Ab initio determination of heavy oxide perovskite related structures from precession electron diffraction data

Two complex perovskite-related structures were solved by ab initio from precession electron diffraction intensities. Structure models were firstly derived from HREM images and than have been confirmed independently using two and three-dimensional sets of precession intensities. Patterson techniques prove to be effective for ab initio structure resolution, specially in case of projections with no overlapping atoms. Quality of precession intensity data may be suitable enough to resolve unknown heavy oxide structures.     

“Ab initio” structure solution from electron diffraction data obtained by a combination of automated diffraction tomography and precession technique

Using a combination of our recently developed automated diffraction tomography (ADT) module with precession electron technique (PED), quasi-kinematical 3D diffraction data sets of an inorganic salt (BaSO₄) were collected. The lattice cell parameters and their orientation within the data sets were found automatically. The extracted intensities were used for “ab initio” structure analysis by direct methods. The data set covered almost the complete set of possible symmetrically equivalent reflections for an orthorhombic structure. The structure solution in one step delivered all heavy (Ba, S) as well as light atoms (O). Results of the structure solution using direct methods, charge flipping and maximum entropy algorithms as well as structure refinement for three different 3D electron diffraction data sets were presented.     

Is precession electron diffraction kinematical? Part II: A practical method to determine the optimum precession angle

A series of experiments was undertaken to investigate the kinematical nature of precession electron diffraction data and to gauge the optimum precession angle for a particular system. Kinematically forbidden reflections in silicon were used to show how a large precession angle is needed to minimise multi-beam conditions for specific reflections and so reduce the contribution from dynamical diffraction. Small precession angles were shown to be detrimental to the kinematical nature of some low-order reflections. By varying precession angles, precession electron diffraction data for erbium pyrogermanate were used to investigate the effect of dynamical diffraction on the output from structure solution algorithms. A good correlation was noted between the precession angle at which the rate of change of relative intensities is small and the angle at which the recovered structure factor phases matched the theoretical kinematical structure factor phases.     

Ab initio determination of the framework structure of the heavy-metal oxide Cs(x)Nb2.54W2.46O14 from 100 kV precession electron diffraction data

The present work deals with the ab initio determination of the heavy metal framework in Cs(x)(Nb, W)(5)O(14) from precession electron diffraction intensities. The target structure was first discovered by Lundberg and Sundberg [Ultramicroscopy 52 (1993) 429-435], who succeeded in deriving a tentative structural model from high-resolution electron microsopy (HREM) images. The metal framework of the compound was solved in this investigation via direct methods from hk0 precession electron diffraction intensities recorded with a Philips EM400 at 100 kV. A subsequent (kinematical) least-squares refinement with electron intensities yielded slightly improved co-ordinates for the 11 heavy atoms in the structure. Chemical analysis of several crystallites by EDX is in agreement with the formula Cs(0.44)Nb(2.54)W(2.46)O(14). Moreover, the structure was independently determined by Rietveld refinement from X-ray powder data obtained from a multi-phasic sample. The compound crystallises in the orthorhombic space group Pbam with refined lattice parameters a=27.145(2), b=21.603(2), and c=3.9463(3)A. Comparison of the framework structure from electron diffraction with the result from Rietveld refinement shows an average agreement for the heavy atoms within 0.09 A.     

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.     

Crystal structure refinement using Bloch-wave method for precession electron diffraction

Procedure for crystal structure refinement using precession electron diffraction data and Bloch-wave method for accounting multibeam scattering is described. Refinement procedure takes into account features of precession geometry. Refining model consists of structural and reduced parameters determining dynamic diffraction. Difference between measured and calculated dynamic intensities of reflections is minimized with application of a nonlinear least squares method. As test example we used Si single nanocrystals. The influence of the reduced parameters on the quality of the obtained model is discussed. Refinement procedure is a part of ASTRA software.     

A quantitative analysis of the cone-angle dependence in precession electron diffraction

Precession electron diffraction (PED) is a technique which is gaining increasing interest due to its ease of use and reduction of the dynamical scattering problem in electron diffraction. To further investigate the usefulness of this technique, we have performed a systematic study of the effect of precession angle on the mineral andalusite where the semiangle was varied from 6.5 to 32 mrad in five discrete steps. The purpose of this study was to determine the optimal conditions for the amelioration of kinematically forbidden reflections, and the measurement of valence charge density. We show that the intensities of kinematically forbidden reflections decay exponentially as the precession semiangle () is increased. We have also determined that charge density effects are best observed at moderately low angles (6.5–13 mrad) even though PED patterns become more kinematical in nature as the precession angle is increased further.     

