Saransh Singh

Error analysis of the crystal orientations obtained by the dictionary approach to EBSD indexing

The efficacy of the dictionary approach to Electron Back-Scatter Diffraction (EBSD) indexing was evaluated through the analysis of the error in the retrieved crystal orientations. EBSPs simulated by the Callahan-De Graef forward model were used for this purpose. Patterns were noised, distorted, and binned prior to dictionary indexing. Patterns with a high level of noise, with optical distortions, and with a 25 × 25 pixel size, when the error in projection center was 0.7% of the pattern width and the error in specimen tilt was 0.8°, were indexed with a 0.8° mean error in orientation. The same patterns, but 60 × 60 pixel in size, were indexed by the standard 2D Hough transform based approach with almost the same orientation accuracy. Optimal detection parameters in the Hough space were obtained by minimizing the orientation error. It was shown that if the error in detector geometry can be reduced to 0.1% in projection center and 0.1° in specimen tilt, the dictionary approach can retrieve a crystal orientation with a 0.2° accuracy.

Orientation sampling for dictionary-based diffraction pattern indexing methods

A general framework for dictionary-based indexing of diffraction patterns is presented. A uniform sampling method of orientation space using the cubochoric representation is introduced and used to derive an empirical relation between the average disorientation between neighboring sampling points and the number of grid points sampled along the semi-edge of the cubochoric cube. A method to uniformly sample misorientation iso-surfaces is also presented. This method is used to show that the dot product serves as a proxy for misorientation. Furthermore, it is shown that misorientation iso-surfaces in Rodrigues space are quadractic surfaces. Finally, using the concept of Riesz energies, it is shown that the sampling method results in a near optimal covering of orientation space.

Quantitative electron backscatter diffraction (EBSD) data analyses using the dictionary indexing (DI) approach: Overcoming indexing difficulties on geological materials

Abstract Electron backscatter diffraction (EBSD) data yield plentiful information on microstructure and texture of natural as well as experimentally produced mineral and rock samples. For instance, the characterization of microstructures and textures by EBSD allows for the evaluation of phase equilibria. Furthermore, determination of the preferred orientations of crystals using EBSD yields constraints on deformation mechanisms and history of the minerals/rocks. The latter affects bulk-rock properites, for example, through the relation between lattice preferred orientation and electrical conductivity and seismic anisotropy. EBSD is also applied to advance our understanding of various phenomena such as seismic wave attenuation in the Earth deep interior and its relation to the presence of interfacial small degrees of melt fractions, or free fluid phases. In standard EBSD software solutions, the original EBSD patterns are rarely saved and indexing routines result in many artifacts, such as pseudo-symmetry or unindexed pixels at interfaces that may be misinterpreted as amorphous material, such as a melt. Here we report the first application of the dictionary indexing (DI) approach proposed by Chen et al. (2015), an alternative indexing routine, which we extended to be applicable to multiphase geologic materials. The DI method is independent of the EBSD system, and thus of the used detector/software. The DI routine generates simulated EBSD patterns for all possible crystal orientations, taking the sample composition and experimental setups into account. The resulting pattern database is called a dictionary. The experimental electron backscattering pattern (EBSP) images are indexed by comparing them to the dictionary using a dot-product algorithm. We evaluate the new DI method in comparison to standard routines and highlight advantages and disadvantages. To test and compare the DI’s reliability and performance, we apply the routine to two scientifically challenging samples: (1) A nominally anhydrous (“dry”) residual eclogite composed of garnet (cubic), clinopyroxene (monoclinic) and an amorphous melt, where the different degrees of hardness of the phases cause surface topology; and (2) a pure forsterite (olivine) polycrystalline sample produced by vacuum sintering. The acquired EBSD patterns are of low quality for the latter as a result of fast data acquisition to reduce the on-line machine time. We conclude that the new DI method is highly precise and surpasses the performance of previously available methods, while being computer time and computer memory consuming. We find that the DI method is free of pseudo-symmetry-related problems. Interpolation of data becomes obsolete and high reproducibility is obtained, which minimizes the operator impact on the final data set. The latter is often caused by applying several cleaning steps on EBSD maps with low indexing fraction. Finally, much higher scientific integrity is ensured by image collections as described above, which requires that all patterns are saved. This in turn allows later re-analyses if required. The DI routine will help to achieve more reliable information on interface properties of geological samples, including amorphous materials, and thus in the long run help to improve the accuracy of large-scale Earth mantle process models.

