Søren Schmidt

Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders

A fast and non-destructive method for generating three-dimensional maps of the grain boundaries in undeformed polycrystals is presented. The method relies on tracking of micro-focused high-energy X-rays. It is verified by comparing an electron microscopy map of the orientations on the 2.5 × 2.5 mm surface of an aluminium polycrystal with tracking data produced at the 3DXRD microscope at the European Synchrotron Radiation Facility. The average difference in grain boundary position between the two techniques is 26 µm, comparable with the spatial resolution of the 3DXRD microscope. As another extension of the tracking concept, algorithms for determining the stress state of the individual grains are derived. As a case study, 3DXRD results are presented for the tensile deformation of a copper specimen. The strain tensor for one embedded grain is determined as a function of load. The accuracy on the strain is Δ∊ ≃ 10−4.

Determining grain resolved stresses in polycrystalline materials using three‐dimensional X‐ray diffraction

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5 in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

X-ray microscopy in four dimensions

Three-dimensional X-ray diffraction (3DXRD) microscopy offers the possibility of time-resolved mapping of structures down to the micrometer scale 1 , 2 , 3 , 4 , 5 , 6 , i.e. four-dimensional studies. In this review, the principles of the 3DXRD microscope are described and various examples of its applications are presented.

Three-Dimensional Orientation Mapping in the Transmission Electron Microscope

Electron microscopy is used to nondestructively map the three-dimensional grain orientations in nanocrystalline aluminum. Over the past decade, efforts have been made to develop nondestructive techniques for three-dimensional (3D) grain-orientation mapping in crystalline materials. 3D x-ray diffraction microscopy and differential-aperture x-ray microscopy can now be used to generate 3D orientation maps with a spatial resolution of 200 nanometers (nm). We describe here a nondestructive technique that enables 3D orientation mapping in the transmission electron microscope of mono- and multiphase nanocrystalline materials with a spatial resolution reaching 1 nm. We demonstrate the technique by an experimental study of a nanocrystalline aluminum sample and use simulations to validate the principles involved.

GrainSpotter: a fast and robust polycrystalline indexing algorithm

A new approach for indexing multigrain diffraction data is presented. It is based on the use of a monochromatic beam simultaneously illuminating all grains. By operating in sub-volumes of Rodrigues space, a powerful vertex-finding algorithm can be applied, with a running time that is compatible with online analysis. The resulting program, GrainSpotter, is sufficiently fast to enable online analysis during synchrotron sessions. The program applies outlier rejection schemes, leading to more robust and accurate data. By simulations it is shown that several thousand grains can be retrieved. A new method to derive partial symmetries, called pseudo-twins, is introduced. Uniquely, GrainSpotter includes an analysis of pseudo-twins, which is shown to be critical to avoid erroneous grains resulting from the indexing.

Dark-field X-ray microscopy for multiscale structural characterization

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes. The technique, which allows ‘zooming’ in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments

This article presents the Monte Carlo simulation package McXtrace, intended for optimizing X-ray beam instrumentation and performing virtual X-ray experiments for data analysis. The system shares a structure and code base with the popular neutron simulation code McStas and is a good complement to the standard X-ray simulation software SHADOW. McXtrace is open source, licensed under the General Public License, and does not require the user to have access to any proprietary software for its operation. The structure of the software is described in detail, and various examples are given to showcase the versatility of the McXtrace procedure and outline a possible route to using Monte Carlo simulations in data analysis to gain new scientific insights. The studies performed span a range of X-ray experimental techniques: absorption tomography, powder diffraction, single-crystal diffraction and pump-and-probe experiments. Simulation studies are compared with experimental data and theoretical calculations. Furthermore, the simulation capabilities for computing coherent X-ray beam properties and a comparison with basic diffraction theory are presented.

Robust structural identification via polyhedral template matching

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as common neighbour analysis, rely on interatomic distances (or thresholds thereof) to classify atomic structure. As a consequence they are sensitive to strain and thermal displacements, and preprocessing such as quenching or temporal averaging of the atomic positions is necessary to provide reliable identifications. We propose a new method, polyhedral template matching (PTM), which classifies structures according to the topology of the local atomic environment, without any ambiguity in the classification, and with greater reliability than e.g. common neighbour analysis in the presence of thermal fluctuations. We demonstrate that the method can reliably be used to identify structures even in simulations near the melting point, and that it can identify the most common ordered alloy structures as well. In addition, the method makes it easy to identify the local lattice orientation in polycrystalline samples, and to calculate the local strain tensor. An implementation is made available under a Free and Open Source Software license.

Heterogeneous grain-scale response in ferroic polycrystals under electric field

Understanding coupling of ferroic properties over grain boundaries and within clusters of grains in polycrystalline materials is hindered due to a lack of direct experimental methods to probe the behaviour of individual grains in the bulk of a material. Here, a variant of three-dimensional X-ray diffraction (3D-XRD) is used to resolve the non-180° ferroelectric domain switching strain components of 191 grains from the bulk of a polycrystalline electro-ceramic that has undergone an electric-field-induced phase transformation. It is found that while the orientation of a given grain relative to the field direction has a significant influence on the phase and resultant domain texture, there are large deviations from the average behaviour at the grain scale. It is suggested that these deviations arise from local strain and electric field neighbourhoods being highly heterogeneous within the bulk polycrystal. Additionally, the minimisation of electrostatic potentials at the grain boundaries due to interacting ferroelectric domains must also be considered. It is found that the local grain-scale deviations average out over approximately 10–20 grains. These results provide unique insight into the grain-scale interactions of ferroic materials and will be of value for future efforts to comprehensively model these and related materials at that length-scale.

A discrete spherical x-ray transform of orientation distribution functions using bounding cubes

We investigate a cubed sphere parametrization of orientation space with the aim of constructing a discrete voxelized version of the spherical x-ray transform. For tracing the propagation of a unit great circle through the partition subsets, the frustums of the cubed sphere, a fast procedure is proposed. The circles parts in each frustum are gnomonically mapped into line segments inside the bounding cubes. The line segments constitute a convex polygon with vertexes indicating frustum exit–entry points. Thus the problem of system matrix calculation is reduced to the tracing of line segments within rectangular voxel arrays partitioning the bounding cubes. Hence algebraic reconstruction techniques can be used in a comprehensive way for orientation distribution function estimation from diffraction data.