round2Miller

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  
 size: 1 x 1
 symmetry: 432
  h 1
  k 1
  l 1
 
n2 = Miller  
 size: 1 x 1
 symmetry: 432
  h 1
  k 1
  l 1
 
d1 = Miller  
 size: 1 x 1
 symmetry: 432
  u  0
  v  1
  w -1
 
d2 = Miller  
 size: 1 x 1
 symmetry: 432
  u -1
  v  1
  w  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)