orientation.round2Miller edit page

find lattice alignments for arbitrary orientations and misorientations

Description

Given an orientation ori find [hkl](uvw) such that ori * [hkl] = Z and ori * (uvw) = X.

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

Syntax

[uvw,hkl] = round2Miller(ori)
[n1,n2,d1,d2] = round2Miller(mori)
[n1,n2,d1,d2] = round2Miller(mori,'penalty',0.01)
[n1,n2,d1,d2] = round2Miller(mori,'maxIndex',6)

Input

ori orientation
mori misorientation

Output

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

Example

revert sigma3 misorientation relationship

[n1,n2,d1,d2] = round2Miller(CSL(3,crystalSymmetry('432')))
n1 = Miller (432)
  h k l
  1 1 1
 
n2 = Miller (432)
  h k l
  1 1 1
 
d1 = Miller (432)
  u  v  w
  0  1 -1
 
d2 = Miller (432)
   u  v  w
  -1  1  0

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] = round2Miller(mori)
mori = misorientation (Ferrite → Austenite)
 
 (011) || (001)   [100] || [100]
 
 
n_gamma = Miller (Ferrite)
  h k l
  0 1 1
 
n_alpha = Miller (Austenite)
  h k l
  0 0 1
 
d_gamma = Miller (Ferrite)
  u v w
  1 0 0
 
d_alpha = Miller (Austenite)
  u v w
  1 0 0

See also

CSL

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.round2Miller.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.