Tutorial: Crystal orientations and EBSD — Or which way is up?

In this paper, we demonstrate that the shift between similar features in two electron backscatter diffraction (EBSD) patterns can be measured using cross-correlation based methods to +/- 0.05 pixels. For a scintillator screen positioned to capture the usual large solid angle employed in EBSD orientation mapping this shift corresponds to only approximately 8.5 x 10(-5)rad at the pattern centre. For wide-angled EBSD patterns, the variation in the entire strain and rotation tensor can be determined from single patterns. Repeated measurements of small rotations applied to a single-crystal sample, determined using the shifts at four widely separated parts of the EBSD patterns, showed a standard deviation of 1.3 x 10(-4) averaged over components of the displacement gradient tensor. Variations in strains and rotations were measured across the interface in a cross-sectioned Si1-x Gex epilayer on a Si substrate. Expansion of the epilayer close to the section surface is accommodated by tensile strains and lattice curvature that extend a considerable distance into the substrate. Smaller and more localised shear strains are observed close to the substrate-layer interface. EBSD provides an impressive and unique combination of high strain sensitivity, high spatial resolution and ease of use.

A novel algorithm for ODF (orientation density function) estimation from diffraction pole figures is presented which is especially well suited for sharp textures and high-resolution pole figures measured with respect to arbitrarily scattered specimen directions,e.g.by area detectors. The estimated ODF is computed as the solution of a minimization problem which is based on a model of the diffraction counts as a Poisson process. The algorithm applies discretization by radially symmetric functions and fast Fourier techniques to guarantee smooth approximation and high performance. An implementation of the algorithm is freely available as part of the texture analysis softwareMTEX.

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.