Character and Distribution of Geometrically Necessary Dislocations in Polycrystalline Tantalum.

Geometrically necessary dislocations (GNDs) play a key role in accommodating strain incompatibility between neighboring grains in polycrystalline materials. One critical step toward accurately capturing GNDs in deformation models involves studying the microstructural features that promote GND accumulation and the resulting character of GND fields. This study utilizes high-resolution electron backscatter diffraction to map GND populations in a large polycrystalline sample of pure tantalum, under simple tension. A total of 1,989 grains, 3,518 grain boundaries (GBs), and 3,207 triple junctions (TJs) were examined in a subsurface region of the sample. Correlations between GND density and GB character, and to some extent, TJ character, are investigated. Statistical geometrical relationships between these entities are quantified, and also visualized, using a novel application of two-point statistics. The nature of GNDs across the sample is also visualized and assessed using a recently developed method of mapping the local net Burgers vectors. The different approaches to characterizing GND distribution are compared in terms of how they quantify the size of near boundary gradient zones.

Determining Grain Boundary Position and Geometry from EBSD Data: Limits of Accuracy.

As the feature size of crystalline materials gets smaller, the ability to correctly interpret geometrical sample information from electron backscatter diffraction (EBSD) data becomes more important. This paper uses the notion of transition curves, associated with line scans across grain boundaries (GBs), to correctly account for the finite size of the excitation volume (EV) in the determination of the geometry of the boundary. Various metrics arising from the EBSD data are compared to determine the best experimental proxy for actual numbers of backscattered electrons that are tracked in a Monte Carlo simulation. Consideration of the resultant curves provides an accurate method of determining GB position (at the sample surface) and indicates a significant potential for error in determining GB position using standard EBSD software. Subsequently, simple criteria for comparing experimental and simulated transition curves are derived. Finally, it is shown that the EV is too shallow for the curves to reveal subsurface geometry of the GB (i.e., GB inclination angle) for most values of GB inclination.

Phase determination in dual phase steels via HREBSD-based tetragonality mapping.

Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (body centred cubic and body centred tetragonal, with small tetragonality) phases in steels using standard EBSD software. One method to tackle the problem of phase distinction is to measure the tetragonality of the phases, which can be done using simulated patterns and cross-correlation techniques to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both kinetically simulated and dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate ∼0.2% error in carbon content estimation. Such an error makes the technique unsuitable for estimation of total carbon content of most commercial steels, which often have carbon levels below 0.1%. However, even in the DP steel for this study (0.1 wt.% carbon) it can be used to map carbon in regions with higher accumulation (such as in martensite with nonhomogeneous carbon content). LAY DESCRIPTION: Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (BCC and BCT) phases in steels using standard EBSD software due to the small difference in crystal structure. One method to tackle the problem of phase distinction is to measure the tetragonality, or apparent 'strain' in the crystal lattice, of the phases. This can be done by comparing experimental EBSD patterns with simulated patterns via cross-correlation techniques, to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both simple kinetically simulated and more complex dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate error in carbon content estimation. Such an error makes an estimate of total carbon content particularly unsuitable for low carbon steels; although maps of local carbon content may still be revealing. Application of the method developed in this paper will lead to better understanding of the complex microstructures of steels, and the potential to design microstructures that deliver higher strength and ductility for common applications, such as vehicle components.

Digital Image Correlation of Forescatter Detector Images for Simultaneous Strain and Orientation Mapping.

