intensity of the collected reflections and the 3-D indexing of all recorded patterns, giving as results the lattice parameters of the investigated structure and a series of data files (one for each diffraction pattern) containing the measured intensities and the relative e.s.d.s of the 3-D indexed reflections. The software package is mainly conceived for the treatment of diffraction patterns taken with a Gatan CCD Slow-Scan Camera, but it can also deal with generic digitised plates. The program is designed to extract intensity data suitable for structure solution techniques in electron crystallography. The integration routine is optimised for a correct background evaluation, a necessary condition to deal with weak spots of irregular shape and an intensity just above the background.     

Precession electron diffraction using a digital sampling method

A software-based method for collecting precession electron diffraction (PED) patterns is described. The PED patterns are obtained on a computer controlled transmission electron microscope. A series of electron diffraction (ED) patterns are collected as still ED frames at equal intervals, while the electron beam is precessed by one period (360°) around the optical axis. A PED pattern is obtained by combining the different ED frames, which resembles the sampling of a conventional PED pattern. Since intermediate ED frames are collected, it is possible to perform different post-processing strategies on the ED data. This can be used for geometric corrections to obtain accurate integrated intensities. The alignments and data collection are fully automated and controlled by software. The data quality is comparable to what can be achieved using specialized hardware for precession. The PED data can be used for structure solution and refinement with reasonably good R-values.