 XR/(HAR)EBSD: Crosscorrelation/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
socalled 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
crosscorrelation
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. 
Picture / Figure / Diagram: 

(a) Screen shot of the commercial program crosscourt for EBSD crosscorrelation. (b) Mapping of elastic stress components on a slightly bent single crystal TWIP steel.


SFBLink:  The pattern crosscorrelation 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 

