A common way to interpret 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 Quartz ODF from Neutron pole figure data.
% import Neutron pole figure data from a Quartz specimen
mtexdata dubna silent
% reconstruct the ODF
odf = calcODF(pf,'zeroRange');
% visualize the ODF in sigma sections
plotSection(odf,'sigma','sections',12,'layout',[3,4])
mtexColorbar
![](images/ODFComponents_01.png)
The preferred orientation
First of all we observe that the ODF posses a strong maximum. To find this orientation that corresponds 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 attained. 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)
![](images/ODFComponents_02.png)
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(2:end),'MarkerFaceColor','red')
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
![](images/ODFComponents_03.png)
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 entire 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 preferred orientation. At the end of this process the command returns these preferred orientation and the percentage of orientations that crawled to each of them.
[ori, vol] = calcComponents(odf);
ori
vol * 100
ori = orientation (Quartz → xyz)
size: 5 x 1
Bunge Euler angles in degree
phi1 Phi phi2
133.312 34.8711 206.946
140.237 36.4105 257.542
85.6217 22.7987 269.598
79.0658 34.6428 215.331
148.062 47.1683 152.633
ans =
45.1145
27.4373
19.6022
6.0787
1.0655
These volumes always sums up to approximately 100 percent. While the preferred orientations should be the same as those computed by the max
command.
annotate(ori,'MarkerFaceColor','none','MarkerEdgeColor','white',...
'linewidth',2,'MarkerSize',15,'marker','o')
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![](images/ODFComponents_04.png)