ODF Component Analysis edit page

A common way to interprete ODFs is to think of them as superposition of different components that originate from different deformation processes and describe the texture of the material. In this section we describe how these components can be identified from a given ODF.

We start by reconstruction a Quarz ODF from Neutron pole figure data.

% import Neutron pole figure data from a Quarz specimen
mtexdata dubna silent

% reconstruct the ODF
odf = calcODF(pf,'zeroRange');

% visualize the ODF in sigma sections
plotSection(odf,'sigma','sections',9,'layout',[3,3])
mtexColorbar

The prefered orientation

First of all we observe that the ODF posses a strong maximum. To find this orientation that correspondes to the maximum ODF intensity we use the max command.

[value,ori] = max(odf)
value =
  114.1435
 
ori = orientation (Quartz → xyz)
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  133.236 34.8193 207.184

Note that, similarly as the Matlab max command, the second output argument is the position where the maximum is atained. In our case we observe that the maximum value is about 121. To visualize the corresponding preferred orientation we plot it into the sigma sections of the ODF.

annotate(ori)

We may not only use the command max to find the global maximum of an ODF but also to find a certain amount of local maxima. The number of local maxima MTEX should search for, is specified as by the option 'numLocal', i.e., to find the three largest local maxima do

[value,ori] = max(odf,'numLocal',3)

annotate(ori)
value =
  114.1435
   48.7649
   38.2181
 
ori = orientation (Quartz → xyz)
  size: 3 x 1
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  133.236 34.8193 207.184
  140.249 36.5231 257.419
   86.017 22.9142  269.46

Note, that orientations are returned sorted according to their ODF value.

Volume Portions

It is important to understand, that the value of the ODF at a preferred orientation is in general not sufficient to judge the importance of a component. Very sharp components may result in extremely large ODF values that represent only very little volume. A more robust and physically more relevant quantity is the relative volume of crystal that have an orientation close to the preferred orientation. This volume portion can be computed by the command volume(odf,ori,delta) where ori is a list of preferred orientations and delta is the maximum disorientation angle. Multiplying with \(100\) the output will be in percent

delta = 10*degree;
volume(odf,ori,delta) * 100
ans =
   11.2417
    4.8778
    4.1377

We observe that the sum of all volume portions is far from \(100\) percent. This is very typical. The reason is that the portion of the full orientations space that is within the \(10\) degree disorientation distance from the preferred orientations is very small. More precisely, it represents only

volume(uniformODF(odf.CS),ori(1),delta) * 100
ans =
    0.1690

percent of the entiere orientations space. Putting these values in relation it becomes clear, that all the components are multiple times stronger than the uniform distribution. We may compute these factors by

volume(odf,ori,delta) ./ volume(uniformODF(odf.CS),ori,delta)
ans =
   66.5289
   28.8672
   24.4873

It is important to understand, that all these values above depend significantly from the chosen disorientation angle delta. If delta is chosen too large

delta = 40*degree
volume(odf,ori,delta)*100
delta =
    0.6981
ans =
   56.3022
   38.7490
   53.1369

it may even happen that the components overlap and the sum of the volumes exceeds 100 percent.

Non circular components

A disadvantage of the approach above is that one is restricted to circular components with a fixed disorientation angle which makes it hard to analyze components that are close together. In such settings one may want to use the command calcComponents. This command starts with evenly distributed orientations and lets the crawl towards the closest prefered orientation. At the end of this process the command returns these prefered orientation and the percentage of orientations that crawled to each of them.

[ori, vol] = calcComponents(odf);
ori
vol * 100
ori = orientation (Quartz → xyz)
  size: 8 x 1
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  133.195 34.7588  207.18
  140.237 36.4105 257.542
  85.7179 22.9427 269.892
  78.4817 34.3989 215.027
   84.475 23.4234 271.429
   86.595 22.2852 268.747
   87.194 23.8579  268.18
  88.5989  23.035 266.953
 
ans =
   42.6736
   24.9396
   11.8260
    2.6058
    1.5750
    1.4833
    1.2851
    1.0563

These volumes allways sums up to apprximately 100 percent. While the prefered orientations should be the same as those computed by the max command.

annotate(ori,'MarkerFaceColor','red')