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 → y↑→x)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  156.958 161.468 197.878

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 (y↑→x)
 size: 1 x 6
          x         y         z
   0.879711 -0.739424 -0.112668
    1.07555  0.340498  0.246148
   -1.07555 -0.340498 -0.246148
  -0.879711  0.739424  0.112668
   0.195838   1.07992  0.358817
  -0.195838  -1.07992 -0.358817

and plotted in a spherical projection

plot(r)

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

A shortcut for the above computations is the command

% a pole figure plot
plotPDF(ori,Miller({1,0,-1,0},{0,0,0,1},{1,1,-2,1},ori.CS))

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

plotPDF(ori,Miller({1,0,-1,0},{0,0,0,1},{1,1,-2,1},ori.CS),'contourf')
mtexColorbar