preferred orientations versus all orientations present in ODF

[YvesFl]

Dear all,

In order to verify that the results of an exported ODF of a cubic structure is correct, I tend to plot the ODF in Phi, phi2 Euler orientation space. In this case, as can be seen in figure 1, the orientations seem to be distributed equally in the three regions pictured in the figure 2 (plot published in "Tables for Texture analysis of Cubic Crystals, J. Hansen, J. Pospiech, K. Lücke, (1978), Springer"). Thus it looks like each orientation of the ODF is present three times, once in region 1, once in region 2 and once in region 3.
Extracting the 32 preferred orientations from the same dataset using the calcComponents command, and plotting the orientations on the same plot, I do no longer obtain a plot where the orientations are equally distributed in all three regions of the Phi, phi2 Euler orientation space although each orientation should be present three times for reasons of symmetry (see figure 3).
Thus, a certain point in region I must appear somewhere in region II and region III due to symmetrical constraints. Since this is not the case, or there is something wrong, or something that I am missing?

For your information, I projected each preferred orientation to the fundamental region (Phi1, Phi, phi2) = (360°, 90°, 90°) before exporting the Euler angles to a text file.

Thank you in advance for your help,

Yves Fleming

[ralfHielscher]

I do not understand, how it is possible to plot an ODF in an Phi, phi2 orientation space. What about phi1? Do you consider a fixed phi1, i.e, phi1-section, or do sum the intensities over all phi1 values?
If we are speaking about phi1-sections. Then you will in general not find symmetrically equivalent orientation within one section.

Ralf.

[YvesFl]

Dear Ralf,
Thank you for your comment.
Sorry for my non precise description. I agree that the ODF is plotted in Phi, phi2, phi1 orientation space and that no symmetrically equivalent orientation are found within one phi1-section.
In this case, I summed the intensities over all phi1 values and plotted the latter in Phi, phi2.

Yves

[YvesFl]

Dear Ralf,

When plotting phi1-sections of the ODF, I see that the preferred orientations I obtain using the calcComponents command, one of these preferred orientations is annotated on the phi1=0° plot (see figure1). When plotting all preferred orientations using the plot(ori) command an orientation at phi1=0° is not visible (see figures 2 and 3). Why does it seem to be different? Have I forgotten to take something into account when using the plot(ori) function?

[YvesFl]

Dear all,
One comment about the plots above... The code relating to these plots can be found in #2300.