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.     

Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images

In this paper, we discuss the application of the maximum entropy method to atomic resolution Z -contrast images acquired in a scanning transmission electron microscope. Z -contrast is an incoherent imaging technique, and can be described as a convolution between an object function (the real-space map of the columnar scattering cross-section to high angles) and a point spread function (the effective electron probe). As such, we show that the technique is ideally suited to maximum entropy analysis which can, given an electron probe distribution, retrieve the 'most likely' Z -contrast object function. Using both simulated and experimentally acquired data, we explore the capabilities of maximum entropy analysis when applied to atomic resolution Z -contrast images, drawing conclusions on both the range of applicability of the technique and the nature of the retrieved crystal structures. Ultimately, we show the way in which the combination of Z -contrast imaging with maximum entropy analysis can be used to yield important information on unexpected atomic structures.     

Characterization of dual-periodic structures with optical scattering

Laser scattering method as a non-contact method provides an opportunity to real-time monitor the evolution of periodic nanostructures during fabrication, e.g. when the surface is irradiated with a focused ion beam. Using the method, the diffraction angle needs calibrating according to the grating equation. In this paper, we used scalar analysis to demonstrate the use of a dual-period structure for formation of dual spectral peaks at the 1st diffraction order. We then made use of numerical study based on rigorous coupled-wave analysis to optimize these Al-grating structures in terms of depth. It is found that dual-peak wavelengths can be selected by using different angles of incidence and low-loss reflection is obtained using an optimized structure. It is further proposed that these wavelengths can be used to determine the diffraction angle during fabrication without the need for pre-calibration of an optical scattering system.     

Refinements in the collection of energy filtered diffraction patterns from disordered materials

In this paper a method for collecting electron diffraction patterns using a Gatan imaging filter is presented. The method enables high-quality diffraction data to be measured at scattering angles comparable to those that can be obtained using X-ray and neutron diffraction. In addition, the method offers the capability for examining small regions of sample in, for example, thin films and nano-structures. Using X-ray, neutron and electron diffraction data collected from the same sample, we demonstrate quantitative agreement between all three. We also present a novel method for obtaining the single scattering contribution to the total diffracted intensity by collecting data at various electron wavelengths. This approach allows pair distribution functions to be determined from electron diffraction in cases where there exists significant multiple scattering.     

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.     

Electron crystallography of organic materials

The application of electron crystallography to the study of organic materials is reviewed, mainly in context of the author's own experience. Direct methods for crystallographic phase determination have been shown to be very effective for ab initio structure analyses with electron diffraction intensities, permitting the elucidation of previously uncharacterized crystal structures. Fruitful applications areas have included chain-folded linear polymers, pigments, polydisperse linear chain arrays and, surprisingly, the subgroup assembly of certain proteins.     

Structure analysis of embedded nano-sized particles by precession electron diffraction. eta'-precipitate in an Al-Zn-Mg alloy as example

The Vincent-Midgley precession technique has been used to collect three-dimensional electron diffraction intensity data from a dispersion of coherent precipitates in a matrix. In order to suppress severe effects from multiple diffraction via matrix reflections, a fairly large precession (tilt) angle had to be used. This implied a high background from the surrounding matrix, and limited the number of reflections that could be measured from patterns on image plates. The heavily faulted hexagonal eta'-precipitates (a = 0.496 nm, c = 1.405 nm) with thickness 3-5 nm occur in four equivalent orientations relative to the aluminium matrix; with frequent overlap of reflections. A model of the average structure in the space group P6(3)/mmc with assumed composition Mg(2)Zn(5-x)Al(2+x), have been derived by Patterson analysis and intensity comparisons.     

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.     

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.     

Is precession electron diffraction kinematical? Part I:: "Phase-scrambling" multislice simulations

Results from multislice simulations are presented which demonstrate that diffracted intensities obtained using precession electron diffraction are less sensitive to the phases of structure factors compared to electron diffraction intensities recorded without precession. Since kinematical diffraction intensities depend only on the moduli of the structure factors, this result supports previous research indicating that the application of precession leads to electron diffraction intensities becoming more kinematical in nature.