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

Improved Method for Electron Powder Diffraction-Based Rietveld Analysis of Nanomaterials

Multiphase nanomaterials are of increasing importance in material science. Providing reliable and statistically meaningful information on their average nanostructure is essential for synthesis control and applications. In this paper, we propose a novel procedure that simplifies and makes more effective the electron powder diffraction-based Rietveld analysis of nanomaterials. Our single step in-TEM method allows to obtain the instrumental broadening function of the TEM directly from a single measurement without the need for an additional X-ray diffraction measurement. Using a multilayer graphene calibration standard and applying properly controlled acquisition conditions on a spherical aberration-corrected microscope, we achieved the instrumental broadening of ±0.01 Å in terms of interplanar spacing. The shape of the diffraction peaks is modeled as a function of the scattering angle using the Caglioti relation, and the obtained parameters for instrumental broadening can be directly applied in the Rietveld analysis of electron diffraction data of the analyzed specimen. During peak shape analysis, the instrumental broadening parameters of the TEM are controlled separately from nanostructure-related peak broadening effects, which contribute to the higher reliability of nanostructure information extracted from electron diffraction patterns. The potential of the proposed procedure is demonstrated through the Rietveld analysis of hematite nanopowder and two-component Cu-Ni nanocrystalline thin film specimens.

Acquisition and evaluation procedure to improve the accuracy of SAED

The achievement of this work is that fine tuning of experimental and evaluation parameters can improve the absolute accuracy and reproducibility of selected area electron diffraction (SAED) to 0.1% without using internal standard. Due to the proposed procedure it was possible to reach a reproducibility better than 0.03% for camera length between sessions by careful control of specimen height and illumination conditions by monitoring lens currents. We applied a calibration specimen composed of nanocrystalline grains free of texture and providing narrow diffraction rings. Refinements of the centre of the diffraction pattern and corrections for elliptic ring distortions allowed for determining the ring diameters with an accuracy of 0.1%. We analyze the effect of different error sources and reason the achieved absolute accuracy of the measurement. Application of the proposed evaluation procedure is inevitable in case of multicomponent nanocomposites or textured materials and/or having close diffraction rings where application of automated procedures is limited. The achieved accuracy of 0.1% without internal standard is approaching that of routine laboratory XRD, and reduction of instrumental broadening due to the elaborated evaluation procedure allows for separation of close reflections, provides more reliable ring width and thus improved input parameters for further nanostructure analysis as demonstrated on dental enamel bioapatite.

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.

Determination and correction of distortions and systematic errors in low-energy electron diffraction

We developed and implemented an algorithm to determine and correct systematic distortions in low-energy electron diffraction (LEED) images. The procedure is in principle independent of the design of the apparatus (spherical or planar phosphorescent screen vs. channeltron detector) and is therefore applicable to all device variants, known as conventional LEED, micro-channel plate LEED, and spot profile analysis LEED. The essential prerequisite is a calibration image of a sample with a well-known structure and a suitably high number of diffraction spots, e.g., a Si(111)-7×7 reconstructed surface. The algorithm provides a formalism which can be used to rectify all further measurements generated with the same device. In detail, one needs to distinguish between radial and asymmetric distortion. Additionally, it is necessary to know the primary energy of the electrons precisely to derive accurate lattice constants. Often, there will be a deviation between the true kinetic energy and the value set in the LEED control. Here, we introduce a method to determine this energy error more accurately than in previous studies. Following the correction of the systematic errors, a relative accuracy of better than 1% can be achieved for the determination of the lattice parameters of unknown samples.