round2Miller edit page

find lattice alignements for arbitrary orientations and misorientations

Description

Given an orienation 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