Improved plasticity models require simultaneous experimental local strain and microstructural evolution data. Microscopy tools, such as electron backscatter diffraction (EBSD), that can monitor transformation at the relevant length-scale, are often incompatible with digital image correlation (DIC) techniques required to determine local deformation. In this paper, the viability of forescatter detector (FSD) images as the basis for the DIC study is investigated. Standard FSD and an integrated EBSD/FSD approach (Pattern Region of Interest Analysis System: PRIAS™) are analyzed. Simultaneous strain and microstructure maps are obtained for tensile deformation of Q&P 1180 steel up to ~14% strain. Tests on an undeformed sample that is simply shifted indicate a standard deviation of error in strain of around 0.4% without additional complications from a deformed surface. The method resolves strain bands at ~2 µm spacing but does not provide significant sub-grain strain resolution. Similar resolution was obtained for mechanically polished and electropolished samples, despite electropolished surfaces presenting a smoother, simpler topography. While the resolution of the PRIAS approach depends upon the EBSD step size, the 80 nm step size used provides seemingly similar resolution as 8,000× (22.7 nm) FSD images. Surface feature evolution prevents DIC analysis across large strain steps (>6% strain), but restarting DIC, using an FSD reference image from an interim strain step, allows reasonable DIC across the stress­strain curve. Furthermore, the data are obtained easily and provide complementary information for EBSD analysis.

Influence of Noise-Generating Factors on Cross-Correlation Electron Backscatter Diffraction (EBSD) Measurement of Geometrically Necessary Dislocations (GNDs).

Studies of dislocation density evolution are fundamental to improved understanding in various areas of deformation mechanics. Recent advances in cross-correlation techniques, applied to electron backscatter diffraction (EBSD) data have particularly shed light on geometrically necessary dislocation (GND) behavior. However, the framework is relatively computationally expensive-patterns are typically saved from the EBSD scan and analyzed offline. A better understanding of the impact of EBSD pattern degradation, such as binning, compression, and various forms of noise, is vital to enable optimization of rapid and low-cost GND analysis. This paper tackles the problem by setting up a set of simulated patterns that mimic real patterns corresponding to a known GND field. The patterns are subsequently degraded in terms of resolution and noise, and the GND densities calculated from the degraded patterns using cross-correlation ESBD are compared with the known values. Some confirmation of validity of the computational degradation of patterns by considering real pattern degradation is also undertaken. The results demonstrate that the EBSD technique is not particularly sensitive to lower levels of binning and image compression, but the precision is sensitive to Poisson-type noise. Some insight is also gained concerning effects of mixed patterns at a grain boundary on measured GND content.

Performance of Dynamically Simulated Reference Patterns for Cross-Correlation Electron Backscatter Diffraction.

High-resolution (or "cross-correlation") electron backscatter diffraction analysis (HR-EBSD) utilizes cross-correlation techniques to determine relative orientation and distortion of an experimental electron backscatter diffraction pattern with respect to a reference pattern. The integrity of absolute strain and tetragonality measurements of a standard Si/SiGe material have previously been analyzed using reference patterns produced by kinematical simulation. Although the results were promising, the noise levels were significantly higher for kinematically produced patterns, compared with real patterns taken from the Si region of the sample. This paper applies HR-EBSD techniques to analyze lattice distortion in an Si/SiGe sample, using recently developed dynamically simulated patterns. The results are compared with those from experimental and kinematically simulated patterns. Dynamical patterns provide significantly more precision than kinematical patterns. Dynamical patterns also provide better estimates of tetragonality at low levels of distortion relative to the reference pattern; kinematical patterns can perform better at large values of relative tetragonality due to the ability to rapidly generate patterns relating to a distorted lattice. A library of dynamically generated patterns with different lattice parameters might be used to achieve a similar advantage. The convergence of the cross-correlation approach is also assessed for the different reference pattern types.

Computationally efficient barycentric interpolation of large grain boundary octonion point sets.

We present a method for performing efficient barycentric interpolation for large grain boundary octonion point sets which reside on the surface of a hypersphere. This method includes removal of degenerate dimensions via singular value decomposition (SVD) transformations and linear projections, determination of intersecting facets via nearest neighbor (NN) searches, and interpolation. This method is useful for hyperspherical point sets for applications such as grain boundaries structure-property models, robotics, and specialized neural networks. We provide a case study of the method applied to the 7-sphere. We provide 1-sphere and 2-sphere visualizations to illustrate important aspects of these dimension reduction and interpolation methods. A MATLAB implementation is available at github.com/sgbaird-5dof/interp.•Barycentric interpolation is combined with hypersphere facet intersections, dimensionality reduction, and linear projections to reduce computational complexity without loss of information•A max nearest neighbor threshold is used in conjunction with facet intersection determination to reduce computational runtime.

