Multislice image simulations of sheared needle-like precipitates in an Al-Mg-Si alloy.

The image contrast of sheared needle-like ß ' ' precipitates in the Al-Mg-Si alloy system is investigated with respect to shear-plane positions, the number of shear-planes, and the active matrix slip systems through multislice transmission electron microscopy image simulations and the frozen phonon approximation. It is found that annular dark field scanning transmission electron microscopy (ADF STEM) images are mostly affected by shear-planes within a distance ∼6-18 unit cells from the specimen surface, whereas about 5-10 equidistant shear-planes are required to produce clear differences in HRTEM images. The contrast of the images is affected by the Burgers vector of the slip, but not the slip plane. The simulation results are discussed and compared to experimental data. LAY DESCRIPTION: Pure aluminium is too soft to be viable in most structural applications, but this may be remedied by alloying the metal with various elements. Adding small amounts of silicon and magnesium to pure aluminium allows small particles to precipitate during heat treatment. These precipitates resist plastic deformation and can increase the strength of the alloy and make it viable for a range of industrial applications, such as automotive door panels and load-bearing profiles. However, if subjected to large loads, the precipitates are sheared and the strength of the alloy changes dynamically. Designing safe products such as cars or buildings require physically based predictions on this dynamical change. Developing models that can provide such predictions depend in turn on experimental observations of the shearing process. Because the precipitates are nm long, experimental observations must be done by transmission electron microscopy. However, understanding these results sometimes require computer simulations of atomic models. In this work, we have performed image simulations of various models of sheared precipitates and compared the results with earlier experiments. The simulations indicate that certain conditions must be met for the sheared precipitates to appear different from unsheared precipitates. These conditions are most likely to be met if precipitates are sheared several times in a relatively homogeneous manner. This is important for two reasons. First, a localized shearing process would lead to large dynamical changes in precipitate strength during deformation, and in turn drastically reduce the work hardening of the alloy. Secondly, a localized shearing process would have promoted earlier fracture and failure of the alloy during deformation. Finally, our results also show how different slip directions influences the images of precipitates. In the future, these influences can be used to further understand the shearing process of these precipitates. Hence, our results can be used to improve model predictions of strength, work hardening, and fracture. In turn, this may improve alloy design and reduce the use of prototype testing in, e.g. the automotive industry.

Nanocrystal segmentation in scanning precession electron diffraction data.

Scanning precession electron diffraction (SPED) enables the local crystallography of materials to be probed on the nanoscale by recording a two-dimensional precession electron diffraction (PED) pattern at every probe position as a dynamically rocking electron beam is scanned across the specimen. SPED data from nanocrystalline materials commonly contain some PED patterns in which diffraction is measured from multiple crystals. To analyse such data, it is important to perform nanocrystal segmentation to isolate both the location of each crystal and a corresponding representative diffraction signal. This also reduces data dimensionality significantly. Here, two approaches to nanocrystal segmentation are presented, the first based on virtual dark-field imaging and the second on non-negative matrix factorization. Relative merits and limitations are compared in application to SPED data obtained from partly overlapping nanoparticles, and particular challenges are highlighted associated with crystals exciting the same diffraction conditions. It is demonstrated that both strategies can be used for nanocrystal segmentation without prior knowledge of the crystal structures present, but also that segmentation artefacts can arise and must be considered carefully. The analysis workflows associated with this work are provided open-source. LAY DESCRIPTION: Scanning precession electron diffraction is an electron microscopy technique that enables studies of the local crystallography of a broad selection of materials on the nanoscale. The technique involves the acquisition of a two-dimensional diffraction pattern for every probe position in an area of the sample. The four-dimensional dataset collected by this technique can typically comprise up to 500 000 diffraction patterns. For nanocrystalline materials, it is common that single diffraction patterns contain signals from overlapping crystals. To process such data, we use nanocrystal segmentation, where a representative diffraction pattern is constructed for each individual crystal, together with a real space image showing its morphology and location in the data. This reduces the dimensionality of the data and allows unmixing of signals from overlapping crystals. In this work, we demonstrate two methods for nanocrystal segmentation, one based on creating virtual dark-field images, and one based on unsupervised machine learning. A model system of partly overlapping nanoparticles is used to demonstrate the segmentation, and a demanding case for segmentation is highlighted, where some crystals are not discernible based on their diffraction patterns. To obtain a more complete nanocrystal segmentation, we add an image segmentation routine to both methods, and we discuss benefits and limitations of the two methods. The demonstration data and the used code are provided open-source, so that it can be used by everyone for analysis of nanocrystalline materials or as a starting point for further development of nanocrystal segmentation in scanning precession electron diffraction data.

Experimental and theoretical study of electron density and structure factors in CoSb3.

We refine two low-order structure factors of the skutterudite CoSb3 using convergent beam electron diffraction. The relatively large unit cell of this material causes the disks to overlap and introduces a series of challenges in the refinement procedure. These challenges and future work-arounds are discussed. The refined structure factors F200 and F600 are compared to X-ray diffraction and density functional calculated values, the latter calculated using two different functionals. Both relaxed and experimental lattice parameters are tested to explicitly highlight the impact of the lattice geometry and atomic position on the structure factors.

A study of charge density in copper.

Quantitative convergent-beam electron diffraction (QCBED) experiments allow absolute scale measurements of low-order structure factors with very high accuracy. In this paper, eight low-order structure factors for copper measured by QCBED have been combined with the higher-order gamma-ray structure factors in order to obtain a larger highly accurate experimental data set. The gamma-ray values were relativistically corrected and rescaled. The new data set was then used for studying the charge distribution in copper. Charge deformation maps have been produced and both a maximum-entropy and a multipole analysis have been applied to the data. The result is compared to density functional theory calculations. An almost spherical charge depletion is found around the atomic sites showing typical metal bonding in copper.

Use of quantitative convergent-beam electron diffraction in materials science.

Methods for quantitative convergent-beam electron diffraction are outlined and some results of our applications of convergent-beam electron diffraction are shown, with emphasis on quantitative analysis of crystal structures in materials science. Examples of thickness measurements and determination of lattice parameters are presented. Measurements of low-order structure factors to obtain information on bonding charge-density distributions are reviewed, with examples from TiAl intermetallics. For non-centrosymmetric crystals, a method to determine three-phase structure invariants is given. Determination of polarity is also discussed.

Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method.

Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for param-eter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depend on the choice of the initial parameters in the refinement. Even unrealistic starting assumptions and incorrect temperature factor lead to stable results for the structure invariant. The examples show that the accuracy varies from 1 to 10 degrees in the electron three-phase invariants determined and from 0.5 to 5% for the amplitudes. Individual phases could not be determined in the present case owing to spatial intensity correlations between phase-sensitive pixels. However, for the three-phase structure invariant, stable solutions were found.