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 new approach to structure amplitude determination from 3-beam convergent beam electron diffraction patterns

The intensity distribution in three-beam CBED patterns from centrosymmetric crystals can be inverted analytically to enable the direct measurement of crystal structure amplitudes and three-phase invariants. The accuracy of the measurements depends upon the accuracy and precision with which specific loci within the discs can be identified. The present work exploits the equivalence in form of the intensity distribution along these loci to provide an algorithm for their automated location, enabling the rapid and unequivocal identification of their position. Moreover, it demonstrates how the loci can be used to determine directly the relative magnitudes of structure amplitudes with superior accuracy and without recourse to complex pattern-matching calculations.     

Crystal structure solution via precession electron diffraction data: the BEA algorithm

The statistical features of the amplitudes obtained via precession electron diffraction have been studied, with particular concern with their effects on direct phasing procedures. A new algorithm, denoted by BEA, is described: according to it, the average amplitude of the symmetry equivalent reflections is used in the Direct Methods step. Once an even imperfect structural model is available, the best amplitude among the equivalent reflections is used to improve the model. It is shown that BEA is able to provide more complete structural models, to make the phasing process more straightforward and to end with crystallographic residual much better than those usually obtained by electron diffraction.     

Crystal structure solution via precession electron diffraction data: The BEA algorithm

The statistical features of the amplitudes obtained via precession electron diffraction have been studied, with particular concern with their effects on direct phasing procedures. A new algorithm, denoted by BEA, is described: according to it, the average amplitude of the symmetry equivalent reflections is used in the Direct Methods step. Once an even imperfect structural model is available, the best amplitude among the equivalent reflections is used to improve the model. It is shown that BEA is able to provide more complete structural models, to make the phasing process more straightforward and to end with crystallographic residual much better than those usually obtained by electron diffraction.     

“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.     

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.     

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.     

Observations on the real space computation of dynamical electron diffraction intensities

The computational procedures and theoretical approximations used in the real space approach to dynamical electron diffraction calculations are discussed. Although the method is theoretically sound it is found to be unsuitable for rapid and accurate computation of electron wavefunctions.     

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 method to determine long-range order parameters from electron diffraction intensities detected by a CCD camera

To determine long-range order parameters from electron diffraction intensities, the authors have developed a CCD camera system to detect precisely electron diffraction intensities, a method for quickly and precisely measuring specimen thickness, and a computer programming to calculate long-range order parameters from the ratio of superlattice and fundamental diffraction intensities. Thickness variation over a diffraction area is taken into consideration in the calculation of electron diffraction intensities on the basis of the multi-slice method, and long-range order parameters are calculated by the successive approximation method. The absorptive form factors are also calculated from experimental data of diffraction intensities by parameter fitting, and the effect of absorption on the calculation of long-range order parameters is examined. The values of Cu(3)Au alloys aged at 523 and 653 K that were obtained by averaging long-range order parameters determined for several diffraction areas with the developed method are close to the reported data obtained by the X-ray diffraction method. The main causes for the deviation of long-range order parameters determined for several diffraction areas are also discussed.     

Rapid structure determination of a metal oxide from pseudo-kinematical electron diffraction data

The electron precession diffraction technique is employed to provide quasi-kinematical data for determination of atom positions in the (Ga,In)2SnO5m-phase. Precession data are compared with conventional diffraction data captured under identical conditions and show a distinct superiority because they exhibit kinematical characteristics in the structure-defining reflections. Precessed data are not usable within a kinematical interpretation in all cases, and a simple basis is presented for omission of errant reflections to improve adherence to kinematical behavior. A second approach is demonstrated where intensities are used with direct methods instead of amplitudes, enhancing the contrast between strong and weak beams. The unrefined atom positions recovered a priori via direct methods are consistent between the two approaches and fall on average within 4 picometers of positions in the previously refined structure.     

The relative intensities of electron diffraction maxima in mixed rare-earth oxides

The relative intensities of electron diffraction maxima from yttrium aluminium perovskite were analysed in terms of the atomic scattering contribution to the structure factors and in terms of double diffraction. It has been shown that double diffraction influences the visible intensity between diffraction spots in electron diffraction patterns to a greater extent than does the magnitude of the structure factor. A direct consequence of this is that the intensity of diffraction maxima can increase when a specimen is tilted off an exact zone axis.     

