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XR/(HAR)-EBSD

XR/(HAR)-EBSD: Cross-correlation/High Angular Resolution Electron BackScatter Diffraction
Definition:A particular way to analyse electron backscatter diffraction (→EBSD) patterns which allows measuring elastic distortions and residual stresses as well as very small rotations of a crystal lattice.
Explanation:EBSD patterns are a direct projection of the crystal lattice on the detector plane. Therefore, they convey information on the shape of the crystal lattice (including elastic distortions) and on the position of the crystal lattice with respect to the projection plane (the crystal orientation) in principle. The conventional analysis of EBSD patterns using a so-called Hough transform, allows to measure the orientation of a crystal with a precision of only about 0.5°. Elastic lattice distortions cannot be detected at all. Therefore, Wilkinson et al. (see references) developed a method, which enables to determine relative lattice distortions and rotations by a very sensitive pattern comparison using a cross-correlation technique. In this technique, a pattern at a given position on the sample is compared to a pattern at a reference point which is supposed to be free of elastic strain (or of known elastic strain) and which is very close in orientation to that of the measured position.

The comparison is performed by dividing the two patterns into several small regions of interest. These regions are supposed to be unstrained (or the strain is below the detection limit). During the comparison it is determined how every part of these regions is shifted with respect to the reference pattern. The shift vector directly relates to the distortion vector of a crystallographic direction. From all distortion vectors of the whole pattern, the displacement gradient tensor can be calculated, and from this, the stretch tensor and the rigid body rotation tensor can be derived.

As a result elastic strains of about 10-4 and rotations of 0.01° can be measured.
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Diagram:

(a) Screen shot of the commercial program cross-court for EBSD cross-correlation. (b) Mapping of elastic stress components on a slightly bent single crystal TWIP steel.
SFB-Link:The pattern cross-correlation technique has been used in project C9 to measure local elastic strains. Unfortunately, the method did not deliver reliable results when materials show relatively large orientation gradients.
References:A.J. Wilkinson, G. Meaden, and D.J. Dingley. High resolution mapping of strains and rotations using electron backscatter diffraction. Mat. Sci. Tech., 22:1271–1278, 2006