Three-dimensional texture visualization approaches: theoretical analysis and examples

Crystallographic textures are commonly represented in terms of Euler angle triplets and contour plots of planar sections through Euler space. In this paper, the basic theory is provided for the creation of alternative orientation representations using three-dimensional visualizations. The use of homochoric, cubochoric, Rodrigues and stereographic orientation representations is discussed, and illustrations are provided of fundamental zones for all rotational point-group symmetries. A connection is made to the more traditional Euler space representations. An extensive set of three-dimensional visualizations in both standard and anaglyph movies is available.

Dynamical scattering image simulations for two-phase γ–γ′ microstructures: A theoretical model

We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni-Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves.

EMsoft: open source software for electron diffraction/image simulations

EMsoft is an open source package for the simulation of electron diffraction patterns and images for both SEM and TEM modalities. The package has been under development since the late 1990’s and is currently available as version 3.1 from a GitHub repository [1]. The main component of the package is a source code library of functions and subroutines that cover crystallography, symmetry, electron scattering factors, geometry, rotation representations, basic image filters, defect displacement fields, reciprocal space sampling schemes, and so on. The code is mostly written in fortran-90, with occasional routines making use of the C-bindings that are available in fortran-2003. A second library covers routines used to read and write files in the open source HDF5 (Hierarchical Data Format) file format [2], which is the default format for all computational results. At the time of writing of this abstract, more than 200, 000 lines of source code have been written, about half of which are available via the source code repository.

Application of forward models to crystal orientation refinement

Two approaches are proposed for the refinement of electron diffraction pattern indexing. The approaches require two basic ingredients: an accurate physicsbased forward model and an algorithm to search the local orientation neighborhood. Forward models for electron backscatter diffraction (EBSD) and electron channeling pattern (ECP) modalities are coupled with either a multi-resolution brute-force search algorithm or a bound optimization by quadratic approximation algorithm. The efficacy of the methods is evaluated for varying levels of error in the pattern projection center. The EBSD modality shows an orientation improvement when the projection center error is within 1% of the full detector width, whereas the ECP modality shows improvement up to a 5% error. The algorithms are applied to an experimental EBSD scan for partially recrystallized 90/10 brass; the results show that the refinement is necessary to remove the artifacts introduced by the discrete sampling nature of the dictionary indexing method. Finally, a pattern center correction factor is derived for orientations obtained from dictionary indexing for large-area EBSD scans.

High resolution low kV EBSD of heavily deformed and nanocrystalline Aluminium by dictionary-based indexing

We demonstrate the capability of a novel Electron Backscatter Diffraction (EBSD) dictionary indexing (DI) approach by means of orientation mapping of a highly deformed graded microstructure in a shot peened Aluminium 7075-T651 alloy. A low microscope accelerating voltage was used to extract, for the first time from a bulk sample, statistically significant orientation information from a region close to a shot crater, showing both recrystallized nano-grains and heavily deformed grains. We show that the robust nature of the DI method allows for faster acquisition of lower quality patterns, limited only by the camera hardware, compared to the acquisition speed and pattern quality required for the conventional Hough indexing (HI) approach. The proposed method paves the way for the quantitative and accurate EBSD characterization of heavily deformed microstructures at a sub-micrometer length scale in cases where the current indexing techniques largely fail.

Dynamical simulations of transmission Kikuchi diffraction (TKD) patterns

Truly nanostructured materials pose a significant spatial resolution challenge to the conventional Electron Backscatter Diffraction (EBSD) characterization technique. Nevertheless, the interaction volume can be reduced by the use of electron transparent samples and the acquisition of electron backscatterlike patterns (EBSP) in transmission mode instead. These transmission Kikuchi diffraction (TKD) patterns are typically acquired by mounting a thin foil, similar to transmission electron microscopy (TEM), and tilting it at a slight angle (20◦ -30◦ ) from horizontal towards a standard EBSD camera.

Accurate Grain and Phase Boundary Location by Dictionary-based Indexing of Geological EBSD Data

Dictionary-based indexing (DI) is a recent approach [1] to the indexing of electron diffraction pat-terns, including electron backscatter diffraction (EBSD), in which a library of precomputed patterns is compared to a series of experimentally acquired patterns. The library is generated using an accurate physics-based forward model that incorporates the geometry of the sample-detector configuration as well as the dynamical and stochastic nature of the generation of backscattered electrons (BSEs) in the sample. Combined with a uniform sampling of orientation space, SO(3), DI uses a similarity metric (normalized dot product between pattern vectors) to select from the dictionary the pattern that best matches the experimental pattern; the orientation corresponding to the best match is assigned as the orientation of the experimental pattern. Since a similarity measure is obtained for each dictionary en-try, one can rank the top N matches and store them for further analysis; below we show that an analysis of the common matches in this set provides an accurate location of grain and phase boundaries, which are often incorrectly indexed using Hough transform based methods due to pattern overlaps.