orientation.variants edit page

variants parent to child orientation relationship

Syntax

p2cVariants = variants(p2c, 'child')
p2cVariants = variants(p2c, 'parent')
% compute all child variants
oriChild = variants(p2c, oriParent)
% compute child variants specified by variantId
oriChild = variants(p2c, oriParent, variantId)
% compute transformation ODF
odfChild = variants(p2c, odfParent)
% compute all parent variants
oriParent = variants(p2c, oriChild)
% compute parent variants specified by variantId
oriParent = variants(p2c, oriChild, variantId)

Input

p2c parent to child orientation relationship
oriParent parent orientation
odfParent parent ODF SO3Fun
hklParent parent direction Miller
oriChild child orientation
hklChild child direction Miller
variantId id of the variant

Output

p2cVariants parent to child variants
oriParent parent orientation (numOri × numVariants)
hklParent parent directions (numOri × numVariants)
oriChild child orientation (numOri × numVariants)
hklChild child directions (numOri × numVariants)
odfPChild child ODF SO3Fun

Options

parent return parent variants
child return child variants (default)

Example

parent symmetry

cs_fcc = crystalSymmetry('432', [3.6599 3.6599 3.6599], 'mineral', 'Iron fcc');

child symmetry

cs_bcc = crystalSymmetry('432', [2.866 2.866 2.866], 'mineral', 'Iron bcc')
cs_bcc = crystalSymmetry (⊙c→a)
 
  mineral : Iron bcc     
  symmetry: 432          
  elements: 24           
  a, b, c : 2.9, 2.9, 2.9

define a fcc parent orientation

ori_fcc = orientation.brass(cs_fcc)
ori_fcc = orientation (Iron fcc → y↓→x)
 
  Bunge Euler angles in degree
  phi1  Phi phi2
    35   45    0

define Nishiyama Wassermann fcc to bcc orientation relation ship

NW = orientation.NishiyamaWassermann(cs_fcc,cs_bcc)
NW = misorientation (Iron fcc → Iron bcc)
 
 (111) || (011)   [11̅0] || [1̅00]

compute a bcc child orientation related to the fcc orientation

ori_bcc = ori_fcc * inv(NW)
ori_bcc = orientation (Iron bcc → y↓→x)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  166.305 68.0853 32.6118

compute all symmetrically possible child orientations

ori_bcc = unique(ori_fcc.symmetrise * inv(NW))
ori_bcc = orientation (Iron bcc → y↓→x)
  size: 12 × 1
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  25.2644      90     270
  224.736      90      90
  96.8294 127.761 39.2315
  96.8294 52.2388 140.768
      305 9.73561       0
      125 9.73561       0
  166.305 68.0853 32.6118
  346.305 68.0853 32.6118
  83.6949 68.0853 327.388
  263.695 68.0853 327.388
  153.171 127.761 320.768
  153.171 52.2388 219.232

same using the function variants

ori_bcc2 = variants(NW,ori_fcc)
ori_bcc2 = orientation (Iron bcc → y↓→x)
  size: 1 × 12
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  166.305 68.0853 32.6118
      125 170.264     180
  83.6949 68.0853 327.388
  25.2644      90     270
  276.829 52.2388 140.768
  96.8294 52.2388 140.768
  263.695 68.0853 327.388
  166.305 111.915 147.388
      125 9.73561     360
  153.171 127.761 320.768
  44.7356      90      90
  153.171 52.2388 219.232

we may also compute all possible child to child misorientations

bcc2bcc = unique(variants(NW,'child') * inv(NW))
bcc2bcc = misorientation (Iron bcc → Iron bcc)
  size: 7 × 1
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
        0       0       0
  320.768 104.478 219.232
   99.598 91.6386  80.402
      180 19.4712       0
  212.612 136.171 327.388
  315.528 60.9415 334.724
  205.276 60.9415 224.472

See also

calcParents

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.variants.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.