Pole Figures edit page

Pole figures are two dimensional representations of orientations. To illustrate this we define a random orientation with trigonal crystal symmetry

cs = crystalSymmetry('321')
ori = orientation.rand(cs)
cs = crystalSymmetry
  symmetry       : 321               
  elements       : 6                 
  a, b, c        : 1, 1, 1           
  reference frame: X||a*, Y||b, Z||c*
ori = orientation (321 → xyz)
  Bunge Euler angles in degree
      phi1      Phi     phi2
  0.572564  61.1121  197.428

Starting point is a fixed crystal direction h, e.g.,

% the fixed crystal directions (100)
h = Miller({1,0,0},cs);

Next the specimen directions corresponding to all crystal directions symmetrically equivalent to h are computed

r = ori * h.symmetrise
r = vector3d
 size: 1 x 6
          x         y         z
   -1.09997 -0.178076 -0.302808
  -0.854083  0.368866  0.683969
   0.854083 -0.368866 -0.683969
    1.09997  0.178076  0.302808
   0.245885  0.546942  0.986777
  -0.245885 -0.546942 -0.986777

and ploted in a spherical projection


Since the trigonal symmetry group has six symmetry elements the orientation appears at six possitions.

A shortcut for the above computations is the command

% a pole figure plot

We observe, that for some crystal directions only the upper hemisphere is plotted while for other upper and lower hemisphere are plotted. The reason is that if h and -h are symmetrically equivalent the upper and lower hemisphere of the pole figure are symmetric as well.

Contour plots