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Misorientations Group

Misorientation
MisorientationStats

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Misorientation

Misorientation
- Return misorientation data for quaternions.

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Usage

[angle, mis] = Misorientation(q1, q2, sym)

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Interactive Documentation

Misorientation - Return misorientation data for quaternions.
USAGE:
angle = Misorientation(q1, q2, sym)
[angle, mis] = Misorientation(q1, q2, sym)
INPUT:
q1 is 4 x n1,
is either a single quaternion or a list of n quaternions
q2 is 4 x n,
a list of quaternions
OUTPUT:
angle is 1 x n,
the list of misorientation angles between q2 and q1
mis is 4 x n, (optional)
is a list of misorientations in the fundamental region
(there are many equivalent choices)
NOTES:
* The misorientation is the linear tranformation which
takes the crystal basis given by q1 to that given by
q2. The matrix of this transformation is the same
in either crystal basis, and that is what is returned
(as a quaternion). The result is inverse(q1) * q2.
In the sample reference frame, the result would be
q2 * inverse(q1). With symmetries, the result is put
in the fundamental region, but not into the Mackenzie cell.

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MisorientationStats

MisorientationStats
- Misorientation correlation statistics.

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Usage

stats = MisorientationStats(misorient, locations)

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Interactive Documentation

MisorientationStats - Misorientation correlation statistics.
USAGE:
stats = MisorientationStats(misorient, locations)
INPUT:
misorient is 4 x n,
a list of misorientation quaternions,
assumed to have been derived from properly clustered
orientation data
locations is d x n, (d <= 3)
a list of spatial locations corresponding to the
misorientations
OUTPUT:
stats is a structure with five components:
W is a 3 x 3 matrix (A in Barton paper)
X is a d x d matrix (M in Barton paper)
WX is a 3 x d matrix (cross-correlation
of normalized variables; X in
Barton paper)
wi is 3 x n, the unnormalized axial vectors
xi is d x n, the unnormalized spatial directions
from the centroid
REFERENCE:
"A Methodology for Determining Average Lattice Orientation and
Its Application to the Characterization of Grain Substructure",
Nathan R. Barton and Paul R. Dawson,
Metallurgical and Materials Transactions A,
Volume 32A, August 2001, pp. 1967--1975