RESUMEN
For phase transformations within polycrystalline materials, the connection between the crystal orientations of parent grains and those of child grains is usually expressed in terms of (theoretical or measured) orientation relationships. This paper introduces a new approach to various problems associated with orientation relationships: (i) estimation, (ii) whether or not a single orientation relationship fits the data adequately, (iii) whether or not a set of children comes from a common parent, and (iv) reconstruction of a parent or of grain boundaries. The approach is an extension to the crystallographic context of the well established embedding approach to directional statistics. It is inherently statistical, producing precise probabilistic statements. Explicit coordinate systems are not used and arbitrary thresholds are avoided.
RESUMEN
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.