Orientation Density Functions edit page

This example demonstrates the most important MTEX tools for analysing Pole Figure Data.

% specify crystal and specimen symmetry
CS = crystalSymmetry('-3m',[4.9 4.9 5.4]);
SS = specimenSymmetry;

% specify file names
fname = {...
  fullfile(mtexDataPath,'PoleFigure','dubna','Q(10-10)_amp.cnv'),...
  fullfile(mtexDataPath,'PoleFigure','dubna','Q(10-11)(01-11)_amp.cnv'),...
  fullfile(mtexDataPath,'PoleFigure','dubna','Q(11-22)_amp.cnv')};

% specify crystal directions
h = {Miller(1,0,-1,0,CS),...
     [Miller(0,1,-1,1,CS),Miller(1,0,-1,1,CS)],... % superposed pole figures
     Miller(1,1,-2,2,CS)};

% specify structure coefficients
c = {1,[0.52 ,1.23],1};

% import data
pf = PoleFigure.load(fname,h,CS,SS,'interface','dubna','superposition',c);

plot(pf)
mtexColorbar

Extract information from imported pole figure data

Get raw data

Data stored in a PoleFigure variable can be extracted by

I = pf.intensities; % intensities
h = pf.h;            % Miller indice
r = pf.r;            % specimen directions

Basic Statistics

There are also some basic statics on pole figure intensities

min(pf)
max(pf)
isOutlier(pf);
ans =
     0     0     0
ans =
   1.0e+03 *
    0.0898    1.3600    0.9620

Manipulate pole figure data

pf_modified = pf(pf.r.theta < 70*degree | pf.r.theta > 75*degree)

plot(pf_modified)
pf_modified = PoleFigure (xyz)
  crystal symmetry : -3m1, X||a*, Y||b, Z||c*
 
  h = (10-10), r = 1 x 1224 points
  h = (01-11)(10-11), r = 1 x 1224 points
  h = (11-22), r = 1 x 1224 points
rot = rotation.byAxisAngle(xvector-yvector,25*degree);
pf_modified = rotate(pf,rot)

plot(pf_modified)
pf_modified = PoleFigure (xyz)
  crystal symmetry : -3m1, X||a*, Y||b, Z||c*
 
  h = (10-10), r = 72 x 19 points
  h = (01-11)(10-11), r = 72 x 19 points
  h = (11-22), r = 72 x 19 points

PDF - to - ODF Reconstruction

rec = calcODF(pf,'RESOLUTION',10*degree,'iter_max',6)

plotPDF(rec,h)
mtexColorbar
rec = SO3FunRBF (-3m1 → xyz)
 
  multimodal components
  kernel: de la Vallee Poussin, halfwidth 10°
  center: 2472 orientations, resolution: 10°
  weight: 1
odf = SantaFe

% define specimen directions
r = regularS2Grid('antipodal')
odf = SO3FunRBF (m-3m → xyz (222))
 
  uniform component
  weight: 0.73
 
  unimodal component
  kernel: van Mises Fisher, halfwidth 10°
  center: 1 orientations
 
  Bunge Euler angles in degree
     phi1     Phi    phi2  weight
  296.565 48.1897 26.5651    0.27
 
 
r = S2Grid
 size: 72 x 19
 antipodal: true

define crystal directions

h = [Miller(1,0,0,odf.CS),Miller(1,1,0,odf.CS),Miller(1,1,1,odf.CS)];

simulate pole figure data

pf_SantaFe = calcPoleFigure(SantaFe,h,r);

estimate an ODF with ghost correction

rec = calcODF(pf_SantaFe,'RESOLUTION',10*degree,'background',10)

plot(rec,'sections',6)
rec = SO3FunRBF (m-3m → xyz (222))
 
  uniform component
  weight: 0.73
 
  multimodal components
  kernel: de la Vallee Poussin, halfwidth 10°
  center: 150 orientations, resolution: 10°
  weight: 0.27

without ghost correction

rec_ng = calcODF(pf_SantaFe,'RESOLUTION',10*degree,'background',10,'NoGhostCorrection')

plot(rec_ng,'sections',6)
rec_ng = SO3FunRBF (m-3m → xyz (222))
 
  multimodal components
  kernel: de la Vallee Poussin, halfwidth 10°
  center: 150 orientations, resolution: 10°
  weight: 1

Error Analysis

calcError(pf_SantaFe,rec)
calcError(pf_SantaFe,rec_ng)
ans =
    0.0202    0.0261    0.0240
ans =
    0.0358    0.0283    0.0252

Difference plot 

plotDiff(pf_SantaFe,rec)

ODF error 

calcError(SantaFe,rec)
calcError(SantaFe,rec_ng)
ans =
    0.0312
ans =
    0.0893

Exercises

3)

a) Load the pole figure data of a quartz specimen from: data/dubna!

b) Inspect the raw data. Are there noticeable problems?

c) Compute an ODF from the pole figure data.

d) Plot some pole figures of that ODF and compare them to the measured pole figures.

e) Compute the RP errors for each pole figure.

f) Plot the difference between the raw data and the calculated pole figures. What do you observe?

g) Remove the erroneous values from the pole figure data and repeat the ODF calculation. How do the RP error change?

h) Vary the number of pole figures used for the ODF calculation. What is the minimum set of pole figures needed to obtain a meaningful ODF?