orientation.matchLattice edit page

find lattice alignments for arbitrary misorientations

Description

Given a misorientation mori find all face normals n1, n2 and crystal directions d1, d2, such that mori * n1 = n2 and mori * d1 = d2.

Syntax

matchLattice(mori)
[n1,n2,d1,d2] = matchLattice(mori)
[n1,n2,d1,d2] = matchLattice(mori,'threshold',1*degree)
[n1,n2,d1,d2] = matchLattice(mori,'maxIndex',3)

Input

mori misorientation

Output

uvw,hkl Miller
n1,n2,d1,d2 Miller

Example

revert sigma3 misorientation relationship

[n1,n2,d1,d2] = matchLattice(CSL(3,crystalSymmetry('432')))
n1 = Miller (432)
 size: 37 x 1
 
n2 = Miller (432)
 size: 37 x 1
 
d1 = Miller (432)
 size: 37 x 1
 
d2 = Miller (432)
 size: 37 x 1

revert back Bain misorientation ship

cs_alpha = crystalSymmetry('m-3m', [2.866 2.866 2.866], 'mineral', 'Ferrite');
cs_gamma = crystalSymmetry('m-3m', [3.66 3.66 3.66], 'mineral', 'Austenite');
mori = orientation.Bain(cs_alpha,cs_gamma)
[n_gamma,n_alpha,d_gamma,d_alpha] = matchLattice(mori)
mori = misorientation (Ferrite → Austenite)
 
 (011) || (001)   [100] || [100]
 
 
n_gamma = Miller (Ferrite)
 size: 13 x 1
  h  k  l
  0  1 -3
  0  1 -2
  0  1 -1
  0  2 -1
  0  3 -1
  0  1  0
  1  0  0
  0  0  1
  0  1  1
  0  2  1
  0  3  1
  0  1  2
  0  1  3
 
n_alpha = Miller (Austenite)
 size: 13 x 1
  h  k  l
  0  2 -1
  0  3 -1
  0  1  0
  0  3  1
  0  2  1
  0  1  1
  1  0  0
  0 -1  1
  0  0  1
  0  1  3
  0  1  2
  0 -1  3
  0 -1  2
 
d_gamma = Miller (Ferrite)
 size: 13 x 1
  u  v  w
  0  1 -3
  0  1 -1
  0  2 -1
  0  3 -1
  0  1  0
  1  0  0
  0  0  1
  0  1  1
  0  3  1
  0  1  2
  0  1  3
  0  1 -2
  0  2  1
 
d_alpha = Miller (Austenite)
 size: 13 x 1
  u  v  w
  0  2 -1
  0  1  0
  0  3  1
  0  2  1
  0  1  1
  1  0  0
  0 -1  1
  0  0  1
  0  1  2
  0 -1  3
  0 -1  2
  0  3 -1
  0  1  3

See also

round2Miller

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.matchLattice.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.