ODF Characteristics edit page

Let us first begin with some constructed ODFs to be analyzed below

A bimodal ODF:

cs = crystalSymmetry('mmm');
odf1 = unimodalODF(orientation.byEuler(0,0,0,cs)) + ...
  unimodalODF(orientation.byEuler(30*degree,0,0,cs))
odf1 = ODF (mmm → xyz)
 
  Radially symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 10°
    center: (0°,0°,0°)
    weight: 1
 
  Radially symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 10°
    center: (30°,0°,0°)
    weight: 1

A fibre ODF:

odf2 = fibreODF(Miller(0,0,1,cs),xvector)
odf2 = ODF (mmm → xyz)
 
  Fibre symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 10°
    fibre: (001) - 1,0,0
    weight: 1

An ODF estimated from diffraction data

mtexdata dubna

odf3 = calcODF(pf,'resolution',5*degree,'zero_Range')
pf = PoleFigure
  crystal symmetry : Quartz (321, X||a*, Y||b, Z||c*)
  specimen symmetry: 1
 
  h = (02-21), r = 72 x 19 points
  h = (10-10), r = 72 x 19 points
  h = (10-11)(01-11), r = 72 x 19 points
  h = (10-12), r = 72 x 19 points
  h = (11-20), r = 72 x 19 points
  h = (11-21), r = 72 x 19 points
  h = (11-22), r = 72 x 19 points
 
odf3 = ODF (Quartz → xyz)
 
  Radially symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 5°
    center: 19836 orientations, resolution: 5°
    weight: 1

Modal Orientations

The modal orientation of an ODF is the crystallographic prefered orientation ori_pref of the texture. It is characterized as the maximum of the ODF. In MTEX it is returned as the second output argument of the command max

[~,ori_pref] = max(odf3)
ori_pref = orientation (Quartz → xyz)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2    Inv.
  132.867 34.7888 207.108       0

Lets mark this prefered orientation in the pole figures

plotPDF(odf3,pf.allH,'antipodal','superposition',pf.c);
annotate(ori_pref,'marker','s','MarkerFaceColor','black')

Texture Characteristics

Texture characteristics are used for a rough classification of ODF into sharp and weak ones. The two most common texture characteristics are the entropy and the texture index.

Compute the texture index:

textureindex(odf1)
ans =
  288.6802

Compute the entropy:

entropy(odf2)
ans =
   -2.8402

Volume Portions

Volume portions describes the relative volume of crystals having a certain orientation. The relative volume of crystals having a orientation close to a given orientation is computed by the command volume and the relative volume of crystals having a orientation close to a given fibre is computed by the command fibreVolume

The relative volume in percent of crystals with missorientation maximum 30 degree from the preferred orientation ori_pref:

volume(odf3, ori_pref, 30*degree) * 100
ans =
   35.6781

The relative volume of crystals with missorientation maximum 20 degree from the prefered fibre in percent: TODO

%fibreVolume(odf2,Miller(0,0,1),xvector,20*degree) * 100

Extract Internal Representation

The internal representation of the ODF can be addressed by the command

properties(odf3.components{1})
Properties for class unimodalComponent:
    center
    psi
    weights
    CS
    SS
    antipodal
    bandwidth

The properties in this list can be accessed by

odf3.components{1}.center

odf3.components{1}.psi
ans = SO3Grid (Quartz → xyz)
  grid: 19836 orientations, resolution: 5°
 
ans = deLaValleePoussinKernel
  bandwidth: 48
  halfwidth: 5°