Parent grain reconstruction from partially or fully transformed microstructures in MTEX.

A versatile generic framework for parent grain reconstruction from fully or partially transformed child microstructures has been integrated into the open-source crystallographic toolbox MTEX. The framework extends traditional parent grain reconstruction, phase transformation and variant analysis to all parent-child crystal symmetry combinations. The inherent versatility of the universally applicable parent grain reconstruction methods and the ability to conduct in-depth variant analysis are showcased via example workflows that can be programmatically modified by users to suit their specific applications. This is highlighted by three applications, namely α'-to-γ reconstruction in a lath martensitic steel, α-to-ß reconstruction in a Ti alloy, and a two-step reconstruction from α' to ɛ to γ in a twinning and transformation-induced plasticity steel. Advanced orientation relationship discovery and analysis options, including variant analysis, are demonstrated via the add-on function library ORTools.

Approximant-based orientation determination of quasicrystals using electron backscatter diffraction.

Orientation mapping of quasicrystalline materials is demonstrated using crystalline approximant structures in the technique of electron backscatter diffraction (EBSD). The approximant-based orientations are symmetrised according to the rotational point group of the quasicrystal, including the visualization of orientation maps using proper colour keys for quasicrystal symmetries. Alternatively, approximant-based orientation data can also be treated using pseudosymmetry post-processing options in the EBSD system software, which enables basic grain size estimations. Approximant-based orientation analyses are demonstrated for icosahedral and decagonal quasicrystals.

Visualization of texture components using MTEX.

Knowledge of the appearance of texture components and fibres in pole figures, in inverse pole figures and in Euler space is fundamental for texture analysis. For cubic crystal systems, such as steels, an extensive literature exists and, for example, the book by Matthies, Vinel & Helming [Standard Distributions in Texture Analysis: Maps for the Case of Cubic Orthorhomic Symmetry, (1987), Akademie-Verlag Berlin] provides an atlas to identify texture components. For lower crystal symmetries, however, equivalent comprehensive overviews that can serve as guidance for the interpretation of experimental textures do not exist. This paper closes this gap by providing a set of scripts for the MTEX package [Bachmann, Hielscher & Schaeben (2010). Solid State Phenom. 160, 63-68] that allow the texture practitioner to compile such an atlas for a given material system, thus aiding orientation distribution function analysis also for non-cubic systems.

Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations.

Crystallographic textures, as they develop for example during cold forming, can have a significant influence on the mechanical properties of metals, such as plastic anisotropy. Textures are typically characterized by a non-uniform distribution of crystallographic orientations that can be measured by diffraction experiments like electron backscatter diffraction (EBSD). Such experimental data usually contain a large number of data points, which must be significantly reduced to be used for numerical modeling. However, the challenge in such data reduction is to preserve the important characteristics of the experimental data, while reducing the volume and preserving the computational efficiency of the numerical model. For example, in micromechanical modeling, representative volume elements (RVEs) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method. In this work, a new method is developed for extracting a reduced set of orientations from EBSD data containing a large number of orientations. This approach is based on the established integer approximation method and it minimizes its shortcomings. Furthermore, the L 1 norm is applied as an error function; this is commonly used in texture analysis for quantitative assessment of the degree of approximation and can be used to control the convergence behavior. The method is tested on four experimental data sets to demonstrate its capabilities. This new method for the purposeful reduction of a set of orientations into equally weighted orientations is not only suitable for numerical simulation but also shows improvement in results in comparison with other available methods.

Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross correlation on the sphere.

We present spherical analysis of electron backscatter diffraction (EBSD) patterns with two new algorithms: (1) band localisation and band profile analysis using the spherical Radon transform; (2) orientation determination using spherical cross correlation. These new approaches are formally introduced and their accuracies are determined using dynamically simulated patterns. We demonstrate their utility with an experimental dataset obtained from ferritic iron. Our results indicate that the analysis of EBSD patterns on the sphere provides an elegant method of revealing information from these rich sources of crystallographic data.

On three-dimensional misorientation spaces.

Determining the local orientation of crystals in engineering and geological materials has become routine with the advent of modern crystallographic mapping techniques. These techniques enable many thousands of orientation measurements to be made, directing attention towards how such orientation data are best studied. Here, we provide a guide to the visualization of misorientation data in three-dimensional vector spaces, reduced by crystal symmetry, to reveal crystallographic orientation relationships. Domains for all point group symmetries are presented and an analysis methodology is developed and applied to identify crystallographic relationships, indicated by clusters in the misorientation space, in examples from materials science and geology. This analysis aids the determination of active deformation mechanisms and evaluation of cluster centres and spread enables more accurate description of transformation processes supporting arguments regarding provenance.

Grain detection from 2d and 3d EBSD data--specification of the MTEX algorithm.

We present a fast and versatile algorithm for the reconstruction of the grain structure from 2d and 3d Electron Back Scatter Diffraction (EBSD) data. The algorithm is rigorously derived from the modeling assumption that grain boundaries are located at the bisectors of adjacent measurement locations. This modeling assumption immediately implies that grains are composed of Voronoi cells corresponding to the measurement locations. Thus our algorithm is based on the Voronoi decomposition of the 2d or 3d measurement domain. It applies to any geometrical configuration of measurement locations and allows for missing data due to measurement errors. The definition of grains as compositions of Voronoi cells implies another fundamental feature of the proposed algorithm--its invariance with respect to spatial displacements, i.e., rotations or shifts of the specimen. This paper also serves as a reference paper for the texture analysis software MTEX, which is a comprehensive and versatile, freely available MATLAB toolbox that covers a wide range of problems in quantitative texture analysis, including the analysis of EBSD data.