define orientations by pairs of vectors
Description
orientation.map(h1,r1,h2,r2) defines the orientation that maps the crystal direction h1 onto the specimen direction r1 and h2 onto r2; h1 and h2 have to enclose the same angle as r1 and r2. The orientation of the first example below appears
* in the |(100)| pole figure at position |x| and in the |(001)| pole figure at position |y|, * in the |x| inverse pole figure at position |(100)| and in the |y| inverse pole figure at position |(001)|.
The second example defines a misorientation that aligns the lattice plane (100) of the alpha phase with the lattice plane (011) of the beta phase and the lattice direction [111] of the alpha phase with the lattice direction [01-1] of the beta phase.
Syntax
h = Miller({1,0,0},{0,0,1},cs) % two crystal directions
r = [xvector, yvector] % two specimen directions
ori = orientation.map(h(1),r(1),h(2),r(2))An orientation from two crystal and two specimen directions.
nAlpha = Miller({1,0,0},csAlpha,'hkl')
nBeta = Miller({0,1,1},csBeta, 'hkl')
dAlpha = Miller({1,1,1},csAlpha,'uvw')
dBeta = Miller({0,1,-1},csBeta, 'uvw')
mori = orientation.map(nAlpha,nBeta,dAlpha,dBeta)A misorientation from two pairs of crystal directions.
ori = orientation.map(h1,r1)An arbitrary orientation that maps h1 onto r1.
Input
| h | Miller |
| r | vector3d |
| nAlpha, nBeta | Miller |
| dAlpha, dBeta | Miller |
Output
| ori | orientation |
See also
DefinitionAsCoordinateTransform orientation.byMiller orientation.byAxisAngle orientation.byEuler
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/orientation.map.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.