Aluminum alloy compositions and properties extracted from a corpus of scientific manuscripts and US patents.

Researchers continue to explore and develop aluminum alloys with new compositions and improved performance characteristics. An understanding of the current design space can help accelerate the discovery of new alloys. We present two datasets: 1) chemical composition, and 2) mechanical properties for predominantly wrought aluminum alloys. The first dataset contains 14,884 entries on aluminum alloy compositions extracted from academic literature and US patents using text processing techniques, including 550 wrought aluminum alloys which are already registered with the Aluminum Association. The second dataset contains 1,278 entries on mechanical properties for aluminum alloys, where each entry is associated with a particular wrought series designation, extracted from tables in academic literature.

Simulation of kinematic Kikuchi diffraction patterns from atomistic structures.

One of the limitations of atomistic simulations is that many of the computational tools used to extract structural information from atomic trajectories provide metrics that are not directly compatible with experiments for validation. In this work, to bridge between simulation and experiment, a method is presented to produce simulated Kikuchi diffraction patterns using data from atomistic simulations, without requiring a priori specification of the crystal structure or defect periodicity. The Kikuchi pattern simulation is based on the kinematic theory of diffraction, with Kikuchi line intensities computed via a discrete structure factor calculation. Reciprocal lattice points are mapped to Kikuchi lines using a geometric projection of the reciprocal space data. This method is validated using single crystal atomistic models, and the novelty of this approach is emphasized by simulating kinematic Kikuchi diffraction patterns from an atomistic model containing a nanoscale dislocation loop. Deviations in kinematic Kikuchi line intensities are explained considering the displacement field of the dislocation loop, as is done in diffraction contrast theory.

Improved twin detection via tracking of individual Kikuchi band intensity of EBSD patterns.

Twin detection via EBSD can be particularly challenging due to the fine scale of certain twin types - for example, compression and double twins in Mg. Even when a grid of sufficient resolution is chosen to ensure scan points within the twins, the interaction volume of the electron beam often encapsulates a region that contains both the parent grain and the twin, confusing the twin identification process. The degradation of the EBSD pattern results in a lower image quality metric, which has long been used to imply potential twins. However, not all bands within the pattern are degraded equally. This paper exploits the fact that parent and twin lattices share common planes that lead to the quality of the associated bands not degrading; i.e. common planes that exist in both grains lead to bands of consistent intensity for scan points adjacent to twin boundaries. Hence, twin boundaries in a microstructure can be recognized, even when they are associated with thin twins. Proof of concept was performed on known twins in Inconel 600, Tantalum, and Magnesium AZ31. This method was then used to search for undetected twins in a Mg AZ31 structure, revealing nearly double the number of twins compared with those initially detected by standard procedures.

Grain Boundary Plane Orientation Fundamental Zones and Structure-Property Relationships.

Grain boundary plane orientation is a profoundly important determinant of character in polycrystalline materials that is not well understood. This work demonstrates how boundary plane orientation fundamental zones, which capture the natural crystallographic symmetries of a grain boundary, can be used to establish structure-property relationships. Using the fundamental zone representation, trends in computed energy, excess volume at the grain boundary, and temperature-dependent mobility naturally emerge and show a strong dependence on the boundary plane orientation. Analysis of common misorientation axes even suggests broader trends of grain boundary energy as a function of misorientation angle and plane orientation. Due to the strong structure-property relationships that naturally emerge from this work, boundary plane fundamental zones are expected to simplify analysis of both computational and experimental data. This standardized representation has the potential to significantly accelerate research in the topologically complex and vast five-dimensional phase space of grain boundaries.