LACDIF, a new electron diffraction technique obtained with the LACBED configuration and a C(s) corrector: comparison with electron precession

By combining the large-angle convergent-beam electron diffraction (LACBED) configuration together with a microscope equipped with a C(s) corrector it is possible to obtain good quality spot patterns in image mode and not in diffraction mode as it is usually the case. These patterns have two main advantages with respect to the conventional selected-area electron diffraction (SAED) or microdiffraction patterns. They display a much larger number of reflections and the diffracted intensity is the integrated intensity. These patterns have strong similarities with the electron precession patterns and they can be used for various applications like the identification of the possible space groups of a crystal from observations of the Laue zones or the ab-initio structure identifications. Since this is a defocused method, another important application concerns the analysis of electron beam-sensitive materials. Successful applications to polymers are given in the present paper to prove the validity of this method with regards to these materials.     

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.     

An efficient approach to characterize pseudo-merohedral twins by precession electron diffraction: Application to the LaGaO3 perovskite

Pseudo-merohedral twins are frequently observed in crystals displaying pseudo-symmetry. In these crystals, many [u v w] zone axis electron diffraction patterns are very close and can only be distinguished from intensity considerations. On conventional diffraction patterns (selected-area electron diffraction or microdiffraction), a strong dynamical behaviour averages the diffracted intensities so that only the positions of the reflections on a pattern can be considered. On precession electron diffraction patterns, the diffracted beams display an integrated intensity and a “few-beam” or “systematic row” behaviour prevails which strongly reduces the dynamical interactions. Therefore the diffracted intensity can be taken into account. A procedure based on observation of the weak extra-reflections connected with the pseudo-symmetry is given to identify without ambiguity any zone axis. It is successfully applied to the identification and characterization of {1 2 1} reflection twins present in the LaGaO₃ perovskite.     

The characterization of periodic dislocation arrays from the fine structure of electron diffraction patterns

The accuracy of the technique of using the fine-structure observed in electron diffraction patterns to determine the periodicity and characteristic direction associated with a periodic strain field is assessed. This is done by applying the technique to dislocation multipoles which have a strain field with only a single periodic component and which can be well characterized by other means. It is shown that, for such a single-component strain field, precision measurement of the diffraction patterns combined with numerical analysis of the data allows the determination of the direction and spacing characterizing the strain field with an accuracy of about 0.25° to 1.0° in direction (depending upon periodicity) and ± 2% in spacing. This is better than can usually be achieved from measurements of corresponding features in the electron micrographs.     

Contribution of electron precession to the identification of the space group from microdiffraction patterns

In a previous study, it was reported that the possible space groups of a crystal can be identified at a microscopic or nanoscopic scale, thanks to microdiffraction patterns obtained with a nearly parallel electron incident beam focused on a very small area of the specimen. A systematic method was proposed, which consists of the observation of a few microdiffraction patterns displaying at least two Laue zones. These microdiffraction patterns can also be obtained by using an electron precession equipment. In this case, the patterns display a very large number of reflections in the Laue zones whose intensity is the integrated intensity. These original features greatly facilitate the space group identification method and are particularly useful when the high-order Laue zones (HOLZ) are not visible on microdiffraction patterns or when very thin specimens are not available.     

Local structure studies of Fe-Nb-B metallic glasses using electron diffraction

Local atomic structures in Fe₈₄Nb₇B₉ and Fe₇₀Nb₁₀B₂₀ amorphous alloys were examined by means of electron diffraction with the help of computer calculation. Electron diffraction patterns were taken by using energy‐filtered transmission electron microscopy (TEM) to eliminate inelastic scattering. We constructed structure models with 5000 atoms fitting to experimental interference functions. Voronoi polyhedral analyses were performed for the obtained final structure models. Local atomic structures of the alloys were closely related to those of the crystalline phases that appeared on annealing. A difference of stability of two amorphous phases was discussed on the basis of structure models.     

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.     

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.