Precession electron diffraction using a digital sampling method

Modelling fine-sliced three dimensional electron diffraction data with dynamical Bloch-wave simulations

Recent interest in structure solution and refinement using electron diffraction (ED) has been fuelled by its inherent advantages when applied to crystals of sub-micrometre size, as well as its better sensitivity to light elements. Currently, data are often processed with software written for X-ray diffraction, using the kinematic theory of diffraction to generate model intensities - despite the inherent differences in diffraction processes in ED. Here, dynamical Bloch-wave simulations are used to model continuous-rotation electron diffraction data, collected with a fine angular resolution (crystal orientations of ∼0.1°). This fine-sliced data allows a re-examination of the corrections applied to ED data. A new method is proposed for optimizing crystal orientation, and the angular range of the incident beam and the varying slew rate are taken into account. Observed integrated intensities are extracted and accurate comparisons are performed with simulations using rocking curves for a (110) lamella of silicon 185 nm thick. R₁ is reduced from 26% with the kinematic model to 6.8% using dynamical simulations.

Aluminosilicate Zeolite EMM-28 Containing Supercavities Determined by Continuous Rotation Electron Diffraction

A new aluminosilicate zeolite, denoted EMM-28, has been successfully synthesized on a large scale using 1,1-(3,3-(1,3-phenylene)bis(propane-3,1-diyl))bis(1-methylpyrrolidinium) hydroxide as an organic structure directing agent (OSDA), which was scaled up to an ∼20 g scale with a yield of 77%. It crystallizes as thin plates (40–100 nm in thickness), and the corresponding powder X-ray diffraction (PXRD) pattern shows significant peak broadening which makes it insufficient for structure determination. Continuous rotation electron diffraction (cRED) data collected from 13 crystals were successfully used to solve and refine the structure of EMM-28. This illustrates that cRED data are capable of performing structure determination despite limited PXRD data quality. EMM-28 has a unique framework structure containing supercavities, >21 Å in size, connected by one-dimensional 10-ring channels. High-resolution transmission electron microscopy (HRTEM) confirmed the structure model. The structure of EMM-28 is related to several known zeolite structures with large cavities.

The properties of zeolites are largely determined by their atomically well-defined microporous structures of molecular dimensions. The new aluminosilicate zeolite, EMM-28, has a unique framework structure containing large supercavities connected by one-dimensional channels limited by 10 SiO₄/AlO₄ tetrahedra. The atomic structure of EMM-28 was determined using continuous rotation electron diffraction (cRED) data collected from 13 crystals. Despite limited powder X-ray diffraction data quality, the structure could be successfully refined using cRED data.

Quantitative order-parameter measurement in lattice-mismatched AlInP using precession electron diffraction

Precession electron diffraction (PED) was used to measure the long-range order parameter in lattice-mismatched AlInP epitaxial films under investigation for solid-state-lighting applications. Both double- and single-variant films grown at 620, 650 and 680 °C were analysed in TEM cross-section. PED patterns were acquired in selected-area-diffraction mode through external microscope control using serial acquisition, which allows inline image processing. The integrated peak intensities from experimental patterns were fit using dynamical simulations of diffraction from the ordered domain structures. Included in the structure-factor calculations were mean atomic displacements of the anions (P) due to ordering, which were found by valence-force-field calculations to have a nearly linear dependence on order parameter. A maximum order parameter of S = 0.36 was measured for a double-variant specimen grown at 650 °C.

Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns

New software and algorithms for the accurate measurement of crystal lattice parameters from Kikuchi bands in a diffraction pattern are presented.

A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 × 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.

Serial electron crystallography for structure determination and phase analysis of nanocrystalline materials

Serial electron crystallography has been developed as a fully automated method to collect diffraction data on polycrystalline materials using a transmission electron microscope. This enables useful data to be collected on materials that are sensitive to the electron beam and thus difficult to measure using the conventional methods that require long exposure of the same crystal. The data collection strategy combines goniometer translation with electron beam shift, which allows the entire sample stage to be probed. At each position of the goniometer, the locations of the crystals are identified using image recognition techniques. Diffraction data are then collected on each crystal using a quasi-parallel focused beam with a predefined size (usually 300-500 nm). It is shown that with a fast and sensitive Timepix hybrid pixel area detector it is possible to collect diffraction data of up to 3500 crystals per hour. These data can be indexed using a brute-force forward-projection algorithm. Results from several test samples show that 100-200 frames are enough for structure determination using direct methods or dual-space methods. The large number of crystals examined enables quantitative phase analysis and automatic screening of materials for known and unknown phases.

On the alignment for precession electron diffraction

Precession electron diffraction has seen a fast increase in its adoption as a technique for solving crystallographic structures as well as an alternative to conventional selected-area and converged-beam diffraction methods. One of the key issues of precession is the pivot point alignment, as a stationary apparent beam does not guarantee a fixed pivot point. A large precession tilt angle, along with pre-field and post-field misalignment, induces shift in the image plane. We point out here that the beam should be aligned to the pre-field optic axis to keep the electron illumination stationary during the rocking process. A practical alignment procedure is suggested with the focus placed on minimizing the beam wandering on the specimen, and is demonstrated for a (110)-oriented silicon single crystal and for a carbide phase (∼20nm in size) within a cast cobalt-chromium-molybdenum alloy.

Aberration-compensated large-angle rocking-beam electron diffraction

The application of convergent beam electron diffraction (CBED) to determine symmetry, refine structure factors, and measure specimen thickness requires rather thick specimen and is very difficult or even impossible in the case of large unit cell materials. The large-angle rocking-beam electron diffraction (LARBED) technique introduced in this paper gives access to the kind of experimental data contained in CBED patterns but over a much larger angular range. In addition to symmetry determination and thickness measurement even for thin samples this technique also allows, in principle, very accurate measurements of structure factors. Similar to precession electron diffraction (PED), LARBED uses the illumination tilt coils to sequentially change the angle of incidence of the electron beam over a very large range. I will present results obtained by a recently developed self-calibrating acquisition software which compensates for aberration-induced probe shifts during the acquisition of LARBED patterns and keeps the probe within a few nm, while covering a tilt range from 0 to 100 mrad. This paper is dedicated to Prof. John C. H. Spence on the occasion of his 65th birthday.